Effect Of Contact Angle Hysteresis Research Articles

On liquid bridge adhesion to fibrous surfaces under normal and shear forces

This paper reports on adhesion forces between a liquid bridge and two parallel plates coated with electrospun fibers experimentally and computationally. For the experiments, a DI water droplet containing 15% glycerol was placed on one of the plates and compressed, stretched, or sheared using the other plate. The assembly was mounted on a sensitive scale to measure the forces applied to the plates during the experiment. For the computational part, an efficient modeling approach was developed to predict the 3-D shape of the liquid bridge and to calculate its resistance to normal and tangential forces in the presence of contact angle hysteresis effects, using the Surface Evolver finite element code.Despite the inherent non-uniformity of the fibrous surfaces used in the experiments and the simplifying assumptions considered for the simulations, reasonable agreement was observed between the measurements and their computational counterparts. In addition, the hysteresis behavior of a liquid bridge during a compression–stretching process is mapped in an energy or force diagram versus spacing between the plates using radius-constant and contact-angle-constant lines describing the triple contact-line. It was also observed that a liquid bridge between two electrospun coatings tends to maintain its symmetricity despite the anisotropic roughness of the coatings, due perhaps to the minuteness of the electrospun fibers relative to the size of the liquid bridge.

On a two-point boundary value problem for the 2-D Navier-Stokes equations arising from capillary effect

In this article, we consider the motion of a liquid surface between two parallel surfaces. Both surfaces are non-ideal, and hence, subject to contact angle hysteresis effect. Due to this effect, the angle of contact between a capillary surface and a solid surface takes values in a closed interval. Furthermore, the evolution of the contact angle as a function of the contact area exhibits hysteresis. We study the two-point boundary value problem in time whereby a liquid surface with one contact angle at t = 0 is deformed to another with a different contact angle at t = ∞ while the volume remains constant, with the goal of determining the energy loss due to viscosity. The fluid flow is modeled by the Navier-Stokes equations, while the Young-Laplace equation models the initial and final capillary surfaces. It is well-known even for ordinary differential equations that two-point boundary value problems may not have solutions. We show existence of classical solutions that are non-unique, develop an algorithm for their computation, and prove convergence for initial and final surfaces that lie in a certain set. Finally, we compute the energy lost due to viscous friction by the central solution of the two-point boundary value problem.

Hydrodynamics and mechanism of hydrophobic foam column tray: Contact angle hysteresis effect

AbstractInterfacial wettability adjustment is a new method for intensifying vapor–liquid mass transfer process. Contact angle effect has been well investigated but not complete due to interfacial wettability consisting of both static behavior (contact angle) and dynamic behavior (contact angle hysteresis). Here, methods of adjusting contact angle hysteresis (CAH) were proposed, and then, the CAH effect on the hydrodynamics was investigated. A multiscale analysis of CAH effect, from interfacial force and wettability to single‐bubble and gas–liquid two‐phase flow inside the foam to bubble swarm hydrodynamics, was conducted, and thus, the hydrodynamic performance criteria were derived. The interfaces had similar contact angles, whereas a significant difference in the CAH was prepared by using the developed sol dip‐coating and spray coating methods. Subsequent experiments revealed that lower CAH can decrease the pressure drop, homogenize the gas distribution, and increase the weeping rate, which are consistent with the derived criteria.

Lattice Boltzmann method for contact-line motion of binary fluids with high density ratio.

Within the phase-field framework, we present an accurate and robust lattice Boltzmann (LB) method for simulating contact-line motion of immiscible binary fluids on the solid substrate. The most striking advantage of this method lies in that it enables us to handle two-phase flows with mass conservation and a high density contrast of 1000, which is often unavailable in the existing multiphase LB models. To simulate binary fluid flows, the present method utilizes two LB evolution equations, which are respectively used to solve the conservative Allen-Cahn equation for interface capturing, and the incompressible Navier-Stokes equations for hydrodynamic properties. Besides, to account for the substrate wettability, two popular contact angle models including the cubic surface-energy model and the geometrical one are incorporated into the present method, and their performances are numerically evaluated over a wide range of contact angles. The contact-angle hysteresis effect, which is inherent to a rough or chemically inhomogeneous substrate, is also introduced in the present LB approach through the strategy proposed by Ding and Spelt [J. Fluid Mech. 599, 341 (2008)10.1017/S0022112008000190]. The present method is first validated by simulating droplet spreading and capillary intrusion on the ideal or smooth pipes. It is found that the cubic surface-energy and geometrical wetting schemes both offer considerable accuracy for predicting a static contact angle within its middle region, while the former is more stable at extremely small contact angles. Besides, it is shown that the geometrical wetting scheme enables us to obtain better accuracy for predicting dynamic contact points in capillary pipe. Then we use the present LB method to simulate the droplet shearing processes on a nonideal substrate with contact angle hysteresis. The geometrical wetting model is found to be capable of reproducing four typical motion modes of contact line, while the surface-energy wetting scheme fails to predict the hysteresis behaviors in some cases. At last, a complex contact-line dynamic problem of three-dimensional microscale droplet impact on a wettable solid is simulated, and it is found that the numerical results for droplet shapes agree well with the experimental data.

