Contact Angle Hysteresis and Hysteresis Tension on Rough Solid Surface

Observation and measurement were conducted to investigate contact angle and its hysteresis on rough surface. The experimental results indicate that the increase in solid surface roughness enlarges advancing contact angle and decreases receding contact angle, resulting in enhanced hysteresis. It was observed that when Young's contact angle θY < 90°, as the roughness of solid surface increased the extent of the decrease in     

Surface wettability and flow properties of non-metallic pipes in laminar flow

In this paper, three liquids flowing in five pipes with the same inner diameter of 14 mm were studied to determine the relationship between the surface wettability and flow properties in laminar flow(Re b 2000). This was motivated by oilfield observations of increased pressure drops in non-metallic pipes compared to those in metal pipes,which was contrary to expectations. A new expression for the frictional coefficient that considers the Reynolds number and contact angle θ in laminar flow for non-metallic pipes was proposed based on the experimental results of single-phase flow using dimension and regression analyses. The solutions of the anomalous phenomenon were proposed from the perspectives of the pipe diameter, contact-angle difference, and the compatibility between flexible composite pipe and JLHW105 oil according to the new formula. The surprising finding was that the surface wettability could control the frictional resistance by the critical contact angle(39.9°) obtained at the same Reynolds number. If 0° b θ≤ 39.9°, the frictional coefficient increased as the contact angle increased. In contrast, if 39.9° b θ b 180°,the frictional coefficient decreased with increasing contact angle. The influences of the pipe diameter and contactangle difference on the pressure drop difference of JLHW105 oil showed an inversely proportional relation. A series of materials and liquids were tested. The selection of pipe material for transporting a given fluid can be based on the contact angle, surface tension, and critical limit of the contact angle obtained. The research results are expected to provide some guidelines for the selection of the appropriate pipe material for a given set of fluids.     

液体在固体表面上的铺展动力学

Based on assuming that there is the precursor film in the front of the apparent contact line （ACL）, a model was proposed to understand the dynamic wetting process and associated dynamic contact angle. The present model indicated that a new dimensionless characteristic parameter, 2, attects the dynamic wetting process and associated dynamic contact angle as well. However, the previous model suggested that the dynamic contact angle is dependent＇on the capillary number and static contact angle only. An experimental investigation was conducted to measure the dynamic wetting behavior of silicon oil moving over glass, aluminum and stainless steel surfaces. It concluded that when the value of 2 was selected as 0.07, 0.16 and 0.35 for glass, aluminum and stainless steel, respectively, the experimental results were in good accordance with the prediction of the model. Furthermore, the comparison of the model with Strom＇s experimental data showed that 2 is independent on the species of liquids. Apparently, 2 should be interpreted as the effect of the solid surface properties on the dynamic wetting process.Meanwhile, it is found in the present experiment that the Hoffman-Voinov-Tanner law, which is valid at very low capillary number （Ca 〈〈 1 or 80〈 10°） recommend by Cazabat, still holds for higher contact angles, even up to 70°-80°. This is explained by （he present model very well.     

INTERPRETATION OF FLOW NONUNIFORMITY AND HYSTERESIS WITH A CAPILLARY ARRAY MODEL

A novel capillary array model is proposed to shed light on the development of themaldistribution of cocurrent downward gas-liquid flow and the hysteretic performance behavior in apacked column.The model is based on the principle of nonequilibrium thermodynamics and incombination with lateral random walk of elemental liquid rivulets.The liquid distribution over aone-dimensional array of capillaries is simulated and the basic features of gas-liquid flow in packedbeds are demonstrated.With proper correspondence of hysteresis branches with nonuniformity of flowdistribution assumed,the experimentally observed hysteresis in pressure drop,liquid holdup and masstransfer rate can be qualitatively simulated.Strenuous efforts are still required for further developingthis model into a predictive tool for the evaluation of performance of packed-bed type devices.     

