Journal of Colloid and Interface Science 417 (2014) 171–179
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Correlation between shape, evaporation mode and mobility of small water droplets on nanorough fibres C.S. Funk, B. Winzer, W. Peukert ⇑ Institute of Particle Technology (LFG), University of Erlangen-Nuremberg, Cauerstr. 4, D-91058 Erlangen, Germany
a r t i c l e
i n f o
Article history: Received 6 August 2013 Accepted 5 November 2013 Available online 18 November 2013 Keywords: Coalescing media Wettability of fibres Nanoparticle coating Droplet mobility Three phase contact line Evaporation mode Contact angle Silica Droplet conformation Fibre surface energy
a b s t r a c t The dynamic wetting behaviour and the mobility of droplets on fibres is a very important factor in coating processes, textile fabrication, in self-cleaning processes and in the filtration of fluids. In principal, filter regeneration depends on the mobility of the droplets on the fibre surface. Mobile droplets tend to coalesce which greatly simplifies their removal from the filter. In this contribution mobility analyses of water droplets on monofilaments in air are performed. Studies of droplet evaporation on pure PET fibres and on nanorough fibres coated with SiO2 nanoparticles of diameters between 6 nm and 50 nm in a hydrophilic binder system were done. We show that the mobility of water droplets correlates with the droplet conformation which in turn is determined by the droplet–fibre interface. We demonstrate that fibre coatings can be used to tailor the conformation and mobility of water droplets. The smaller the nanoparticle diameters in the coating are, the smaller are the contact angles between water droplets and fibre and the better is the mobility of the droplets on the fibre. Our results allow a fast optimization of the fibre surface properties which are directly influencing the contact angle, the mobility and the coalescence of water droplets and thus filter regeneration. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Over the last years the wettability of fibres has become more and more important in many industrial areas such as coating processes, textile fabrication, self-cleaning processes and especially the filtration of fluids. Applications are the separation of water droplets from diesel fuel or the vapour-phase deposition of waterand oil droplets out of compressed air by fibre filters. In fluid filtration the droplet transport towards the fibre surface and the dynamic wetting behaviour are crucial. Whereas the impaction of droplets on fibres is well understood, the regeneration of the droplets in fibre filters remains elusive. Basically the regeneration of coalescing filters depends on the mobility of the droplets on the fibre surface: mobile droplets tend to coalesce leading to larger droplets and hence simplifies their removal from the filter. Due to the cylindrical shape of the fibre, the wetting behaviour of droplets on fibres differs from the wetting of flat surfaces. Early studies on the wetting phenomena of droplet-on-fibre systems have reported on determining the droplet shape and on extracting the contact angle accurately [1]. A fluid that forms a completely wetting film on a flat surface (vanishing contact angle) may not completely wet a fibre of the same material. In the case of flat
⇑ Corresponding author. Fax: +49 9131 8529402. E-mail address: [email protected] (W. Peukert). 0021-9797/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2013.11.005
surfaces, the spreading pressure, S = csv (csl + clv) where c is the interfacial tension, determines whether a film or a macroscopic droplet with a non-zero contact angle is formed [2]. In case of fibres, a film only forms when S exceeds a finite positive value dependent on the fibre radius. A vanishing contact angle can be consistent with a macroscopic droplet [2–6]. Wagner et al. studied the spreading of liquid droplets on cylindrical surfaces [7]. Yamaki and Katayama describe a theoretical method to calculate the contact angle by observing the shape of a liquid drop attached to a monofilament and point out that the shapes of droplets attached to monofilaments change depending on liquid volume. Moreover, it was found for very small droplets that the effect of gravity is negligible [8]. Carroll studied properties of fluid droplets on cylinders, such as the equilibrium conformation of droplets, contact angles and the stability of small droplets [1,9–11]. Depending on the fibre radius, the droplet volume and the surface energy of the fibre, he found two fundamentally different conformations of macroscopic droplets: i.e. barrel and a clam-shell conformation (see Fig. 1). At the critical contact angle a change of droplet conformation takes place. This ‘roll-up’-process results in a change of the contact area which leads to a significant change of the droplet profile. The critical contact angle depends on the fibre radius and the surface energy of the fibre. The most complete experimental data on the roll-up-process was given by Carroll [9]. Barrel shapes occur for large droplets relative to the fibre radius or for low contact angles. Clam-shell shapes occur for small droplets or high contact angles.
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(a)
(b)
Fig. 1. Conformations of water droplets on a cylindrical fibre [10]: (a) barrel-type; axially symmetric and (b) clam-shell-type; non-symmetric.
In a coalescing filter it is desirable that droplets have a high radial adhesion and a low axial adhesion to the fibre. Droplets of the barrel-type have a bigger radial adhesion to the fibre compared with the clam shell shape droplets and thus the residence time and the probability of droplet coalescence on the fibre is increased. In addition, the clamshell droplet has a longer three phase contact line with the fibre, compared with the relatively short contact line of the barrel conformation. The surface tension force along the fibre is hence relatively small for the barrel shape droplet compared to the clamshell droplet. Thus, the barrel shaped droplets are more likely to slide down the fibre. This demonstrates the highly improved drainage of barrel droplets down the fibre due to a connecting film between the droplets compared to clamshell droplets. Therefore the barrel droplets have a better axial mobility on the fibres at higher residences time, which leads to an increased coalescence, to larger droplets and simplifies the removal of the droplets from the filter [9,12]. Clam shell droplets roll axially on the fibre which increases the probability of leaving the fibre before coalescing with other droplets while barrel droplets slide [13]. Therefore, they are the preferred conformation in coalescing filters. Also in wet filters a good wetting of the fibres is required [30]. In this case the particles are captured by a liquid film rather than being directly captured by the fibres. Therefore barrel droplets or film formation of the liquid on the fibres is desired in this technique. The symmetrical drop conformation is characterized by two linear, dimensionless parameters, the reduced drop diameter n = x2/x1 and the reduced drop length Ł = Lw/x1. Lw describes the droplet base diameter, x1 the fibre radius and x2 the drop height (see Fig. 1). The three parameters can be directly obtained from a photomicrograph ([1,10,11]). In this publication the influence of the fibre roughness on the contact angle and on the mobility of droplets on fibres is studied. As the mobility of droplets on fibres is determined by the mobility of the three-phase-contact line [14] an analysis of the evaporation behaviour of droplets on fibres is performed as well. Upon evaporation the three-phase contact line of the droplet must shift. Various studies of the evaporation behaviour of droplets on flat surfaces exist [15–21]. McHale and Newton [17–19] investigated the adsorption and evaporation of droplets on flat surfaces by video microscopy. For initial contact angles less than 90°, the contact area remains constant upon evaporation. In case of structured surfaces a stepwise contraction of droplets depending on the surface structure was observed. Water droplets on textured surfaces evaporate in a stick-slip mode. Few studies concerning the evaporation behaviour of droplets on fibre surfaces are known [22,23]. Murarova et al. functionalised the fibre surface by pigments via a sol–gel procedure [24]. They found a dependence of the contact angle on time. Mullins investigated the wetting process during filtration of droplets in air [21]. They observed adsorption of water droplets on glass fibres, oscillatory droplet motion and detachment or flow of these droplets along the fibre. Mobility and coalescence of droplets were investigated on flat and on curved surfaces [25–30]. Bitten et al. found that the maximum diameter of droplets adhering to the fibre surface depends
strongly on the fibre material [25]. Mullins et al. studied the influence of fibre orientation on the fibre wetting process and flow of liquid droplets along filter fibres [12]. By determining the forces acting on a droplet on a fibre, it is possible to determine an optimum angle such that the flow of droplets down the fibre will be maximized ensuring maximal filter self-cleaning. Dawar et al. proposed correlations of the droplet mobility as a function of drop and fibre sizes and on the Reynolds (Re) and Capillary (Ca) numbers [14,31]. Mead-Hunter et al. present a theoretical model describing the force required to move coalesced liquid droplets of two different oils along an oleophilic filter fibre and determine the influence of droplet displacement perpendicular to the fibre on the force required to move the droplet experimentally. Additional it was found that fibre surface inhomogeneities strongly influence the results [13,29]. The wetting of flat textured surfaces can be described by two different models, i.e. the Wenzel model and the Cassie–Baxter equation. The Wenzel model describes the homogeneous complete wetting regime and is defined by the following equation:
cos hW ¼ r cos h
ð1Þ
In this equation the apparent contact angle hw depends on the surface roughness r which is defined as the actual, rough surface area divided by the projected surface area. h is the equilibrium contact angle on a smooth surface exhibiting the same surface chemistry as the structured surface [32]. If air is assumed to be entrapped in the voids of a rough surface, the contact angle on the rough surface can be described by the Cassie–Baxter equation.
