Effect Of Contact Angle Hysteresis Research Articles

Three-Dimensional Lattice Boltzmann Simulations for Droplet Impact and Freezing on Cold Surfaces with a Large Density Ratio

Droplet impact and freezing on solid surfaces are ubiquitous in many natural and engineering processes. Simulating the impacting-freezing process of a droplet is still challenging because it involves the complex multiphase flow and the liquid-solid phase change. This paper establishes a three-dimensional lattice Boltzmann model that considers the effects of contact angle hysteresis and volume expansion to simulate this complex process under realistic conditions. We adopt an enhanced cascaded lattice Boltzmann method to calculate the flow field and a multiple-relaxation-time scheme to solve the liquid-solid phase change model. In addition, a new contact angle model based on the pseudopotential multiphase lattice Boltzmann model is proposed to mimic the contact angle hysteresis. The simulations of droplet impact and freezing on both hydrophobic and hydrophilic surfaces with different surface temperatures and Weber numbers are conducted, and the temporal droplet profile and dimensionless contact length agree well with the experiments, which effectively validates the accuracy and robustness of the present model. Finally, the effects of surface temperatures ( 0 , − 15 , − 30 ∘ C ) and Weber numbers (4.4, 19.2, 40.0, 71.1) on droplet dynamics are also examined.

The effect of contact angle hysteresis on a droplet in a viscoelastic two-phase system

We investigate the dynamic behavior of a two-dimensional droplet adhering to a wall in Poiseuille flow at low Reynolds numbers, in a system where one of the phases is viscoelastic represented by a Giesekus model. The Cahn–Hilliard Phase-Field method is used to capture the interface between the two phases. The presence of polymeric molecules alters the viscoelastic drop's deformation over time, categorizing it into two stages before contact line depinning. In the first stage, the viscoelastic droplet deforms faster, while in the second stage, the Newtonian counterpart accelerates and its deformation outpaces the viscoelastic droplet. The deformation of viscoelastic drop is retarded significantly in the second stage with increasing Deborah number De. The viscous bending of viscoelastic drop is enhanced on the receding side for small De, but it is weakened by further increase in De. On the advancing side, the viscous bending is decreased monotonically for Ca < 0.25 with a non-monotonic behavior for Ca = 0.25. The non-monotonic behavior on the receding side is attributed to the emergence of outward pulling stresses in the vicinity of the receding contact line and the inception of strain-hardening at higher De, while the reduction in the viscous bending at the advancing side is the result of just strain-hardening. Finally, when the medium is viscoelastic, the viscoelasticity suppresses the droplet deformation on both receding and advancing sides, and this effect becomes more pronounced with increasing De. Increasing the Giesekus mobility parameter enhances the weakening effect of viscous bending on the advancing side.

Effects of contact angle hysteresis on frosting and defrosting characteristics on vertical superhydrophobic surfaces

Contact angle hysteresis has a significant influence on dynamic frosting and defrosting of vertical superhydrophobic surface, however, the characteristics under the effect of contact angle hysteresis have not been clarified. Therefore, superhydrophobic surfaces with similar contact angles but different contact angle hysteresis were prepared in this paper, and visualization experiment was carried out to discover the effects of contact angle hysteresis on frosting and defrosting characteristics of vertical superhydrophobic surface. Experimental results show that the bounce behavior, size, distribution density and freezing time of condensate droplets are obviously different in the early stage of frosting, and reducing the hysteresis of superhydrophobic surface reduces the distribution of condensate droplets and effectively delay droplet freezing. The anti-frosting performance of the superhydrophobic surface is improved with the decrease of contact angle hysteresis. The frost layer thickness of the surface with the smallest contact angle hysteresis is 50% lower than that of the surface with the smallest. The frost layer peels off from the superhydrophobic surface with smallest contact angle hysteresis at the beginning of defrosting and falls away under the action of gravity. This can effectively improve the defrosting efficiency by reducing defrosting time and retained defrosting water.