Experimental and Numerical Investigations of Single Drop Mass Transfer in Solvent Extraction Systems with Resistance in Both Phases

Numerical simulation of transient mass transfer to a single drop controlled by the internal resistance or by the resistance in both phases was mathematically formulated and simulated in a boundary-fitted orthogonal coordinate system. The simulated results on the transient mass transfer dominated by the internal resistance are in good agreement with the Newman and Kronig-Brink models for drops with low Reynolds number. When the drop Reynolds number is up to 200, the mass transfer coefficient from numerical simulation is very low as compared with the Handlos-Baron model. The cases with mass transfer resistance residing in both the continuous and drop phases were simulated successfully and compared with the experimental data in three extraction systems recommended by European Confederation of Chemical Engineering (EFCE). For single drops with Re < 200, the numerically predicted values of the extraction fraction and overall mass transfer coefficient are in reasonable coincidence with the experimental data. I     

散相液滴在搅拌萃取塔内的停留时间分布

A resident time model is proposed to evaluate the performance of agitated extraction columns. In this model, the resident time of dispersed drops is simulated with the discrete phase modeling, where the continuous phase and the dispersed phase （drops） are described by the single-phase Navier-Stokes （turbulence） model and Lagrangian model, respectively. The interaction of dispersed phase and continuous phase is neglected for the low concentration of drop in the cases studied. The statistical parameters of drops （the average resident time and standard deviation） under different operation conditions are computed for four columns. The relation of the above statistical parameters with the performance of columns is discussed and the criterions for an optimal compartment are outlined. Our results indicate that the resident time model is useful to evaluate the performance and optimize the design of extraction columns.     

基于单气泡非稳膜机理的相际传质模型

A gas-liquid mass transfer model based on an unsteady state film mechanism applied to a single bubble is presented. The mathematical model was solved using Laplace transform to obtain an analytical solution of concentration profile in terms of the radial position r and time t. The dynamic mass transfer flux was deduced and the influence of the bubble size was also determined. A mathematical method for deducing the average mass transfer flux directly from the Laplace transformed concentration is presented. Its accuracy is verified by comparing the numerical results with those from the indirect method. The influences of the model parameters, namely, the bubble size R, liquid film thickness δ, and the surface renewal constant s on the average mass transfer flux were investigated. The proposed model is useful for a better understanding of the mass transfer mechanism and an optimum design of gas-liquid contact equipment.     

萃取体系滴内和两相阻力控制的单液滴传质实验和数值模拟研究

Numerical simulation of transient mass transfer to a single drop controlled by the internal resistance or by the resistance in both phases was mathematically formulated and simulated in a boundary-fitted orthogonal coordinate system. The simulated results on the transient mass transfer dominated by the internal resistance are in good agreement with the Newman and Kronig-Brink models for drops with low Reynolds number. When the drop Reynolds number is up to 200, the mass transfer coefficient from numerical simulation is very low as compared with the Handlos-Baron model. The cases with mass transfer resistance residing in both the continuous and drop phases were simulated successfully and compared with the experimental data in three extraction systems recommended by European Confederation of Chemical Engineering (EFCE). For single drops with Re ＜ 200, the numerically predicted values of the extraction fraction and overall mass transfer coefficient are in reasonable coincidence with the experimental data. It is concluded that the numerical simulation can be resorted in some cases of solvent extraction for conducting numerical experiments and parametric study. Nevertheless, for better resolution as higher Reynolds number drops are simulated, more sophisticated techniques should be developed and incorporated to deal with the large deformation and transient shape oscillation as well as possible Marangoni effect.     

液滴凝并端效应对单液滴传质测定的影响及消除

For the mass transfer to single drops during the stage of steady buoyancy-driven motion, experimental measurement is complicated with the terminal effect of additional mass transfer during drop formation and coalescence at the drop collector. Analysis reveals that consistent operating conditions and experimental procedure are of critical significance for minimizing the terminal effect of drop coalescence on the accuracy of mass transfer The novel design of a totally-closed extraction column is proposed for this purpose, which guarantees that the volumetric rate of drop phase injection is exactly equal to that of withdrawal of drops. Tests in two extraction systems demonstrate that the experimental repeatability is improved greatly and the terminal effect of mass transfer during drop coalescence is brought well under control.     