cos hCB ¼ r fs cos h þ fs 1
ð2Þ
fs is the fraction of the solid surface area wetted by the liquid [33] and hCB the contact angle on the rough surface. It is important to realize that when f = 1, the Cassie–Baxter equations becomes the Wenzel equation. For water droplets the Cassie–Baxter case generally occurs on hydrophobic surfaces and the Wenzel case on hydrophilic surfaces as in the present case. Several fundamental questions concerning the influence of surface roughness of fibres on droplet mobility are not sufficiently understood. This contribution shows that the droplet mobility on coated fibres correlates with the droplet conformation on fibres and the wetting behaviour of fibres. As the droplet conformation is determined by the droplet–fibre interface the wetting behaviour of PET fibres was tailored by a surface coating with silica nanoparticles of different sizes embedded in a hydrophilic binding system. The coatings, including nanoparticles, create a certain fibre surface roughness, depending on the nanoparticle diameter. 2. Materials and methods 2.1. Preparation of the fibres For the analysis of the wetting and the evaporation behaviour of water droplets in air PET fibres (diameter 100 lm) were coated with a hydrophilic binding system excluding and including SiO2
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nanoparticles in the range of 6 nm to 50 nm provided by Nano-X, Germany. The particles were available in diluted suspensions of 5 wt% solid fraction. The fraction of nanoparticles in the hydrophilic binder material was set to 60 vol%. The coating procedure of the PET fibres consists of three steps: first, the fibre is cleaned with pure ethanol to remove impurities. Followed by a plasma treated (Plasma Prep2; Gala Instruments) to improve the wettability of the coating suspension on the fibre surface. The energy of the plasma and the activation time are chosen in such manner that the surface does show good wetting behaviour without any indication of degradation or melting. Directly after this activation the fibres are drawn with a constant velocity through the nanoparticle coating suspension and subsequently air dried at 20° C. In this way it is possible to generate close and homogenous layers of nanoparticles (see Fig. 2). 2.2. Fibre characterization To determine the roughness of the nanoparticle coated fibres Atomic Force Microscopy (AFM) measurements of the fibre surface were performed. AFM images were taken with a NanoScopeIIIa Scanning Probe Microscope Controller from Digital Instruments working in the tapping mode using high frequency cantilevers. Measurements have been taken with scanning lengths of 1 lm and 10 lm. The used cantilever (DP 14 Hi‘Res) was from MikroMasch with a specified spring constant of 1.8–13 N/m and 1 nm radius of curvature on the tip, according to the manufacturer’s specification. With sufficient sensitivity in the spring deflection sensor, the tip can reveal surface profiles with nanometer or even with subnanometer resolution [35]. For one roughness factor according to Wenzel we analysed 5 AFM images of one fibre surface with the NanoScopeIIIa Software. The roughness factors r were calculated from the AFM measured
surface areas of the coatings including particles divided by the one excluding particles. In a regular cubic lattice of spheres the roughness factor should stays constant at a value of 1.9 independent of particle size [36]. The measured roughness factors are between 1.33 for the 6 nm particles and slightly decrease to 1.26 for a particle of 50 nm. In Fig. 3 the AFM images of the surface topography of a fibre coated with the hydrophilic binding system including nanoparticles with diameters of 25 nm (a) and the hydrophilic binding system excluding particles (b) are shown. The diameter of the measured particles in (b) has increased to 70 nm since the binder coats the particles. Additionally to the AFM measurements the coated fibres were characterized by low-voltage SEM (Ultra 55; Zeiss), see Fig. 2. The characterization of the fibre surface regarding the surface energy of the network building silica binding system were done by OWRK (Owens, Wendt, Rabel and Kaelble) measurements on flat surfaces of identical coating [34]. For the contact angle measurements and the evaporation experiments droplets with volumes in the range of 0.5 nl to 1 ll are produced and deposited on the fibre surface using a fluid dosing unit (Xeno-Works with 500 ll and 100 ll syringe) with glass capillaries (end diameter smaller than 10 lm, silanized with 2% solution of dichlorodimethylsilane in octamethylcyclotetrasiloxane), combined with a micromanipulator (MP 285; Sutter Instruments Company). Using a light microscope with cold light source (Axio Imager M1m; Zeiss; transmitted light; objective 20) in combination with a camera the droplet depostion, growth, mobility and evaporation on a single fibre have been carefully monitored by taking images and videos of the droplet profiles (up to 25 frames per second). The characteristic parameters (x1, x2, Lw, H; see Fig. 1) are extracted from the recordings using the evaluation software of a contact angle measuring system (OCA20; dataphysics). The contact
20µm
1µm
Fig. 2. SEM images of PET fibres coated with hydrophilic binding system including 15 nm SiO2 particles (SE2 detector; acceleration voltage: 1.2 kV).
(a)
93.1 nm
20.0 nm
(b)
0.0 nm 0 µm
1 µm
x (µm)
0.0 nm 0 µm
1 µm
x (µm)
Fig. 3. AFM image of the surface topography of a PET fibre coated with hydrophilic binding system including nanoparticles with diameters of 25 nm (a) and hydrophilic binding system without particles (b).
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angle at the fibre is obtained by the Young–Laplace fitting method. All experiments were carried out at 21 °C and a relative humidity of 42%. The measurements of the static contact angles (left and right side of droplet) of at least 20 drops were carried out at different locations on the fibre. The standard deviation of the average value is ±2.1°. To determine the mobility of the contact line and the receding contact angle, the droplet evaporation was observed. Video films were taken during the evaporation. Both, the contact angles over time and the droplet base diameter over time were determined. Cleaned PET-fibres served as reference. 2.3. Droplet growth, coalescence and mobility A stream of small fluid droplets with diameters in the order of
lm is produced by a nebulizer. Droplets adsorb at the fibre surface and grow by deposition of further droplets from the gas stream. The experimental set-up is shown in Fig. 4. In the experiments the aerosol stream is under a 15° angle with respect to the fibre axis. Growth, coalescence and movement of droplets can be observed directly. Droplets grow until the drag force of the droplet Fd,krit against the air flow is larger than the adhesion force Fad between droplet and fibre. The drag force can be calculated by the following equation:
F ad ¼ F d;krit: ¼
1 cd m2rel qfluid Adroplet ¼ f ðAdroplet Þ 2
ð3Þ
Adroplet is the axial cross section of the droplet, vrel is the relative velocity between droplet and air, qfluid is the density of the fluid flow and cd (Re) is the drag coefficient as a function of Re number. The behaviour of the small drops in contact with the fibre was observed by light microscopy. During droplet growth and movement along the fibre videos at 90 frames per second were taken. The velocity of the water droplets in the stream was measured by a PIV (Particle Image Velocimetry) system of ILA with a CCD camera pco.2000, a Nd:YAG-Laser (k = 532 mm) from Big Sky Laser series of Quantel and a Canon EF 100 mm f/2.8 Macro USM objective. From the PIV data the droplet velocity was averaged from 10 measurements. We found a mean droplet velocity in axial direction vax of 1.73 ± 0.03 m/s in the experiments. For the determination of the drag coefficient on the droplet flow around a rigid spheroid was taken. Using the air flow velocity of 1.73 m/s the Reynolds number is between 2100 and 3300 depending on the droplet profile. The barrel-type droplets in our experiments exhibit aspect ratios between 1.67 and 2.86. Hence the drag coefficients according to Stringham were used [37,38]. The flow velocity vax can be set as vrel as the droplets are fixed on the fibre before they move.
3. Results and discussion 3.1. Droplet conformation, static contact angle and evaporation behaviour The equilibrium conformation of water droplets placed on cylindrical fibres is determined by the contact angle and thus by the surface energy of the fibre [11]. Barrel shapes with low contact angles occur on fibres with high surface energy and for large droplet volumes. Clam-shell shapes with high contact angles occur for small droplet volumes [10]. Examples of different drop conformations observed in these studies are given in Fig. 5. The wetting experiments of water droplets of 0.030 ± 0.002 ll on fibres with 100 lm show a change of droplet conformation from clam-shell-type to barrel-type by coating them with the hydrophilic silica binder. The contact angles of drops on pure PET (surface energy: 39.5 ± 0.6 mN/m) and on fibres coated with the hydrophilic network building silica coating (surface energy: 61.3 ± 0.2 mN/m) are listed in Fig. 5a and b. The apparent contact angles can be described by the Young equation and the Young–Laplace equation for fibres. An increase of the solid surface energy leads to a decrease of the contact angle of the water droplet. Coating PET fibres with the hydrophilic binding system reduces the contact angle between water droplet and fibre and leads to a change in droplet conformation and thus to an improvement of the radial droplet adhesion to the fibre. Further reduction of the contact angle between fibre and water droplet can be achieved by including nanoparticles in the fibre coating. The contact angle depends on the nanoparticle diameter as can be seen in Fig. 6. The contact angle is, for instance reduced from 54.2° to 19.1° when including nanoparticles with a diameter of 6 nm. The smaller the nanoparticle diameters in the coating are the smaller get the measured contact angles between water droplets and fibres. Wenzel showed that micro-structuring of a surface enforces the natural tendency of the surface. This means that a hydrophilic surface with a contact angle less than 90° gets more hydrophilic when it is micro- or nanostructured. The contact angle on the rough surface is reduced relative to the smooth surface [32]. The bigger the roughness factor is the smaller are the contact angles on a rough hydrophilic surface. If the particles in the fibre coatings get smaller the actual surface and thus the surface roughness factor r increases accordingly. On that account, the contact angle decreases while the particle diameter in the fibre coating decreases and thus the wettability of the fibre surface increases. During the evaporation of water droplets on coated fibres different evaporation modes are observed. In accordance with other researchers we found the constant contact area mode, constant contact angle mode and the ‘‘stick-slip’’ motion on the fibres [15–21].