Effect of contact angle hysteresis on measuring matric suction in unsaturated sandy soil

The contact angle plays an important role in matric suction of unsaturated soils, but few studies consider the effect of contact angle hysteresis on matric suction. In this paper, taking sandy soil as an example, the influence of contact angle hysteresis on the suction of unsaturated soil matric is studied by soil particle model calculation and experimental method. The results show under the same water content condition, the smaller the contact angle is, the larger the matric suction is and the phenomenon of water repellency appears. Under the low water content of unsaturated soil, when the contact angle is less than 90°, it will also produce water repulsion phenomenon, which is different from the hydrophilic characteristics of the contact angle is less than 90° in the capillary law. When the water content is the same, with the increase of contact angle, matric suction will decrease. With the increase of water content, matric suction is not affected by soil contact angle. In the process of dehumidification, the apparent contact angle of the sandy soil with the same water content less than receding contact Angle; there is a difference in matric suction between continuous measurement method and discontinuous measurement method, and continuous measurement’ matric suction greater than discontinuous measurement’ matric suction. This study provides some theoretical basis and reference for the study of matric suction of unsaturated soil.

Super gas wet and gas wet rock surface: State of the art evaluation through contact angle analysis

Recently, super gas wet and gas wet surfaces have been extensively attended in petroleum industry, as supported by the increasing number of publications in the last decade related to wettability alteration in gas condensate reservoirs. In many cases, contact angle measurement has been employed to assess the wettability alteration. Even though contact angle measurement seems to be a straightforward approach, there exist many misuses of this technique and consequently misinterpretation of the corresponding results. In this regard, a critical inspection of the most recent updated concepts and the intervening parameters in the contact angle based wettability evaluation of liquid-solid-gas systems could aid to provide some remediation to alleviate this problem. To this end, this work presents a survey on the accurate terms and rigorous protocols based on the community of surface science and chemistry. As a preliminary step, advancing, receding, static, and the most stable contact angle terminology are defined. The study is followed by the definition of the contact angle hysteresis effect. The application of surface free energy in the selection of the best gas wet agent is then analyzed. Afterward, the impact of the size-dependent behavior of drop on contact angle is discussed. Finally, a sessile drop experiment is explained to achieve the defined parameters. For future contributions to petroleum industry journals, like this journal, this work could offer an easy use of the conceptual framework for analyzing the results and comparative evaluations in chemical wettability modifier agents.

Coalescence-induced jumping of droplets from superhydrophobic surfaces—The effect of contact-angle hysteresis

Droplets coalesce and jump from superhydrophobic surfaces, a result that stems from the dominance of capillary and inertial forces and the presence of high contact angles. This phenomenon has been a subject of intensive numerical research mostly for cases when the degree of hydrophobicity is described by a single contact-angle value (a static contact angle). The introduction of various degrees of contact-angle hysteresis complicates the numerical modeling of the jumping process due to the sensitivity of the results to the effective value of the contact angle. We have developed and validated a comprehensive volume-of-fluid–immersed boundary numerical framework that accounts for the effect of hysteresis by focusing on the representation of actual (i.e., effective) values of contact angles. By comparing the behavior of jumping droplets on superhydrophobic surfaces with several degrees of hysteresis (up to 15°), we quantified the influence of hysteresis on the jumping process and identified various stages of the merged droplet's detachment and re-attachment to the surface. The latter phenomena were observed in all our simulations with droplets of different initial radii. In all the cases with hysteresis, the merged droplet eventually jumps, but we point out the decrease in the jumping velocity as compared to cases with only a static contact angle imposed. Finally, by using the Kistler dynamic contact-angle model, we demonstrate and quantify the importance of accurately capturing the dynamic receding contact angle when droplets jump from superhydrophobic surfaces with various degrees of hysteresis.

Discontinuous dewetting dynamics of highly viscous droplets on chemically heterogeneous substrates

HypothesisDroplet spreading on heterogeneous (chemical/structural) surfaces has revealed local disturbances that affect the advancing contact line. With droplet dewetting being less studied, we hypothesize that a receding droplet can be perturbed by localized heterogeneity which leads to irregular and discontinuous dewetting of the substrate. ExperimentsThe sessile drop method was used to study droplet dewetting at a wettability boundary. One-half of a hydrophilic surface was hydrophobically modified with either i) methyloctyldichlorosilane or ii) clustered macromolecules. A Lattice Boltzmann method (LBM) simulation was also developed to determine the effect of contact angle hysteresis and boundary conditions on the droplet dynamics. FindingsThe two surface treatments were optimized to produce comparable water wetting characteristics. With a negative Gibbs free energy on the hydrophilic-half, the oil droplet receded to the hydrophobic-half. On the silanized surface, the droplet was pinned and the resultant droplet shape was a distorted spherical cap, having receded uniformly on the unmodified surface. Modifying the surface with clustered macromolecules, the droplet receded slightly to form a spherical cap. However, droplet recession was non-uniform and daughter droplets formed near the wettability boundary. The LBM simulation revealed that daughter droplets formed when θR > 164°, with the final droplet shape accurately described by imposing a diffuse wettability boundary condition.