Internal flow patterns of a droplet pinned to the hydrophobic surfaces of a confined microchannel using micro-PIV and VOF simulations

We present both experimental results and numerical simulations of the fluid dynamics of a droplet pinned to the hydrophobic surfaces of a confined microfluidic channel, as a result of contact angle hysteresis. Internal circulations in the droplet are observed and quantified using micro-particle image velocimetry (μPIV). As the channel inlet velocity increases, the difference between the contact angles at the front and the rear part of the contact line is also increased, while the equilibrium Young’s contact angle remains essentially constant. Numerical simulations based on a Volume-Of-Fluid (VOF) method combined with a Laplacian filter for the phase function are also performed to consider contact angle hysteresis effects. Major quantities from the simulations, including the velocity distribution inside the droplet, the contact angles, and the vortex structures, show good agreement with experimental results. In addition, force balance models of the pinned droplet have been built for various inlet conditions, indicating that the adhesion force at the side walls and the blockage of the droplet have significant effects on the liquid motion within the droplet. The recirculation flow rate inside the droplet is found to vary linearly with the Capillary number.

Asymmetric coalescence-induced droplet jumping on hydrophobic fibers

Coalescence of two unequal-sized droplets on hydrophobic fibers is more common in nature. To elucidate the mechanism of merged droplets jumping on hydrophobic fibers, a new theoretical model for two unequal-sized droplets coalescence was first developed, which considered the effects of contact angle hysteresis and droplet-fiber contact area. Then, the influences of Ohnesorge number (Oh), droplet radius ratio (n), droplet-fiber radius ratio (k) and contact angle (CA) on the dimensionless jumping velocity (U/vci) were studied theoretically. The value of U/vci increased with the increase of n, k and CA but decreased as Oh increased. The dimensionless jumping velocity for two unequal-sized droplets coalescence on hydrophobic fibers still followed the capillary-inertial scaling law with U/vci ≈ 0.45 when n = 0.5. In addition, the effects of k and CA on the critical jumping radius ratio were the critical jumping radius ratio being reduced as k and CA increased, and the minimal critical jumping radius ratio was approximately 0.1. These findings will help to characterize coalescence-induced droplet jumping on hydrophobic fibers.

Effect of wall contact angle and carrier phase velocity on the flow physics of gas–liquid Taylor flows inside microchannels

This paper investigates numerically the characteristics of gas–liquid sliding Taylor flow in a two-dimensional (2D) T-junction rectangular microchannel having both inlets perpendicular to the horizontal mixing chamber. The governing equations describing the flow are discretized and solved by employing finite volume method based computational tool ANSYS Fluent 15.0. The volume of fluid (VOF) multiphase method is used for capturing the gas–liquid interface. A dynamic mesh, based on the adaption of gradients of volume fraction, is used for grid refinement to tackle sharp gradients during the two-phase flow. A focus is laid on exploring the influence of wall contact angle on the flow physics of sliding Taylor flows inside the microchannel in which the inlet liquid velocity is varied in the range 0.05 < uL < 0.25 m/s) (or inlet Reynolds number, 4.97 < Re < 248.75), and the wall contact angle is varied in the range 0° < Θo < 170°. The effect of contact angle hysteresis on the overall pressure drop, bubble and liquid slug lengths, and the dispersed phase volume fraction is reported. The bubble length and the overall pressure drop obtained from the simulations are compared with the benchmark correlations available in the literature. It is found that the trends of the variation of bubble length with liquid velocity are in reasonable match with the correlations. In addition, the pressure drop and slug length decrease in hydrophilic channels unlike in hydrophobic channels, which signifies the importance of contact angle in two-phase sliding Taylor flows.