3.1.1. Constant contact area mode Axial component vax
Radial component v rad Total velocity vtot Growing droplet
Fig. 4. Experimental setup to observe droplet growth and mobility.
The typical evaporation behaviour for droplets that evaporate in the mode of constant contact area is illustrated in Fig. 7. The base diameter remains nearly constant over the whole evaporation process, while the contact angle decreases. Such evaporation behaviour was found for fibres with a static contact angle larger than 30°. In Fig. 7 the evaporation behaviour of a water droplet on a pure PET fibre is shown. In Fig. 8a the vapour pressure of the droplet is plotted against the droplet volume during the evaporation process. The vapour pressure is calculated by the Kelvin-equation using the measured droplet profile. The vapour pressure of droplets evaporating in
C.S. Funk et al. / Journal of Colloid and Interface Science 417 (2014) 171–179
(a) 100 µm
(b) θ = 64.5° (±2.5)
θ = 39.5° (±2.2)
(e) 100 µm
100 µm
θ = 54.2° (±3.7)
(d)
(c) 100 µm
175
100 µm θ = 24.3° (±2.1)
(f) θ = 17.2° (±1.4)
100 µm
θ = 13.41° (±1.9)
Fig. 5. Different droplet conformations for water droplets on coated fibres: (a) On PET reference fibre of 100 lm diameter droplets with a volume of 80 ± 5 nl of clam-shelltype (unsymmetrical; even at large drop volumes of 0.4 ll) are observed. (b) On PET-fibres with SiO2-binder coating droplets with a volume of 0.4 ± 0.02 ll show the barreltype conformation. (c) On PET-fibres with a 50 nm SiO2-nanoparticle-binder coating an intermediate state between clam-shell-type and ‘‘barrel’’-type conformation (droplet starts wrapping around the fibre) was observed for very small droplet volumes of 20 ± 5 nl. (d) At large volumes of 0.3 ± 0.02 ll water droplets on PET-fibre with 50 nm SiO2nanoparticle coating are of barrel-type (symmetrical). (e) On PET-fibre with 25 nm SiO2-nanoparticle coating droplets are of barrel-type even at small droplet volume of 50 ± 5 nl. (f) On PET-fibre with 6 nm SiO2-nanoparticle coating droplets are of barrel-type (symmetrical) already at very small droplet volume of 10 ± 5 nl.
Fig. 6. Measured contact angles on fibres coated with hydrophilic binding material including nanoparticles of different diameter.
the constant contact area mode is decreasing because of the continuously decreasing droplet surface curvature. The time dependency of the droplet volume, shown in Fig. 8b, _ D in kg/m2 s from a droplet can be modelled by the mass flux m to the gas phase during droplet evaporation using the well-known Stefan–Maxwell approach which accounts for one-sided diffu-
Fig. 7. Typical clam-shell conformation and time dependency of droplets evaporating in the constant contact area mode. Such drops typically have a ‘‘clam-shell’’type conformation. The contact angle (j) decreases steadily and the droplet diameter (D) remains constant for almost the whole evaporation process. In this evaporation mode the contact line is pinned.
sional and convective mass transfer [40–43]. Temperature effects are neglected and the fluid around the droplet shall be quiescent.
_ D ¼ M m
Deff p _D m rpm þ m RT p
ð4Þ
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Fig. 8. Vapour pressure of the droplet (a) and experimental and modelled droplet volume as a function of the time during evaporation (b), shown in Fig. 7.
The flux from the droplet and consequently the volume decrease of the droplet is dependent on the vapour pressure and the surface area of the droplet. Eqs. (5) and (6) describe the measured droplet volume as function of time very well. Only at the end of evaporation (t > 230 s) larger deviation occur which are probably due the limited resolution of the images of the taken videos. At the end of evaporation a flattening of the droplet occurs and thus only a thin film of liquid on the fibre exists. Therefore, the contour of the droplet cannot be detected exactly by the software of the contact angle device. 3.1.2. Constant contact angle mode
Fig. 9. Typical conformation and time dependency of contact angle and base diameter of droplets that evaporate in the constant contact angle mode. Such drops are typically of ‘‘barrel’’-type. The contact angle (j) remains constant and the droplet diameter (D) decreases steadily during evaporation in constant contact angle mode at early stages of evaporation.
where M is the molar mass of the liquid, Deff is the effective diffusion coefficient of water in air, p the total pressure, pv the vapour pressure of the droplet, R the gas constant and T the temperature. _ D leads to Solving the equation for m
_ D ¼ M m
Deff 1 rpm 1 pm =p R T
ð5Þ
The solution for a spherical droplet of radius r is given by
_D¼ m
M Deff p p ln p pm RrT
ð6Þ
The flow rate from one droplet of radius r can be calculated by using the surface area of the droplet Sdroplet extracted from the images and ql the density of the liquid.
_D m V_ droplet ¼ Sdroplet
ql
ð7Þ
This mode is the expected behaviour for system in equilibrium between solid, liquid and gas where no difference between advancing and receding contact angle exists. On real samples there is always a small contact angle hysteresis. Fig. 9 illustrates the observed evaporation behaviour of symmetrical drops with static contact angles lower than 30° on the coated fibres. In this case the contact line can move easily, the droplet evaporates with nearly constant contact angle, whereas the diameter decreases steadily. Therefore the vapour pressure increases as well. In the experiment with nanoparticles diameters of 6 nm the surface of the coated fibres show a very small contact angle hysteresis of about 3° (see a slight ‘‘stick-slip’’ motion in the diagram). Fig. 10a shows the vapour pressure of the droplet plotted against the droplet volume during the evaporation process. In contrast to Fig. 8a the vapour pressure is increasing while evaporation process because of the continuously increasing droplet surface curvature. The theoretical and experimental droplet volume as a function of the time, shown in Fig. 10b, differs at the end of evaporation (t > 180 s), for the same reason indicated in Fig. 8b. 3.1.3. Stick-slip mode Evaporation in the constant contact angle mode occurs only in the ideal case without contact angle hysteresis [39]. In all other cases a ‘‘stick-slip’’-motion is observed due to contact angle hysteresis. This process is known for droplet evaporation on plane sur-
Fig. 10. Vapour pressure of the droplet (a) and experimental and modelled droplet volume as a function of the time during evaporation (b), shown in Fig. 9.
C.S. Funk et al. / Journal of Colloid and Interface Science 417 (2014) 171–179
Fig. 11. Time behaviour of contact angle (j) and droplet diameter (D) of ‘‘stickslip’’ motion during evaporation of water droplets on fibres coated with nanoparticles.
faces but is observed for the first time on fibres. Fig. 11 shows the temporal evolution of the contact angle and the droplet diameter for a PET fibre coated with 50 nm particles. The contact radius of the droplet decreases with jumps and the contact angle oscillates between 22° and 29°, i.e. a stick-slip behaviour is observed. Therefore the volume of the droplet reduces with time in a stepwise mode. Fig. 12 shows the drop evaporation on fibres coated with SiO2nanoparticles of different diameters in hydrophilic binder material. The PET-reference fibre shows poor contact line mobility, droplets evaporate in constant contact area mode, while the contact angle decreases. The time evolution of contact angle shows an enormous improvement of contact line mobility by coating the fibres with the hydrophilic binder material. In the experiment with the smooth hydrophilic coating excluding particles a very small contact angle hysteresis of about 1° was observed (see Fig. 12a:
177
(⁄) 24.96° to 25.84° from 10 s to 12 s). In the experiments with nanoparticles the surface of the coated fibres show in all cases a contact angle hysteresis between 2° and 5° (see a weak ‘‘stick-slip’’ motion in the diagram). In Fig. 13a the vapour pressure of the droplets are increasing during evaporation due to the continuously increasing droplet surface curvature. The smaller the nanoparticles in the coating are the bigger is the increase of vapour pressure while droplet evaporation. Also here the measured data are described very well by the calculated values. The time evolution of contact angle and drop base diameter both demonstrate a dependency of the mobility of the three phase line on the particle diameter in hydrophilic binder material. As the particles in the coating get smaller the slope (dh/dt) of the contact angle versus time is getting smaller as well. Droplets with a very mobile contact line exhibit a slope of almost zero (see Fig. 9) whereas immobile droplets exhibit a very high negative slope (see Fig. 7). The mobility of the three phase contact line is linked to the slope of the contact angle during evaporation. The lower the mobility of the contact line is the more negative is the slope while evaporation in the first 200 s. The determined slopes of the contact angles in the first 200 s of evaporation process are listed in Table 1 and in Fig. 14. Obviously there is a correlation between wetting properties, contact angle hysteresis, drop shape and evaporation mode. Droplets that evaporate with nearly constant contact angle are always of a symmetrical, barrel-shape. The static contact angle in this case is smaller than 30°. Droplets that evaporate in constant contact area mode, however, have non-symmetrical, clam-shell-shape and their static contact angle is bigger than 30°. The evaporation mode and the static contact angle correlates with the mobility of the contact line. The smaller the static contact angle (axialsymmetric drop shape) the better is the mobility of the three phase contact line. In addition a small contact angle hysteresis enhances the mobility of the contact line.