Effect of Contact Angle Hysteresis on Evaporation Dynamics of a Sessile Drop on a Heated Surface

Contact angle hysteresis (CAH) is a significant factor affecting the drop motion on solid substrates. A model of CAH is introduced to explore the influence of CAH on the dynamics of a sessile drop on a uniformly heated surface, and a two-dimensional evolution equation of the drop thickness is established using the lubrication approximation and Navier slip boundary conditions. A numerical simulation is performed to examine the dynamic behaviors of an evaporating drop, and the drop profile, contact angle, contact line, and moving speed are investigated. Simulated results indicate that the drop evolution process involves drop spreading, pinning, and depinning of the contact line. In the drop spreading stage, when the hysteresis angle increases, the spreading period is shortened, and the spreading radius and spreading speed are reduced; in contrast, the pinning period is raised, and the mass of the drop is apparently reduced with increasing hysteresis angle. In the depinning stage, the CAH declines the contact angle, and a flatter pattern is evolved, thereby improving the heat transfer performance, promoting drop evaporation, and shortening the depinning time. The presence of CAH can speed up the drying of the drop, and the large hysteresis angle leads to faster evaporation. Regulating the CAH is an effective way to manipulate the motion of the contact line for an evaporating drop.

The role of shadowed droplets in condensation heat transfer

Dropwise condensation (DWC) is a phenomenon of common occurrence and significant utility in nature and technology. In energy applications, sustenance of DWC and avoidance of transition to film formation is directly related to efficient heat removal, ensuring high performance of related devices and processes. The efficiency of heat transfer in DWC depends on the heat transfer rates of individual droplets and the droplet size distribution. While the former can be summarily captured in engineering analysis through thermal resistance modeling, the theoretical analysis of the droplet size distribution involves assumptions often oversimplifying the complexity of droplet interactions, especially in the important sub–10 μm regime. Here, a modeling framework based on the thermal resistance approach is coupled with a dynamic model of droplet interactions: Droplet growth, coalescence, jumping, and removal of condensate due to gravity are all present during the unfolding of the phenomenon to accurately predict the droplet size distribution. The motivation is condensation experiments on superhydrophobic surfaces, namely rough aluminum substrates with a hydrophobic coating. Through the “interaction” of computations with measurements, the experimental findings are explained and critical parameters for condensation heat transfer on superhydrophobic surfaces are illuminated. Although larger droplets can be easily observed in experiments, it is shown that large droplets do not significantly affect heat transfer after reaching such state of growth. Instead, it is the small (with radius < 10 μm) and what we term “shadowed” droplets, i.e., the droplets grown in the shadow of the vertical projection area of the larger droplets, that play an important role in the heat transfer process. Due to the growth of these droplets and their concomitant shadowed coalescence and ensuing re-nucleation, the shift in the droplet size distribution towards smaller sizes is significant-enough to render the heat transfer rate rather insensitive to the presence of large droplets. In this regime, the effect of contact angle hysteresis on heat transfer is not crucial. Through the comparison with measurements, the dominant role of the density of nucleation sites on heat transfer is revealed and an estimation of the density of sites (∼105 mm−2) as a function of subcooling is extracted. Finally, the distribution of sites is found critical for heat transfer; an ordered distribution of sites outperforms random and clustered distributions.