Theoretical and experimental analysis of droplet evaporation on solid surfaces

The evaporation of sessile drops is central to a number of important processes, including printing, washing and coating. In this paper, the evaporation of water sessile droplets on hydrophobised silicon wafers and Teflon was analysed from theoretical and experimental perspectives. The contact angle, volume and base radius of the water droplets as a function of time were determined using tensiometry. The theoretical analysis showed different evaporative flux phenomena for acute and obtuse contact angles. The non-linear evolution of residual droplet volume, contact angle and base radius are solved and depend on the hydrophobicity of the solid surface and droplet dimension. Good agreement between the theoretical and experimental results was observed during pinning and depinning stages of evaporation. It was shown that the surface roughness, hydrophobicity and the contact angle hysteresis significantly influenced the evaporation of sessile drops and need to be considered when quantifying the evaporation process.     

Determination of the peripheral contact angle of sessile drops on solids from the rate of evaporation

A method was developed to determine the initial peripheral contact angle of sessile drops on solid surfaces from the rate of drop evaporation for the case where ₁ < 90°. The constant drop contact radius, the initial weight, and the weight decrease with time should be measured at the ambient temperature for this purpose. When water drops are considered, the relative humidity should also be known. The peripheral contact angle so obtained is regarded as the average of all the various contact angles existing along the circumference of the drop. Thus, each determination yields an average result not unduly influenced by irregularities at a given point on the surface. In addition, the error in personal judgment involved in drawing the tangent to the curved drop profile at the point of contact can be eliminated. The application of this method requires the use of the product of the vapor diffusion coefficient with the vapor pressure at the drop surface temperature. This product can be found experimentally by following the evaporation of fully spherical liquid drops.     

Contact Angle Hysteresis on Polymer Surfaces: An Experimental Study

In order to characterize a solid surface, the commonly used approach is to measure the advancing and receding contact angles, i.e., the contact angle hysteresis. However, often an estimate of the average wettability of the solid–liquid system is required, which involves both the dry and wetted states of the surface. In this work, we measured advancing and receding contact angles on six polymer surfaces (polystyrene, poly(ethylene terephthalate), poly(methyl methacrylate), polycarbonate, unplasticized poly(vinyl chloride), and poly(tetrafluoroethylene)) with water, ethylene glycol and formamide using the sessile drop and captive bubble methods. We observed a general disagreement between these two methods in the advancing and receding contact angles values and the average contact angle determined separately by each method, although the contact angle hysteresis range mostly agreed. Surface mobility, swelling or liquid penetration might explain this behaviour. However, we found that the 'cross' averages of the advancing and receding angles coincided. This finding suggests that the cross-averaged angle might be a meaningful contact angle for polymer–liquid systems. Hence, we recommend using both the sessile drop and captive bubble methods.     

Tunability of the Adhesion of Water Drops on a Superhydrophobic Paper Surface via Selective Plasma Etching

We report the fabrication of a sticky superhydrophobic paper surface with extremely high contact angle hysteresis: advancing contact angle ～150° (superhydrophobic) and receding contact angle ～10° (superhydrophilic). In addition, we report the controlled tunability of the contact angle hysteresis from 149.8 ± 5.8° to 3.5 ± 1.1°, while maintaining superhydrophobicity, as defined through an advancing contact angle above 150°. The hysteresis was tuned through the controlled fabrication of nano-scale features on the paper fibers via selective plasma etching. The variations in contact angle hysteresis are attributed to a transition of the liquid–surface interaction from a Wenzel state to a Cassie state on the nano-scale, while maintaining a Cassie state on the micro-scale. Superhydrophobic cellulosic surfaces with tunable stickiness or adhesion have potential applications in the control of aqueous drop mobility and the transfer of drops on inexpensive, renewable substrates.     