Fig. 12. Time evolution of contact angle (a) and relevant drop base diameter (b) determined at drop evaporation for different fibre coatings. The contact angle of droplets on fibres coated with nanoparticles of 6 nm; 15 nm; 25 nm and 50 nm in hydrophilic binder material remains nearly constant over time (a), while the associated base diameter decreases (b).
Fig. 13. Vapour pressure of the droplet (a) and experimental and modelled droplet volume as a function of the time during evaporation (b), shown in Fig. 12.
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C.S. Funk et al. / Journal of Colloid and Interface Science 417 (2014) 171–179 Table 1 Slope (dh/dt) of contact angles versus time on hydrophilic coated fibres extracted from Fig. 12. Fibre coating
dh/dt/°/s
PET-reference Only binder
0.1350 0.0270
Fig. 14. Slopes of contact angles versus time on hydrophilic coated fibres extracted from Fig. 12.
3.2. Droplet growth, coalescence and mobility The droplet mobility was studied for an axial flow velocity along the fibre of 1.73 m/s. Fig. 15 shows the critical droplet volumes at which droplets start to move along the hydrophilic fibres. The bigger the nanoparticles in the coating the higher is the droplet volume at which droplets start to move along the fibre. The adhesion force calculated from the drag force at critical droplet volume increases simultaneously. Figs. 6, 12 and 15 prove that there is a direct interrelation between the mobility of droplets, the mobility of the three phase contact line and the static contact angle on the coatings including nanoparticles. 3.3. Discussion of different evaporation modes and drop mobility We show for the first time correlations between droplet conformation, contact angle of droplets on fibre, evaporation behaviour and droplet mobility. To our knowledge no analyses of the evaporation behaviour and droplet mobility have been performed on rough, coated fibres. We found constant contact angle mode and constant contact area mode droplets on fibres in accordance to other scientists working on flat surfaces [15–21]. In case of low contact angle hysteresis the contact line can move easily and droplets will evaporate with a nearly constant contact angle. However, in case of inhomogeneities like cracks, rough or sharp edges which act as
pinning centres a lower drop mobility is observed. The contact line is pinned until the receding angle is reached. On nanorough fibres the mode of evaporation depends mainly on wetting angle and contact angle hysteresis. The wetting angle leads to a defined droplet conformation on fibres and the mobility of the contact line depends on droplet conformation. Symmetrical, barrel-type droplets are stable (large contact area) and have a short contact line. Mullins et al observed droplets of barrel-type that move along fibres [12]. Non-symmetrical, clamshell-type droplets are unstable and have a long contact line. This leads to a lower mobility for these non-symmetrical drops compared to symmetrical drops. Fig. 5 demonstrates that hydrophilic coatings with nanoparticles exhibit very small contact angles between droplets and fibre surface. It was observed that if the particles in the hydrophilic coating get smaller the contact angle between fibre and droplet decreases and the mobility of the contact line is enhanced. During contact line motion the three phase contact line must overcome a series of non-equilibrium jumps in which the contact line moves from one equilibrium position to the next, a process for which activation energy is required [5,44]. If the particles in the coating grow larger the distance between the nanoparticle elevations rises. Consequently the activation energy for the jump of the contact line increases. During evaporation the contact angle decreases when the contact line is pinned. If the activation energy increases the time for contact angle reduction is longer before a jump of the contact line occurs and thus the slope of the contact angle versus time is getting more negative. Not only is the wetting angle important for a high mobility of contact line but also the contact angle hysteresis. If the contact angle hysteresis is nearly zero the mobility of the three phase contact line is enhanced. The experiments concerning droplet mobility prove that the volume required for droplet motion correlates with the mobility of the contact line. Thus the same interrelation between particle diameter and adhesion force exists. Accordingly, small droplets on fibres become mobile by a nanoparticulate fibre coating. Highly mobile droplets do easily coalescence. This simplifies the removal of the droplets from the filter and leads to a better regeneration of the fibre material in coalescing filters. 4. Summary We studied the correlation between contact angles, evaporation behaviour and mobility of small droplets on fibre surfaces and found a direct relation between these parameters. Thus it is finally possible to draw conclusions about the drop mobility on fibres from observing and analysing the evaporation behaviour of drops on fibres. The smaller the contact angles between fibre and droplet are the better is the mobility of the contact line and the mobility of droplets, at small contact angle hysteresis. If a droplet has a high
Fig. 15. Required droplet volume for droplet movement along fibres coated with hydrophilic binding system including nanoparticle of different diameters at axial stream velocity of 1.73 m/s (a) and calculated adhesion forces from the experiments (b).
C.S. Funk et al. / Journal of Colloid and Interface Science 417 (2014) 171–179
mobility on the surface it evaporates at constant contact angle mode. However, if the mobility is low it evaporates with constant contact area. By coating fibres with nanoparticles it is possible to control the wetting behaviour of the fibres and by this the drop mobility on these fibres. If the coating is homogenous (the contact angle hysteresis must be small, the smaller the better is the drop mobility) and hydrophilic, a high water drop mobility is observed. The smaller nanoparticle diameters in the coating are the smaller the contact angles between water droplets and fibres become. As wettability and mobility of droplets are interrelated, a decrease of the nanoparticle diameter in the coating leads to an improvement of droplet mobility on fibres. Acknowledgments We acknowledge financial support of the BMBF and the cooperating companies Hengst GmbH & Co. KG, Nano-X GmbH, JunkerFilter GmbH and ITV. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
B.J. Carroll, J. Colloid Interface Sci. 57 (1976) 488–495. F. Brochard, J. Chem. Phys. 84 (1986) 4664. D. Quere, Annu. Rev. Fluid Mech. 31 (1999) 347–384. L. Le´ger, J.F. Joanny, Rep. Prog. Phys. 55 (1992) 431. B.J. Carroll, J. Colloid Interface Sci. 9 (1984) 195. J. Bico, U. Thiele, D. Que’re, Colloids Surf., A 206 (2002) 41–46. H.D. Wagner, J. Appl. Phys. 67 (1990) 1352–1355. J. Yamaki, Y. Katayama, J. Appl. Polym. Sci. 19 (1975) 2897–2909. B.J. Carroll, Langmuir 2 (1986) 248–250. B.J. Carroll, J. Appl. Phys. 70 (1991). 493. B.J. Carroll, J. Chem. Soc., Faraday Trans. I (85) (1989) 3853–3860. B.J. Mullins, R.D. Braddock, I.E. Agranovski, R.A. Cropp, J. Colloid Interface Sci. 300 (2006) 704–712. [13] R. Mead-Hunter, B.J. Mullins, T. Becker, R.D. Braddock, Langmuir 27 (2011) 227–232. [14] S. Dawar, G.G. Chase, Sep. Purif. Technol. 60 (2008) 6–13. [15] H.Y. Erbil, G. McHale, S.M. Rowan, M.I. Newton, Langmuir 15 (1999) 7378– 7385.