Inner and outer flow of an adhering droplet in shear flow

Adhering droplets in shear flow start to move downstream when a critical velocity ucrit is reached, i.e. the adhesion force is overcome by aerodynamic force. It is still not clear, whether drag-coefficient-estimation based on an approximation of the droplet as a rigid spherical cap is a valid approach. In contrast to rigid hemispheres there is a gas-liquid-interface, i.e. the velocity of the interface is not zero by all means. Therefore, there is a fluid transport inside the drop that depends on the outer flow structure. We report on a combined numerical and experimental investigation to find out the characteristic inner and outer flow structure of an adhering droplet in shear flow in order to evaluate the rigid-hemisphere-approach.The inner flow structure of the droplet is measured by particle-image velocimetry (PIV) while the wake flow of the droplet in the gas-phase is measured by a modified laser-doppler-velocimeter (laser-doppler profile sensor). Numerical simulations of a droplet have been carried out using a modified volume of fluid (VOF) model taking into account contact angle hysteresis effects in OpenFOAM®. The complete two-phase fluid motion of the liquid droplet and surrounding gas phase is simulated, i.e. the inner and outer flow of the droplet are captured with a three-dimensional simulation model.Experimental and numerical results agree very well concerning flow pattern inside and outside the droplet. There is a strong connection between the inner and outer flow of the droplet. For lower Reynolds numbers based on droplet diameter (Red < 800) the flow inside the droplet rotates in direction of the channel flow. On the leeward side of the droplet there is a small wake flow with slightly decreased flow velocity. At higher Reynolds numbers (Red ≥ 800) the flow pattern inside the droplet changes completely: A strong reverse flow close to the droplet surface appears. Concurrently a strong recirculation zone emerges in the wake of the droplet. This is due to the roll-up process of a separated shear layer originating from the droplet. Due to the coupling of the inner flow with the outer flow via the gas-liquid-interface our data show that at higher Reynolds numbers flow separation takes place on the windward half of the droplet. This is in contrast to the case of a rigid hemisphere, where the separation is located at approximately 90°, i.e. the top of the droplet, and does not move upstream with increasing Reynolds number. The height of the separation zone increases up to 1.29 times the droplet height, which is not observed for rigid hemispheres. Since the pressure field around an obstacle is governed by the flow separation location and the corresponding size of the recirculation zone, the coupling of the inner and outer flow changes the pressure distribution around the droplet with respect to a similar rigid structure. This will affect the aerodynamic forces acting on the droplet, which is why the approximation by a rigid spherical cap does not seem to be a suitable approach. Nevertheless, additional experimental and numerical efforts need to be done to assess the flow structures, pressure distributions and forces acting on the droplet in a suitable precision also considering possible aero-elastic effects.

Effects of contact angle hysteresis on bubble dynamics and heat transfer characteristics in saturated pool boiling

As an inherent physical phenomenon of the contact-line motion, the contact angle hysteresis (CAH) has an important effect on dynamic behaviors of bubble/bubbles from a solid surface. In this study, boiling heat transfer considering the CAH is investigated by employing a phase change lattice Boltzmann (LB) model. Effects of the CAH on the bubble/bubbles dynamics during the boiling process and the boiling curves for both the hydrophilic and hydrophobic hysteresis windows are studied in detail. It is found that the bubble base, bubble height and phase change rate increase as the increase of the width of hysteresis window. On the other hand, the pinning of three-phase contact line is observed during the bubble growth processes. And the pinning times increase with the contact angle hysteresis. For the hydrophilic hysteresis window, the bubble completely departs from the heater if a small range of the hysteresis window is considered, while a residual bubble is left when the bubble departs from the heater in the cases of the hysteresis window larger than an approximate critical value of 45°. For the hydrophobic hysteresis window, a residual bubble can be observed regardless of the level of the contact angle hysteresis. The numerical results also indicate that the CAH affects the position of bubbles coalescence. The bubbles merge above the heater for the hydrophilic hysteresis window with a small level of hysteresis. While the bubbles merge on the heater for the hydrophilic hysteresis window with a large level of hysteresis as well as for the hydrophobic hysteresis window. Moreover, as the increase of the width of the hysteresis window, the critical heat flux (CHF) as well as the Leidenfrost temperature (the minimum temperature for film boiling) decrease, and the transition boiling regimes become shorter. Finally, we present the fitting equations between the width of the hysteresis window and the CHF/Leidenfrost temperature. The results show that the CHF and the Leidenfrost temperature decrease linearly as the width of the hysteresis window increases.

Stimulating relative permeability changes by low-frequency elastic waves: Theory and lab experiments