Hydrodynamic analysis of the advancing dynamic contact angle in microtube

We explored the hydrodynamic features of dynamic wetting both theoretically and experimentally. We studied the triple-line motions of glycerol-water solutions of various viscosities (85-456 mPa·s) in microglass tubes (300, 500 and 1000 μm in diameter). First, dynamic (advancing) contact angles were measured and compared with those of a well-known hydrodynamic model (O.V. Voinov, Hydrodynamics of Wetting, Fluid Dynamics (1976)). Second, the internal flow structures near moving menisci were visualized using micro-particle image velocimetry (μ-PIV). Several differences in flow shape (compared to those predicted by theory) were observed. Ultimately, we present a new method by which dynamic contact angles may be predicted, derived from analysis of wall shearing stress at the moving contact line to reflect on the liquid-solid interaction effect. Our analysis has the advantage of incorporating the effect of contact angle hysteresis on the dynamic contact angle. The modified approach yielded data in good agreement with our experimental results and other open-literature data. We thus fundamentally explored the hydrodynamic aspects of dynamic wetting.

Thick drops climbing uphill on an oscillating substrate

Experiments have shown that a liquid droplet on an inclined plane can be made to move uphill by sufficiently strong, vertical oscillations (Brunet et al., Phys. Rev. Lett., vol. 99, 2007, 144501). In this paper, we study a two-dimensional, inviscid, irrotational model of this flow, with the velocity of the contact lines a function of contact angle. We use asymptotic analysis to show that, for forcing of sufficiently small amplitude, the motion of the droplet can be separated into an odd and an even mode, and that the weakly nonlinear interaction between these modes determines whether the droplet climbs up or slides down the plane, consistent with earlier work in the limit of small contact angles (Benilov and Billingham, J. Fluid Mech. vol. 674, 2011, pp. 93–119). In this weakly nonlinear limit, we find that, as the static contact angle approaches $\unicode[STIX]{x03C0}$ (the non-wetting limit), the rise velocity of the droplet (specifically the velocity of the droplet averaged over one period of the motion) becomes a highly oscillatory function of static contact angle due to a high frequency mode that is excited by the forcing. We also solve the full nonlinear moving boundary problem numerically using a boundary integral method. We use this to study the effect of contact angle hysteresis, which we find can increase the rise velocity of the droplet, provided that it is not so large as to completely fix the contact lines. We also study a time-dependent modification of the contact line law in an attempt to reproduce the unsteady contact line dynamics observed in experiments, where the apparent contact angle is not a single-valued function of contact line velocity. After adding lag into the contact line model, we find that the rise velocity of the droplet is significantly affected, and that larger rise velocities are possible.

Contact angle hysteresis effect on the thermocapillary migration of liquid droplets

Thermocapillary migration describes a phenomenon where a liquid droplet spreads from warm to cold regions due to the interfacial tension gradients. Since the contact angle hysteresis effect is involved during the migration process, we consider the hysteresis effect and rectify the theoretical model to predict the migration velocity on solid surfaces. By conducting migration experiments on surfaces with different magnitudes of the hysteresis effect, we verify the validity of the theoretical derivation. This study advances the understanding of the interfacial phenomenon of thermocapillary migration, moreover, offers an insight into the migration capacity of different materials and guides the design of key components associated with the thermal gradients.

Lattice Boltzmann modeling for the coalescence between a free droplet in gases and a sessile droplet on wettable substrate with contact angle hysteresis

The coalescence between a free droplet and a sessile droplet on wettable substrate is numerically studied. The axisymmetric lattice Boltzmann method for two-phase flows is used in modeling. Here the contact angle hysteresis (prescribed by advancing angle [Formula: see text] and receding angle [Formula: see text]) is taken into account. The effects of Ohnesorge number ( Oh), contact angle and its hysteresis, and the radius of the free droplet on the coalescence dynamics are investigated in detail. The Oh numbers ranging from 0.02 to 0.15 here makes the radius of the liquid bridge r and the time t follow power law. Also, Oh has remarkable impact on the development of capillary wave and on the amount of kinetic energy released from coalescence. It is found that the curve of the wetting radius varying with time includes several plateau stages, which is a typical characteristic for the effect of contact angle hysteresis. The larger window of contact angle hysteresis would result in smaller steady wetting radius after coalescence. Compared with the existence of contact angle hysteresis, the absence of contact angle hysteresis makes the droplets system release more kinetic energy during the coalescence but the released kinetic energy decays more rapidly and soon reduces to zero. Oppositely, if the contact angle hysteresis exists, the released kinetic energy would oscillate for a period of time before approaching zero.