Interfacial tension from height and diameter of a single sessile drop or captive bubble

The silhouette of a sessile drop submerged in a transparent bulk phase appears to possess a contact angle of 180° with a plane solid support, when the drop is separated from the solid surface by a thin film of surrounding fluid. A computer-aided analysis of the generalized sessile drop form leads to an explicit equation for interfacial tension dependent only on drop height (from apex to solid support) and the magnitude of the drop equatorial diameter. The equation is valid for a wide range of physically realizable drops. Measurements of drop profile coordinates or the location of the drop equator are not required for the use of the method, leading to improvements in accuracy relative to current practice.     

Equilibrium shape and contact angle of sessile drops of different volumes—Computation by SPH and its further improvement by DI

Equilibrium shapes of sessile liquid drops over horizontal substrates are modeled using smoothed particle hydrodynamics (SPH). The model can predict the variations of shape and contact angle of drops as a function of drop volume. In the model, a scheme of repositioning the particle at the triple line has been incorporated to attain the in situ contact angle. The simulations show a reasonable match with available analytical results. However, some mismatch of the drop shape near the three-phase contact line is observed. To improve the predictability, combined diffused interface smoothed particle hydrodynamics model (Das and Das, 2009b) is employed. The developed hybrid simulations improve the prediction. Estimated drop shapes and contact angle agree with experimental data reasonably well over a wide range of fluid properties and drop volume. The technique establishes the suitability of a particle-based hydrodynamic simulation for the modeling of complex interfaces and three-phase contact lines.     

Microsphere tensiometry to measure advancing and receding contact angles on individual particles

In this paper, a method to measure the advancing and receding contact angles on individual colloidal spheres is described. For this purpose, the microspheres were attached to atomic force microscope cantilevers. Then the distance to which the microsphere jumps into its equilibrium position at the air-liquid interface of a drop or an air bubble was measured. From these distances the contact angles were calculated. To test the method, experiments were done with silanized silica spheres (4.1 μm in diameter). From the experiments with drops, an advancing contact angle of 101 ± 4° was determined. A receding contact angle of 101 ± 2° was calculated from the jump-in distance into a bubble. Both experimental techniques gave the same contact angle. In contrast, on similarly prepared planar silica surfaces, a clear hysteresis was measured with the sessile drop method; contact angles of 104.5 ± 1° and 93.8 ± 1° were determined for the advancing and receding contact angles, respectively.     

Anisotropic Wetting of Liquids on Finely Grooved Surfaces

A photolithographically-prepared, parallel-grooved surface on silica has been employed as a model to study the influence of roughness on the spreading equilibrium of liquid drops. The equations generated by Oliver, Huh and Mason for cylindrically shaped drops were extended to account for wetting by liquid crystals. The observed drop shapes were dependent upon surface roughness. The equilibrium contact angles on a smooth surface can be calculated from the roughness, contact angles both parallel and perpendicular to the grooves, and the drop shape. Reasonably good agreement with experimental contact angles was obtained.     

Sessile drops: Do they really stand on solid surfaces?

Bangham and Razouk [1] have described the decrease in free energy at a solid-vapor interface on adsorption of vapor to the solid from zero pressure (vacuum) to any pressure up to p^o, the saturation vapor pressure. Derjaguin and Zorin (DZ) [2] have proposed adsorption isotherms of vapor to solid surface which cross the p^o line and then return to p^o to form sessile drops. Adamson and coworkers [3] have presented a theory to generate a DZ type isotherm and point out that the isotherm implies formation of an autophobic layer on all solid surfaces that support sessile drops. Schrader and Weiss [4] have proposed an adsorption isotherm for sessile drop formation which crosses the p^o line but does not return to p^o on formation of the sessile drop. This last approach does not require ubiquitous formation of autophobic layers on solid surfaces in sessile drop systems. Free energy isotherms based on the last approach are presented to describe film formation (Type 1 free energy isotherm), sessile drop formation on low-energy surfaces (Type 2), and sessile drop formation on autophobic layers (Type 3). The approach also enablcs derivation of a new equation for the vapor pressure of sessile drops subject to contact angle hysteresis.