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[16] R.G. Picknett, R. Bexon, J. Colloid Interface Sci. 61 (1977) 336–350. [17] H.Y. Erbil, G. McHale, M.I. Newton, Langmuir 18 (2002) 2636–2641. [18] G. McHale, S. Aqil, N.J. Shirtcliffe, M.I. Newton, H.Y. Erbil, Langmuir 21 (2005) 11053–11106. [19] S.M. Rowan, M.I. Newton, G. McHale, J. Phys. Chem. 99 (1995) 13268–13271. [20] K.S. Birdi, D.T. Vu, A. Winter, J. Phys. Chem. 93 (1989) 3702–3703. [21] Y.C. Jung, B. Bhushan, J. Microsc. 229 (2008) 127–140. [22] E. Bormashenko, A. Musin, G. Whyman, M. Zinigrad, Langmuir 28 (2012) 3460–3464. [23] E. Bormashenko, A. Musin, M. Zinigrad, Colloids Surf., A 385 (2011) 235–240. [24] A. Murarova, S. Podobekoca, Z. Murarova, Fibres Text. Eastern Eur. 15 (2007) 127–130. [25] J.F. Bitten, J. Colloid Interface Sci. 33 (1970) 265–271. [26] A.L. Yarin, G.G. Chase, W. Liu, S.V. Doiphode, D.H. Renecker, AIChE J. 52 (2006) 217–227. [27] L. Gao, Th.J. Mc Carthy, Langmuir 22 (2006) 6234–6237. [28] K.A. Wier, Th.J. McCarthy, Langmuir 22 (2006) 2433–2436. [29] R. Mead-Hunter, T. Bergen, T. Becker, R.A. O‘Leary, G. Kasper, B.J. Mullins, Langmuir 28 (2012) 3483–3488. [30] B.J. Mullins, I.E. Agranovski, R.D. Braddock, C.M. Ho, J. Colloid Interface Sci. 269 (2004) 449–458. [31] S. Dawar, G.G. Chase, Sep. Purif. Technol. 72 (2010) 282–287. [32] R.N. Wenzel, Ind. Eng. Chem. 28 (1936) 988–994. [33] A.B.D. Cassie, S. Baxter, Trans. Faraday Soc. 40 (1944) 546–551. [34] D.K. Owens, R.C. Wendt, J. Appl. Polym. Sci. 13 (1969) 1741–1747. [35] J.D. Miller, S. Veeramasuneni, J. Drelich, M.R. Yalamanchili, G. Yamauchi, Polym. Eng. Sci. 36 (1996) 14. [36] H. Nakae, R. Inui, Y. Hirata, H. Saito, Acta Mater. 46 (1998) 2313–2318. [37] G.E. Stringham, D.B. Simons, H.P. Guy, The Behavior of Large Particles Falling in Quiescent Liquids, United States Gov. Print. Off, U.S. Geological Survey Professional Paper 562-C, 1969. [38] K.V. Bread, H.R. Pruppacher, J. Atmos. Sci. 33 (1976) 851–864. [39] G. McHale, S. Aqil, N.J. Shirtcliff, M.I. Newton, H.Y. Erbil, Langmuir 21 (2005) 11053–11060. [40] O. Krischer, Trocknungstechnik, Springer-Verlag, 1978. [41] H. Brauer, Stoffaustausch einschließlich chemischer Reaktionen, Verlag Sauerländer, 1971. [42] F. Mayinger, Strömung und Wärmeübergang in Gas-Flüssigkeits-Gemischen, Springer-Verlag, 1982. [43] C. Weiß, Modellierung und Simulation der Kristallisation in dispersen Systemen, Fraunhofer IRB Verlag, 2001. [44] B.J. Carrol, The Equilibrium of Liquid Drops on Smooth and Rough Circular Cylinders, Unilever Research, England, 1983, L63 3JW.
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Correlation between shape, evaporation mode and mobility of small water droplets on nanorough fibres C.S. Funk, B. Winzer, W. Peukert ⇑ Institute of Particle Technology (LFG), University of Erlangen-Nuremberg, Cauerstr. 4, D-91058 Erlangen, Germany
a r t i c l e
i n f o
Article history: Received 6 August 2013 Accepted 5 November 2013 Available online 18 November 2013 Keywords: Coalescing media Wettability of fibres Nanoparticle coating Droplet mobility Three phase contact line Evaporation mode Contact angle Silica Droplet conformation Fibre surface energy
a b s t r a c t The dynamic wetting behaviour and the mobility of droplets on fibres is a very important factor in coating processes, textile fabrication, in self-cleaning processes and in the filtration of fluids. In principal, filter regeneration depends on the mobility of the droplets on the fibre surface. Mobile droplets tend to coalesce which greatly simplifies their removal from the filter. In this contribution mobility analyses of water droplets on monofilaments in air are performed. Studies of droplet evaporation on pure PET fibres and on nanorough fibres coated with SiO2 nanoparticles of diameters between 6 nm and 50 nm in a hydrophilic binder system were done. We show that the mobility of water droplets correlates with the droplet conformation which in turn is determined by the droplet–fibre interface. We demonstrate that fibre coatings can be used to tailor the conformation and mobility of water droplets. The smaller the nanoparticle diameters in the coating are, the smaller are the contact angles between water droplets and fibre and the better is the mobility of the droplets on the fibre. Our results allow a fast optimization of the fibre surface properties which are directly influencing the contact angle, the mobility and the coalescence of water droplets and thus filter regeneration. Ó 2013 Elsevier Inc. All rights reserved.
1. Introduction Over the last years the wettability of fibres has become more and more important in many industrial areas such as coating processes, textile fabrication, self-cleaning processes and especially the filtration of fluids. Applications are the separation of water droplets from diesel fuel or the vapour-phase deposition of waterand oil droplets out of compressed air by fibre filters. In fluid filtration the droplet transport towards the fibre surface and the dynamic wetting behaviour are crucial. Whereas the impaction of droplets on fibres is well understood, the regeneration of the droplets in fibre filters remains elusive. Basically the regeneration of coalescing filters depends on the mobility of the droplets on the fibre surface: mobile droplets tend to coalesce leading to larger droplets and hence simplifies their removal from the filter. Due to the cylindrical shape of the fibre, the wetting behaviour of droplets on fibres differs from the wetting of flat surfaces. Early studies on the wetting phenomena of droplet-on-fibre systems have reported on determining the droplet shape and on extracting the contact angle accurately [1]. A fluid that forms a completely wetting film on a flat surface (vanishing contact angle) may not completely wet a fibre of the same material. In the case of flat
⇑ Corresponding author. Fax: +49 9131 8529402. E-mail address: [email protected] (W. Peukert). 0021-9797/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jcis.2013.11.005
surfaces, the spreading pressure, S = csv (csl + clv) where c is the interfacial tension, determines whether a film or a macroscopic droplet with a non-zero contact angle is formed [2]. In case of fibres, a film only forms when S exceeds a finite positive value dependent on the fibre radius. A vanishing contact angle can be consistent with a macroscopic droplet [2–6]. Wagner et al. studied the spreading of liquid droplets on cylindrical surfaces [7]. Yamaki and Katayama describe a theoretical method to calculate the contact angle by observing the shape of a liquid drop attached to a monofilament and point out that the shapes of droplets attached to monofilaments change depending on liquid volume. Moreover, it was found for very small droplets that the effect of gravity is negligible [8]. Carroll studied properties of fluid droplets on cylinders, such as the equilibrium conformation of droplets, contact angles and the stability of small droplets [1,9–11]. Depending on the fibre radius, the droplet volume and the surface energy of the fibre, he found two fundamentally different conformations of macroscopic droplets: i.e. barrel and a clam-shell conformation (see Fig. 1). At the critical contact angle a change of droplet conformation takes place. This ‘roll-up’-process results in a change of the contact area which leads to a significant change of the droplet profile. The critical contact angle depends on the fibre radius and the surface energy of the fibre. The most complete experimental data on the roll-up-process was given by Carroll [9]. Barrel shapes occur for large droplets relative to the fibre radius or for low contact angles. Clam-shell shapes occur for small droplets or high contact angles.
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(a)
(b)
Fig. 1. Conformations of water droplets on a cylindrical fibre [10]: (a) barrel-type; axially symmetric and (b) clam-shell-type; non-symmetric.