Experimental study on effect of surface vibration on micro textured surfaces with hydrophobic and hydrophilic materials

Artificial hydrophobic surfaces have been studied in the last ten years in an effort to understand the effects of structured micro- and nano-scale features on droplet motion and self-cleaning mechanisms. Among these structured surfaces, micro-textured surfaces consisting of a combination of hydrophilic and hydrophobic materials have been designed, fabricated and characterized to understand how surface properties and morphology affect enhanced self-cleaning mechanisms. However, use of micro textured surfaces leads to a strong pinning effect that takes place between the droplets and the hydrophobic-hydrophilic edge, leading to a significant contact angle hysteresis effect. This research study focuses on the effects of surface vibrations on droplet shedding at different inclined angles on micro-textured surfaces. Surface vibration and shedding processes were experimentally characterized using a high speed imaging system. Experimental results show that droplets under the influence of surface vibration depict different contour morphologies when vibrating at different resonance frequencies. Moreover, droplet sliding angles can be reduced through surface vibration when the proper combination of droplet size and surface morphology is prescribed.

Effects of Shaft Surface Wettability on the Friction of Oil-Impregnated Sintered Bearings -Effect of Contact Angle Hysteresis-

Effects of Shaft Surface Wettability on the Friction of Oil-Impregnated Sintered Bearings -Effect of Contact Angle Hysteresis-

Lattice Boltzmann simulation of coalescence of multiple droplets on nonideal surfaces

The interaction dynamics of droplets on a solid surface is a fundamental problem that is important to a wide variety of industrial applications, such as inkjet printing. Most previous research has focused on a single droplet and little research has been reported on the dynamics of multiple-droplet interactions on surfaces. Recently, Zhou et al. [W. Zhou, D. Loney, A. G. Fedorov, F. L. Degertekin, and D. W. Rosen, Lattice Boltzmann simulations of multiple-droplet interaction dynamics, Phys. Rev. E 89, 033311 (2014)] reported an efficient numerical solver based on the lattice Boltzmann method (LBM) that enabled the simulation of the multiple-droplet interaction dynamics on an ideal surface (i.e., smooth and homogeneous). In order to predict the interaction dynamics in the real world, it is necessary to take into consideration the contact angle hysteresis phenomenon on a nonideal surface, which is possibly caused by the surface roughness and chemical inhomogeneity of the surface. In this paper a dynamic contact angle boundary condition is developed to take into account the contact angle hysteresis effect based on the previously reported LBM. The improved LBM is validated with experimental data from the literature. The influence of the droplet impact conditions (e.g., fluid properties and impingement velocity), droplet spacing, and surface conditions on the two-droplet interaction dynamics is investigated with the validated LBM. Interesting phenomena are observed and discussed. The interaction of a line of six droplets on a nonideal surface is simulated to demonstrate the powerful capability of the developed numerical solver in simulating the multiple-droplet interaction dynamics in the real world.

Effect of contact-angle hysteresis on the pressure drop under slug flow conditions in minichannels and microchannels

The effect of the difference between the advancing and receding contact angles (the phenomenon known as contact-angle hysteresis or wetting hysteresis) on the pressure drop in capillaries (minichannels and microchannels) for liquid–liquid and gas–liquid systems is analyzed. It is shown that, in microchannels, for cases of a continuous medium that both does and does not wet the walls, the pressure drop has a positive sign. A relationship is proposed for estimating the dynamic receding contact angle, which is the monotone extension of a similar relationship for the advancing contact angle. The region of the allowable values of the capillary numbers for these equations is found. The fraction of the pressure drop in capillaries due to contact-angle hysteresis in the total pressure drop is estimated.