A model is presented to describe how low-frequency vibrations can induce changes to relative permeabilities in dual-porosity dual-permeability rocks. We show that a combination of two physical processes may cause this effect: 1) the wave-induced two-phase fluid flow between soft pores (fractures or cracks) and stiff pores (matrix); and 2) the contact angle hysteresis effect. These two effects lead to redistribution of fluid saturation between fractures and matrix, which may explain alteration of relative permeabilities by small transient strains (∼10−6) in rocks where the fluid flow occurs primarily through the fracture network, and fluid storage occurs predominantly in the porous matrix. We assume that the frequency is low enough that viscous and inertial effects are negligible and that any stress-induced increments of pore pressure are uniform within wetting and nonwetting fluid phases. We demonstrate that pulse-like vibrations are much more efficient in changing relative permeabilities than sinusoidal-shaped vibrations. Furthermore, we show that two waveforms with the same amplitude and frequency but with different polarities could have opposite effects on the alteration of relative permeabilities. Specifically, extensional pulses increase oil relative permeability and decrease water relative permeability in the water-wet rock. Contrary, compressional pulses decrease oil relative permeability and increase water relative permeability in the water-wet rock. To validate theoretical results, we developed a unique low-frequency laboratory setup and experimental methods. We performed drainage and imbibition cycles on a sandstone sample using oil and water as pore fluids. During flooding, the sample was excited by small-strain seismic pulses of a specific shape, with varying polarization direction, frequency, and amplitude. The preliminary laboratory results validate the theoretical model qualitatively. The proposed model may contribute to environmentally friendly and low-cost methods for stimulating hydrocarbon production in conventional reservoirs without invasive chemicals or fracking. In unconventional reservoirs, however, this technology can be envisioned as supplementary to standard EOR/IOR techniques. Normally, the seismic wave energy is too low to increase absolute permeability or decrease oil viscosity; only relative permeabilities can be affected.

Simulations of contact angle hysteresis effects in droplet sliding on inclined isothermal surfaces and droplet evaporating on heated horizontal surfaces by a lattice Boltzmann method with a variable solid-fluid interaction strength scheme

A variable solid-fluid interaction strength scheme compatible with the lattice Boltzmann method is introduced to investigate contact angle hysteresis phenomena numerically. This method is applied to study two problems: (i) droplet sliding on inclined isothermal plates and (ii) droplet evaporating on horizontal heated plates. It is demonstrated that this method is capable of reproducing the decrease in the receding contact angle and the increase in the advancing contact angle during droplet sliding on an inclined isothermal plate, and the constant contact line (CCL) and constant contact angle (CCA) evaporation periods during droplet evaporation on a horizontal heated plate. These simulated results are in agreement with previous experimental investigations.

Droplet trapping in bendotaxis caused by contact angle hysteresis

Passive droplet transport mechanisms, in which continuous external energy input is not required for motion, have received significant attention in recent years. Experimental studies of such mechanisms often ignore, or use careful treatments to minimize, contact angle hysteresis, which can impede droplet motion, or even arrest it completely. Here, we consider the effect of contact angle hysteresis on bendotaxis, a mechanism in which droplets spontaneously deform an elastic channel via capillary pressure and thereby move. Here, we seek to understand when contact angle hysteresis prevents bendotaxis. We supplement a previous mathematical model of the dynamics of bendotaxis with a simple model of contact angle hysteresis, and show that this model predicts droplet trapping when hysteresis is sufficiently strong. By identifying the equilibrium configurations adopted by these trapped droplets and assessing their linear stability, we uncover a sensitive dependence of bendotaxis on contact angle hysteresis and develop criteria to describe when droplets will be trapped.

Effect of contact angle hysteresis and sensitivity of gas-liquid interfacial tension to temperature of a sessile-drop on evaporation dynamics

The evaporation process of drops on a solid surface is widely applied to daily life and industrial fields. Both contact angle hysteresis and the sensitivity of gas-liquid interfacial tension to temperature are important factors affecting the drop evaporation reflected in the contact line and contact angle. To investigate the internal mechanism, according to the lubrication theory and slip boundary conditions, we establish a mathematical model of the drop evaporation on a uniformly heated solid wall with considering the effect of contact angle hysteresis. This model is numerically solved by using a coordinate transformation method and Freefem++14.3, a highly efficient solver. The accuracy of the numerical calculation method is verified by comparing the numerical results with experimental results, and the grid independence is validated. The effect of contact angle hysteresis on the dynamics of evaporating drops is discussed, and the evaporation characteristics of drops with different tension sensitivities of the air-liquid interface to temperature are further investigated. The results show that the contact angle hysteresis has an apparent influence on the drop evaporation process which includes drop spreading stage, contact line pinning stage, and depinning stage. In the drop spreading stage, the increase in the hysteresis angle shortens the spreading time, and reduces the spreading velocity and radius, while in the contact line pinning stage, the pinning time is prolonged and the reduction of drop mass is significantly increased with hysteresis angle increasing. In the contact line depinning stage, the contact angle hysteresis reduces the contact angle, and a flatter shape emerges, thereby enhancing the ability to transfer heat and accelerating evaporation as well as shortening the depinning time. In addition, the large hysteresis angle leads to a large advancing contact angle and a small receding contact angle. The reduction in receding contact angle is more notable than the increment of advancing contact angle. The temperature sensitivity coefficient of the gas-liquid interfacial tension can be increased by reducing the receding contact angle, thereby improving the wettability of the drops on the wall enhancing the heat transfer and accelerating the evaporation. Regulating the contact angle hysteresis and the sensitivity of the interfacial tension to temperature can realize the manipulation of the drop movement, thus controlling the evaporation process.