In a coalescing filter it is desirable that droplets have a high radial adhesion and a low axial adhesion to the fibre. Droplets of the barrel-type have a bigger radial adhesion to the fibre compared with the clam shell shape droplets and thus the residence time and the probability of droplet coalescence on the fibre is increased. In addition, the clamshell droplet has a longer three phase contact line with the fibre, compared with the relatively short contact line of the barrel conformation. The surface tension force along the fibre is hence relatively small for the barrel shape droplet compared to the clamshell droplet. Thus, the barrel shaped droplets are more likely to slide down the fibre. This demonstrates the highly improved drainage of barrel droplets down the fibre due to a connecting film between the droplets compared to clamshell droplets. Therefore the barrel droplets have a better axial mobility on the fibres at higher residences time, which leads to an increased coalescence, to larger droplets and simplifies the removal of the droplets from the filter [9,12]. Clam shell droplets roll axially on the fibre which increases the probability of leaving the fibre before coalescing with other droplets while barrel droplets slide [13]. Therefore, they are the preferred conformation in coalescing filters. Also in wet filters a good wetting of the fibres is required [30]. In this case the particles are captured by a liquid film rather than being directly captured by the fibres. Therefore barrel droplets or film formation of the liquid on the fibres is desired in this technique. The symmetrical drop conformation is characterized by two linear, dimensionless parameters, the reduced drop diameter n = x2/x1 and the reduced drop length Ł = Lw/x1. Lw describes the droplet base diameter, x1 the fibre radius and x2 the drop height (see Fig. 1). The three parameters can be directly obtained from a photomicrograph ([1,10,11]). In this publication the influence of the fibre roughness on the contact angle and on the mobility of droplets on fibres is studied. As the mobility of droplets on fibres is determined by the mobility of the three-phase-contact line [14] an analysis of the evaporation behaviour of droplets on fibres is performed as well. Upon evaporation the three-phase contact line of the droplet must shift. Various studies of the evaporation behaviour of droplets on flat surfaces exist [15–21]. McHale and Newton [17–19] investigated the adsorption and evaporation of droplets on flat surfaces by video microscopy. For initial contact angles less than 90°, the contact area remains constant upon evaporation. In case of structured surfaces a stepwise contraction of droplets depending on the surface structure was observed. Water droplets on textured surfaces evaporate in a stick-slip mode. Few studies concerning the evaporation behaviour of droplets on fibre surfaces are known [22,23]. Murarova et al. functionalised the fibre surface by pigments via a sol–gel procedure [24]. They found a dependence of the contact angle on time. Mullins investigated the wetting process during filtration of droplets in air [21]. They observed adsorption of water droplets on glass fibres, oscillatory droplet motion and detachment or flow of these droplets along the fibre. Mobility and coalescence of droplets were investigated on flat and on curved surfaces [25–30]. Bitten et al. found that the maximum diameter of droplets adhering to the fibre surface depends
strongly on the fibre material [25]. Mullins et al. studied the influence of fibre orientation on the fibre wetting process and flow of liquid droplets along filter fibres [12]. By determining the forces acting on a droplet on a fibre, it is possible to determine an optimum angle such that the flow of droplets down the fibre will be maximized ensuring maximal filter self-cleaning. Dawar et al. proposed correlations of the droplet mobility as a function of drop and fibre sizes and on the Reynolds (Re) and Capillary (Ca) numbers [14,31]. Mead-Hunter et al. present a theoretical model describing the force required to move coalesced liquid droplets of two different oils along an oleophilic filter fibre and determine the influence of droplet displacement perpendicular to the fibre on the force required to move the droplet experimentally. Additional it was found that fibre surface inhomogeneities strongly influence the results [13,29]. The wetting of flat textured surfaces can be described by two different models, i.e. the Wenzel model and the Cassie–Baxter equation. The Wenzel model describes the homogeneous complete wetting regime and is defined by the following equation:
cos hW ¼ r cos h
ð1Þ
In this equation the apparent contact angle hw depends on the surface roughness r which is defined as the actual, rough surface area divided by the projected surface area. h is the equilibrium contact angle on a smooth surface exhibiting the same surface chemistry as the structured surface [32]. If air is assumed to be entrapped in the voids of a rough surface, the contact angle on the rough surface can be described by the Cassie–Baxter equation.
cos hCB ¼ r fs cos h þ fs 1
ð2Þ
fs is the fraction of the solid surface area wetted by the liquid [33] and hCB the contact angle on the rough surface. It is important to realize that when f = 1, the Cassie–Baxter equations becomes the Wenzel equation. For water droplets the Cassie–Baxter case generally occurs on hydrophobic surfaces and the Wenzel case on hydrophilic surfaces as in the present case. Several fundamental questions concerning the influence of surface roughness of fibres on droplet mobility are not sufficiently understood. This contribution shows that the droplet mobility on coated fibres correlates with the droplet conformation on fibres and the wetting behaviour of fibres. As the droplet conformation is determined by the droplet–fibre interface the wetting behaviour of PET fibres was tailored by a surface coating with silica nanoparticles of different sizes embedded in a hydrophilic binding system. The coatings, including nanoparticles, create a certain fibre surface roughness, depending on the nanoparticle diameter. 2. Materials and methods 2.1. Preparation of the fibres For the analysis of the wetting and the evaporation behaviour of water droplets in air PET fibres (diameter 100 lm) were coated with a hydrophilic binding system excluding and including SiO2
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nanoparticles in the range of 6 nm to 50 nm provided by Nano-X, Germany. The particles were available in diluted suspensions of 5 wt% solid fraction. The fraction of nanoparticles in the hydrophilic binder material was set to 60 vol%. The coating procedure of the PET fibres consists of three steps: first, the fibre is cleaned with pure ethanol to remove impurities. Followed by a plasma treated (Plasma Prep2; Gala Instruments) to improve the wettability of the coating suspension on the fibre surface. The energy of the plasma and the activation time are chosen in such manner that the surface does show good wetting behaviour without any indication of degradation or melting. Directly after this activation the fibres are drawn with a constant velocity through the nanoparticle coating suspension and subsequently air dried at 20° C. In this way it is possible to generate close and homogenous layers of nanoparticles (see Fig. 2). 2.2. Fibre characterization To determine the roughness of the nanoparticle coated fibres Atomic Force Microscopy (AFM) measurements of the fibre surface were performed. AFM images were taken with a NanoScopeIIIa Scanning Probe Microscope Controller from Digital Instruments working in the tapping mode using high frequency cantilevers. Measurements have been taken with scanning lengths of 1 lm and 10 lm. The used cantilever (DP 14 Hi‘Res) was from MikroMasch with a specified spring constant of 1.8–13 N/m and 1 nm radius of curvature on the tip, according to the manufacturer’s specification. With sufficient sensitivity in the spring deflection sensor, the tip can reveal surface profiles with nanometer or even with subnanometer resolution [35]. For one roughness factor according to Wenzel we analysed 5 AFM images of one fibre surface with the NanoScopeIIIa Software. The roughness factors r were calculated from the AFM measured
surface areas of the coatings including particles divided by the one excluding particles. In a regular cubic lattice of spheres the roughness factor should stays constant at a value of 1.9 independent of particle size [36]. The measured roughness factors are between 1.33 for the 6 nm particles and slightly decrease to 1.26 for a particle of 50 nm. In Fig. 3 the AFM images of the surface topography of a fibre coated with the hydrophilic binding system including nanoparticles with diameters of 25 nm (a) and the hydrophilic binding system excluding particles (b) are shown. The diameter of the measured particles in (b) has increased to 70 nm since the binder coats the particles. Additionally to the AFM measurements the coated fibres were characterized by low-voltage SEM (Ultra 55; Zeiss), see Fig. 2. The characterization of the fibre surface regarding the surface energy of the network building silica binding system were done by OWRK (Owens, Wendt, Rabel and Kaelble) measurements on flat surfaces of identical coating [34]. For the contact angle measurements and the evaporation experiments droplets with volumes in the range of 0.5 nl to 1 ll are produced and deposited on the fibre surface using a fluid dosing unit (Xeno-Works with 500 ll and 100 ll syringe) with glass capillaries (end diameter smaller than 10 lm, silanized with 2% solution of dichlorodimethylsilane in octamethylcyclotetrasiloxane), combined with a micromanipulator (MP 285; Sutter Instruments Company). Using a light microscope with cold light source (Axio Imager M1m; Zeiss; transmitted light; objective 20) in combination with a camera the droplet depostion, growth, mobility and evaporation on a single fibre have been carefully monitored by taking images and videos of the droplet profiles (up to 25 frames per second). The characteristic parameters (x1, x2, Lw, H; see Fig. 1) are extracted from the recordings using the evaluation software of a contact angle measuring system (OCA20; dataphysics). The contact
20µm
1µm
Fig. 2. SEM images of PET fibres coated with hydrophilic binding system including 15 nm SiO2 particles (SE2 detector; acceleration voltage: 1.2 kV).
(a)
93.1 nm
20.0 nm
(b)
0.0 nm 0 µm
1 µm
x (µm)
0.0 nm 0 µm
1 µm
x (µm)
Fig. 3. AFM image of the surface topography of a PET fibre coated with hydrophilic binding system including nanoparticles with diameters of 25 nm (a) and hydrophilic binding system without particles (b).
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angle at the fibre is obtained by the Young–Laplace fitting method. All experiments were carried out at 21 °C and a relative humidity of 42%. The measurements of the static contact angles (left and right side of droplet) of at least 20 drops were carried out at different locations on the fibre. The standard deviation of the average value is ±2.1°. To determine the mobility of the contact line and the receding contact angle, the droplet evaporation was observed. Video films were taken during the evaporation. Both, the contact angles over time and the droplet base diameter over time were determined. Cleaned PET-fibres served as reference. 2.3. Droplet growth, coalescence and mobility A stream of small fluid droplets with diameters in the order of
lm is produced by a nebulizer. Droplets adsorb at the fibre surface and grow by deposition of further droplets from the gas stream. The experimental set-up is shown in Fig. 4. In the experiments the aerosol stream is under a 15° angle with respect to the fibre axis. Growth, coalescence and movement of droplets can be observed directly. Droplets grow until the drag force of the droplet Fd,krit against the air flow is larger than the adhesion force Fad between droplet and fibre. The drag force can be calculated by the following equation:
F ad ¼ F d;krit: ¼
1 cd m2rel qfluid Adroplet ¼ f ðAdroplet Þ 2
ð3Þ
Adroplet is the axial cross section of the droplet, vrel is the relative velocity between droplet and air, qfluid is the density of the fluid flow and cd (Re) is the drag coefficient as a function of Re number. The behaviour of the small drops in contact with the fibre was observed by light microscopy. During droplet growth and movement along the fibre videos at 90 frames per second were taken. The velocity of the water droplets in the stream was measured by a PIV (Particle Image Velocimetry) system of ILA with a CCD camera pco.2000, a Nd:YAG-Laser (k = 532 mm) from Big Sky Laser series of Quantel and a Canon EF 100 mm f/2.8 Macro USM objective. From the PIV data the droplet velocity was averaged from 10 measurements. We found a mean droplet velocity in axial direction vax of 1.73 ± 0.03 m/s in the experiments. For the determination of the drag coefficient on the droplet flow around a rigid spheroid was taken. Using the air flow velocity of 1.73 m/s the Reynolds number is between 2100 and 3300 depending on the droplet profile. The barrel-type droplets in our experiments exhibit aspect ratios between 1.67 and 2.86. Hence the drag coefficients according to Stringham were used [37,38]. The flow velocity vax can be set as vrel as the droplets are fixed on the fibre before they move.