Effect of contact angle hysteresis on breakage of a liquid bridge

In this paper, the importance of considering contact angle hysteresis (CAH) during the process of stretching and breaking a liquid bridge between two solid surfaces is addressed. We clearly show that due to the pinning of contact line at the end of the stretching stage, the contact angle between liquid bridge and surfaces cannot be simply assumed to have a constant value (e.g. receding contact angle, θ r ). Simulation results for stretching a liquid bridge with and without CAH, showed that the contact line pinning can lead to breakage at a larger surface separation and smaller value of pull-off force (F p ). A systematic study about the effect of CAH and contact line pinning on the value of F p is provided. It is found that when one of the surfaces has a θ r larger than 90∘, F p decreases with the increase of θ r on either surface delimiting the bridge. For the cases where θ r of both surfaces are smaller than 90∘, significantly smaller F p is seen when contact line pinning occurs on both surfaces, as compared to F p when contact line pinning occurs only on one surface. This smaller F p is caused by more curved profile and later breakage of liquid bridge.

Motion of an isolated liquid plug inside a capillary tube: effect of contact angle hysteresis

Dynamics of a single, small and isolated partially wetting liquid plug (of known length L and wettability), placed at rest inside a long, dry, circular capillary tube (D = 1.5 mm), and subsequently quasi-statically pushed from one end by applying air pressure, the other end being kept exposed to atmosphere, are reported. The air pressure first overcomes the ‘static’ friction manifested by the three-phase contact line at the advancing and receding menisci, and then, the plug motion gets initiated, eventually leading to a terminal velocity (Ca ~ 2.8 × 10−5), when pressure force balances net frictional resistance due to viscous and surface forces. It is seen that, under steady motion, the curvature profiles of the advancing and receding menisci of liquid plug, respectively, remain the same, independent of the plug length. Steady-state pressure drop is dominated by the contribution due to contact angle hysteresis, which is also independent of the plug length. Increasing the system wettability drastically decreased the contact angle hysteresis and the associated net pressure drop.

Droplets impact on textured surfaces: Mesoscopic simulation of spreading dynamics

Superhydrophobic surfaces have attracted much attention due to their excellent water-repellent property. In the present study, droplets in the ideal Cassie state were focused on, and a particle-based numerical method, many-body dissipative particle dynamics, was employed to explore the mechanism of droplets impact on textured surfaces. A solid–fluid interaction with three linear weight functions was used to generate different wettability and a simple but efficient method was introduced to compute the contact angle. The simulated results show that the static contact angle is in good agreement with the Cassie–Baxter formula for smaller ∅S and Fa, but more deviation will be produced for larger ∅S and Fa, and it is related to the fact that the Cassie–Baxter theory does not consider the contact angle hysteresis effect in their formula. Furthermore, high impact velocity can induce large contact angle hysteresis on textured surfaces with larger ∅S and Fa. The typical time-based evolutions of the spreading diameter were simulated, and they were analyzed from an energy transformation viewpoint. These results also show that the dynamical properties of droplet, such as rebounding or pinning, contact time and maximum spreading diameters, largely depend on the comprehensive effects of the material wettability, fraction of the pillars and impact velocities of the droplets.

A simple model for Taylor flow induced contact angle hysteresis and capillary pressure inside mini/micro-scale capillary tubes

Abstract A simple mathematical model is developed to describe the Taylor flow induced contact angle hysteresis and capillary pressure inside mini/micro-scale capillary tubes. The effect of contact angle hysteresis on the capillary pressure is taken into account. Results show that both of the equilibrium contact angle (ECA) and capillary number significantly affect the contact angle hysteresis and capillary pressure. The non-monotonic variations of contact angle hysteresis and capillary pressure as a function of ECA at different capillary number are observed and there exist maximum values for both of them. At a low capillary number (

Modeling the effects of contact angle hysteresis on the sliding of droplets down inclined surfaces

Contact angle hysteresis is an important phenomenon that occurs both in natural and industrial droplet spreading/sliding applications. As they slide, droplets adopt a different contact angle at the front and rear, the advancing and a receding contact angles, respectively. This work investigates the different stages involved in the motion of droplets down inclined surfaces in the lubrication approximation framework. A simplified hysteresis model is proposed, implemented, and tested. This model automatically locates the section of the contact line which is advancing and the section which is receding. This enables the application of different contact angles at the advancing and receding fronts and therefore takes into account contact angle hysteresis. For validation purposes, experiments of fluid droplet spreading/sliding on inclined surfaces have also been performed to measure the terminal sliding velocity. With the inclusion of contact angle hysteresis, simulation results are shown to be in much better agreement with the experimental ones. This paper also presents a simple model based on Newton’s second law which is shown to have reproduced remarkably well the steady and dynamic results if the shape of the droplets does not depart too much from a spherical cap configuration.