3. Results and discussion 3.1. Droplet conformation, static contact angle and evaporation behaviour The equilibrium conformation of water droplets placed on cylindrical fibres is determined by the contact angle and thus by the surface energy of the fibre [11]. Barrel shapes with low contact angles occur on fibres with high surface energy and for large droplet volumes. Clam-shell shapes with high contact angles occur for small droplet volumes [10]. Examples of different drop conformations observed in these studies are given in Fig. 5. The wetting experiments of water droplets of 0.030 ± 0.002 ll on fibres with 100 lm show a change of droplet conformation from clam-shell-type to barrel-type by coating them with the hydrophilic silica binder. The contact angles of drops on pure PET (surface energy: 39.5 ± 0.6 mN/m) and on fibres coated with the hydrophilic network building silica coating (surface energy: 61.3 ± 0.2 mN/m) are listed in Fig. 5a and b. The apparent contact angles can be described by the Young equation and the Young–Laplace equation for fibres. An increase of the solid surface energy leads to a decrease of the contact angle of the water droplet. Coating PET fibres with the hydrophilic binding system reduces the contact angle between water droplet and fibre and leads to a change in droplet conformation and thus to an improvement of the radial droplet adhesion to the fibre. Further reduction of the contact angle between fibre and water droplet can be achieved by including nanoparticles in the fibre coating. The contact angle depends on the nanoparticle diameter as can be seen in Fig. 6. The contact angle is, for instance reduced from 54.2° to 19.1° when including nanoparticles with a diameter of 6 nm. The smaller the nanoparticle diameters in the coating are the smaller get the measured contact angles between water droplets and fibres. Wenzel showed that micro-structuring of a surface enforces the natural tendency of the surface. This means that a hydrophilic surface with a contact angle less than 90° gets more hydrophilic when it is micro- or nanostructured. The contact angle on the rough surface is reduced relative to the smooth surface [32]. The bigger the roughness factor is the smaller are the contact angles on a rough hydrophilic surface. If the particles in the fibre coatings get smaller the actual surface and thus the surface roughness factor r increases accordingly. On that account, the contact angle decreases while the particle diameter in the fibre coating decreases and thus the wettability of the fibre surface increases. During the evaporation of water droplets on coated fibres different evaporation modes are observed. In accordance with other researchers we found the constant contact area mode, constant contact angle mode and the ‘‘stick-slip’’ motion on the fibres [15–21].
3.1.1. Constant contact area mode Axial component vax
Radial component v rad Total velocity vtot Growing droplet
Fig. 4. Experimental setup to observe droplet growth and mobility.
The typical evaporation behaviour for droplets that evaporate in the mode of constant contact area is illustrated in Fig. 7. The base diameter remains nearly constant over the whole evaporation process, while the contact angle decreases. Such evaporation behaviour was found for fibres with a static contact angle larger than 30°. In Fig. 7 the evaporation behaviour of a water droplet on a pure PET fibre is shown. In Fig. 8a the vapour pressure of the droplet is plotted against the droplet volume during the evaporation process. The vapour pressure is calculated by the Kelvin-equation using the measured droplet profile. The vapour pressure of droplets evaporating in
C.S. Funk et al. / Journal of Colloid and Interface Science 417 (2014) 171–179
(a) 100 µm
(b) θ = 64.5° (±2.5)
θ = 39.5° (±2.2)
(e) 100 µm
100 µm
θ = 54.2° (±3.7)
(d)
(c) 100 µm
175
100 µm θ = 24.3° (±2.1)
(f) θ = 17.2° (±1.4)
100 µm
θ = 13.41° (±1.9)
Fig. 5. Different droplet conformations for water droplets on coated fibres: (a) On PET reference fibre of 100 lm diameter droplets with a volume of 80 ± 5 nl of clam-shelltype (unsymmetrical; even at large drop volumes of 0.4 ll) are observed. (b) On PET-fibres with SiO2-binder coating droplets with a volume of 0.4 ± 0.02 ll show the barreltype conformation. (c) On PET-fibres with a 50 nm SiO2-nanoparticle-binder coating an intermediate state between clam-shell-type and ‘‘barrel’’-type conformation (droplet starts wrapping around the fibre) was observed for very small droplet volumes of 20 ± 5 nl. (d) At large volumes of 0.3 ± 0.02 ll water droplets on PET-fibre with 50 nm SiO2nanoparticle coating are of barrel-type (symmetrical). (e) On PET-fibre with 25 nm SiO2-nanoparticle coating droplets are of barrel-type even at small droplet volume of 50 ± 5 nl. (f) On PET-fibre with 6 nm SiO2-nanoparticle coating droplets are of barrel-type (symmetrical) already at very small droplet volume of 10 ± 5 nl.
Fig. 6. Measured contact angles on fibres coated with hydrophilic binding material including nanoparticles of different diameter.
the constant contact area mode is decreasing because of the continuously decreasing droplet surface curvature. The time dependency of the droplet volume, shown in Fig. 8b, _ D in kg/m2 s from a droplet can be modelled by the mass flux m to the gas phase during droplet evaporation using the well-known Stefan–Maxwell approach which accounts for one-sided diffu-
Fig. 7. Typical clam-shell conformation and time dependency of droplets evaporating in the constant contact area mode. Such drops typically have a ‘‘clam-shell’’type conformation. The contact angle (j) decreases steadily and the droplet diameter (D) remains constant for almost the whole evaporation process. In this evaporation mode the contact line is pinned.
sional and convective mass transfer [40–43]. Temperature effects are neglected and the fluid around the droplet shall be quiescent.
_ D ¼ M m
Deff p _D m rpm þ m RT p
ð4Þ
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Fig. 8. Vapour pressure of the droplet (a) and experimental and modelled droplet volume as a function of the time during evaporation (b), shown in Fig. 7.
The flux from the droplet and consequently the volume decrease of the droplet is dependent on the vapour pressure and the surface area of the droplet. Eqs. (5) and (6) describe the measured droplet volume as function of time very well. Only at the end of evaporation (t > 230 s) larger deviation occur which are probably due the limited resolution of the images of the taken videos. At the end of evaporation a flattening of the droplet occurs and thus only a thin film of liquid on the fibre exists. Therefore, the contour of the droplet cannot be detected exactly by the software of the contact angle device. 3.1.2. Constant contact angle mode
Fig. 9. Typical conformation and time dependency of contact angle and base diameter of droplets that evaporate in the constant contact angle mode. Such drops are typically of ‘‘barrel’’-type. The contact angle (j) remains constant and the droplet diameter (D) decreases steadily during evaporation in constant contact angle mode at early stages of evaporation.
where M is the molar mass of the liquid, Deff is the effective diffusion coefficient of water in air, p the total pressure, pv the vapour pressure of the droplet, R the gas constant and T the temperature. _ D leads to Solving the equation for m
_ D ¼ M m
Deff 1 rpm 1 pm =p R T
ð5Þ
The solution for a spherical droplet of radius r is given by
_D¼ m
M Deff p p ln p pm RrT
ð6Þ
The flow rate from one droplet of radius r can be calculated by using the surface area of the droplet Sdroplet extracted from the images and ql the density of the liquid.
_D m V_ droplet ¼ Sdroplet
ql
ð7Þ
This mode is the expected behaviour for system in equilibrium between solid, liquid and gas where no difference between advancing and receding contact angle exists. On real samples there is always a small contact angle hysteresis. Fig. 9 illustrates the observed evaporation behaviour of symmetrical drops with static contact angles lower than 30° on the coated fibres. In this case the contact line can move easily, the droplet evaporates with nearly constant contact angle, whereas the diameter decreases steadily. Therefore the vapour pressure increases as well. In the experiment with nanoparticles diameters of 6 nm the surface of the coated fibres show a very small contact angle hysteresis of about 3° (see a slight ‘‘stick-slip’’ motion in the diagram). Fig. 10a shows the vapour pressure of the droplet plotted against the droplet volume during the evaporation process. In contrast to Fig. 8a the vapour pressure is increasing while evaporation process because of the continuously increasing droplet surface curvature. The theoretical and experimental droplet volume as a function of the time, shown in Fig. 10b, differs at the end of evaporation (t > 180 s), for the same reason indicated in Fig. 8b. 3.1.3. Stick-slip mode Evaporation in the constant contact angle mode occurs only in the ideal case without contact angle hysteresis [39]. In all other cases a ‘‘stick-slip’’-motion is observed due to contact angle hysteresis. This process is known for droplet evaporation on plane sur-
Fig. 10. Vapour pressure of the droplet (a) and experimental and modelled droplet volume as a function of the time during evaporation (b), shown in Fig. 9.
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Fig. 11. Time behaviour of contact angle (j) and droplet diameter (D) of ‘‘stickslip’’ motion during evaporation of water droplets on fibres coated with nanoparticles.
faces but is observed for the first time on fibres. Fig. 11 shows the temporal evolution of the contact angle and the droplet diameter for a PET fibre coated with 50 nm particles. The contact radius of the droplet decreases with jumps and the contact angle oscillates between 22° and 29°, i.e. a stick-slip behaviour is observed. Therefore the volume of the droplet reduces with time in a stepwise mode. Fig. 12 shows the drop evaporation on fibres coated with SiO2nanoparticles of different diameters in hydrophilic binder material. The PET-reference fibre shows poor contact line mobility, droplets evaporate in constant contact area mode, while the contact angle decreases. The time evolution of contact angle shows an enormous improvement of contact line mobility by coating the fibres with the hydrophilic binder material. In the experiment with the smooth hydrophilic coating excluding particles a very small contact angle hysteresis of about 1° was observed (see Fig. 12a:
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(⁄) 24.96° to 25.84° from 10 s to 12 s). In the experiments with nanoparticles the surface of the coated fibres show in all cases a contact angle hysteresis between 2° and 5° (see a weak ‘‘stick-slip’’ motion in the diagram). In Fig. 13a the vapour pressure of the droplets are increasing during evaporation due to the continuously increasing droplet surface curvature. The smaller the nanoparticles in the coating are the bigger is the increase of vapour pressure while droplet evaporation. Also here the measured data are described very well by the calculated values. The time evolution of contact angle and drop base diameter both demonstrate a dependency of the mobility of the three phase line on the particle diameter in hydrophilic binder material. As the particles in the coating get smaller the slope (dh/dt) of the contact angle versus time is getting smaller as well. Droplets with a very mobile contact line exhibit a slope of almost zero (see Fig. 9) whereas immobile droplets exhibit a very high negative slope (see Fig. 7). The mobility of the three phase contact line is linked to the slope of the contact angle during evaporation. The lower the mobility of the contact line is the more negative is the slope while evaporation in the first 200 s. The determined slopes of the contact angles in the first 200 s of evaporation process are listed in Table 1 and in Fig. 14. Obviously there is a correlation between wetting properties, contact angle hysteresis, drop shape and evaporation mode. Droplets that evaporate with nearly constant contact angle are always of a symmetrical, barrel-shape. The static contact angle in this case is smaller than 30°. Droplets that evaporate in constant contact area mode, however, have non-symmetrical, clam-shell-shape and their static contact angle is bigger than 30°. The evaporation mode and the static contact angle correlates with the mobility of the contact line. The smaller the static contact angle (axialsymmetric drop shape) the better is the mobility of the three phase contact line. In addition a small contact angle hysteresis enhances the mobility of the contact line.
Fig. 12. Time evolution of contact angle (a) and relevant drop base diameter (b) determined at drop evaporation for different fibre coatings. The contact angle of droplets on fibres coated with nanoparticles of 6 nm; 15 nm; 25 nm and 50 nm in hydrophilic binder material remains nearly constant over time (a), while the associated base diameter decreases (b).
Fig. 13. Vapour pressure of the droplet (a) and experimental and modelled droplet volume as a function of the time during evaporation (b), shown in Fig. 12.
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C.S. Funk et al. / Journal of Colloid and Interface Science 417 (2014) 171–179 Table 1 Slope (dh/dt) of contact angles versus time on hydrophilic coated fibres extracted from Fig. 12. Fibre coating
dh/dt/°/s
PET-reference Only binder
0.1350 0.0270
Fig. 14. Slopes of contact angles versus time on hydrophilic coated fibres extracted from Fig. 12.
3.2. Droplet growth, coalescence and mobility The droplet mobility was studied for an axial flow velocity along the fibre of 1.73 m/s. Fig. 15 shows the critical droplet volumes at which droplets start to move along the hydrophilic fibres. The bigger the nanoparticles in the coating the higher is the droplet volume at which droplets start to move along the fibre. The adhesion force calculated from the drag force at critical droplet volume increases simultaneously. Figs. 6, 12 and 15 prove that there is a direct interrelation between the mobility of droplets, the mobility of the three phase contact line and the static contact angle on the coatings including nanoparticles. 3.3. Discussion of different evaporation modes and drop mobility We show for the first time correlations between droplet conformation, contact angle of droplets on fibre, evaporation behaviour and droplet mobility. To our knowledge no analyses of the evaporation behaviour and droplet mobility have been performed on rough, coated fibres. We found constant contact angle mode and constant contact area mode droplets on fibres in accordance to other scientists working on flat surfaces [15–21]. In case of low contact angle hysteresis the contact line can move easily and droplets will evaporate with a nearly constant contact angle. However, in case of inhomogeneities like cracks, rough or sharp edges which act as
pinning centres a lower drop mobility is observed. The contact line is pinned until the receding angle is reached. On nanorough fibres the mode of evaporation depends mainly on wetting angle and contact angle hysteresis. The wetting angle leads to a defined droplet conformation on fibres and the mobility of the contact line depends on droplet conformation. Symmetrical, barrel-type droplets are stable (large contact area) and have a short contact line. Mullins et al observed droplets of barrel-type that move along fibres [12]. Non-symmetrical, clamshell-type droplets are unstable and have a long contact line. This leads to a lower mobility for these non-symmetrical drops compared to symmetrical drops. Fig. 5 demonstrates that hydrophilic coatings with nanoparticles exhibit very small contact angles between droplets and fibre surface. It was observed that if the particles in the hydrophilic coating get smaller the contact angle between fibre and droplet decreases and the mobility of the contact line is enhanced. During contact line motion the three phase contact line must overcome a series of non-equilibrium jumps in which the contact line moves from one equilibrium position to the next, a process for which activation energy is required [5,44]. If the particles in the coating grow larger the distance between the nanoparticle elevations rises. Consequently the activation energy for the jump of the contact line increases. During evaporation the contact angle decreases when the contact line is pinned. If the activation energy increases the time for contact angle reduction is longer before a jump of the contact line occurs and thus the slope of the contact angle versus time is getting more negative. Not only is the wetting angle important for a high mobility of contact line but also the contact angle hysteresis. If the contact angle hysteresis is nearly zero the mobility of the three phase contact line is enhanced. The experiments concerning droplet mobility prove that the volume required for droplet motion correlates with the mobility of the contact line. Thus the same interrelation between particle diameter and adhesion force exists. Accordingly, small droplets on fibres become mobile by a nanoparticulate fibre coating. Highly mobile droplets do easily coalescence. This simplifies the removal of the droplets from the filter and leads to a better regeneration of the fibre material in coalescing filters. 4. Summary We studied the correlation between contact angles, evaporation behaviour and mobility of small droplets on fibre surfaces and found a direct relation between these parameters. Thus it is finally possible to draw conclusions about the drop mobility on fibres from observing and analysing the evaporation behaviour of drops on fibres. The smaller the contact angles between fibre and droplet are the better is the mobility of the contact line and the mobility of droplets, at small contact angle hysteresis. If a droplet has a high
Fig. 15. Required droplet volume for droplet movement along fibres coated with hydrophilic binding system including nanoparticle of different diameters at axial stream velocity of 1.73 m/s (a) and calculated adhesion forces from the experiments (b).
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mobility on the surface it evaporates at constant contact angle mode. However, if the mobility is low it evaporates with constant contact area. By coating fibres with nanoparticles it is possible to control the wetting behaviour of the fibres and by this the drop mobility on these fibres. If the coating is homogenous (the contact angle hysteresis must be small, the smaller the better is the drop mobility) and hydrophilic, a high water drop mobility is observed. The smaller nanoparticle diameters in the coating are the smaller the contact angles between water droplets and fibres become. As wettability and mobility of droplets are interrelated, a decrease of the nanoparticle diameter in the coating leads to an improvement of droplet mobility on fibres. Acknowledgments We acknowledge financial support of the BMBF and the cooperating companies Hengst GmbH & Co. KG, Nano-X GmbH, JunkerFilter GmbH and ITV. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
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