Pore-Scale Modeling of the Effect of Wettability on Two-Phase Flow Properties for Newtonian and Non-Newtonian Fluids.

The Darcy-scale properties of reservoir rocks, such as capillary pressure and relative permeability, are controlled by multiphase flow properties at the pore scale. In the present paper, we implement a volume of fluid (VOF) method coupled with a physically based dynamic contact angle to perform pore-scale simulation of two-phase flow within a porous medium. The numerical model is based on the resolution of the Navier–Stokes equations as well as a phase fraction equation incorporating a dynamic contact angle model with wetting hysteresis effect. After the model is validated for a single phase, a two-phase flow simulation is performed on both a Newtonian and a non-Newtonian fluid; the latter consists of a polymer solution displaying a shear-thinning power law viscosity. To investigate the effects of contact angle hysteresis and the non-Newtonian nature of the fluid, simulations of both drainage and imbibition are carried out in order to analyze water and oil saturation—particularly critical parameters such as initial water saturation () and residual oil saturation () are assessed in terms of wettability. Additionally, the model sensitivities to the consistency factor (), the flow behavior index (n), and the advancing and receding contact angles are tested. Interestingly, the model correctly retrieves the variation in and wettability and predicts behavior over a wide range of contact angles that are difficult to probe experimentally.

Numerical investigations of water droplet dynamics in micro-channels considering contact angle hysteresis

The volume of fluid (VOF) method coupled with a contact angle model considering hysteresis effects is used to study the dynamic of water droplets in micro-channels for proton exchange membrane fuel cells. The contact angle hysteresis is modeled by a modified third-order fit relationship for the contact angle and the azimuthal angle. Droplets sliding down the smooth surface, textured surface and carbon paper are firstly solved as examples to evaluate the accuracy of the numerical model to predict the adhesion force. The effects of channel geometry and contact angle hysteresis on the dynamic of water droplets in micro-channels are investigated. Geometrical study reveals that the gap between the droplet and channel wall is an important factor influencing the drag force. Due to the low contact angle of the channel side wall, the droplet at the corner have larger detachment velocity than the droplet at the middle of the channel. The numerical results for the effects of contact angle hysteresis indicate that the changes of the contact angle hysteresis and wetting area both result in the variation of the adhesion force and account for the variation of the detachment velocity.

Effective Fluid Bulk Modulus in the Partially Saturated Rock and the Amplitude Dispersion Effects

AbstractFrequency dispersion is a well‐known effect in geophysics, which means that waves of different wavelengths propagate at different velocities. Amplitude dispersion is a less‐known effect, which means that waves of different amplitudes propagate at different velocities. Herewith, we consider the alteration of the interfacial energy during wave‐induced two‐phase fluid flow in a partially saturated rock and demonstrate that this leads to a nonlinear amplitude dispersion effect. When the wave amplitude is small, seismic waves cause bending of the interface menisci between immiscible fluids at the pore scale. However, when the wave amplitude is sufficiently large, the interface menisci will slip at the pore scale, causing attenuation of the elastic energy by the contact line friction mechanism. At the zero frequency limit, all viscous dissipation models predict zero attenuation of the elastic wave energy, while this approach predicts a nonzero attenuation due to a static contact angle hysteresis effect. Herein, we extend the Gassmann's theory with three extra terms, which can be obtained from standard laboratory tests: pore‐size distribution and interfacial tension between immiscible fluids and rock wettability (advancing and receding contact angles). We derive closed‐form analytical expressions predicting the effective fluid modulus in partially saturated rock, which falls between Voigt and Reuss averages. Next, we demonstrate that the nonlinear amplitude dispersion effect leads to energy transfer between different frequencies. This may explain the low‐frequency microtremor anomalies, frequently observed above hydrocarbon reservoirs, when the low‐frequency energy of ocean waves (0.1–1 Hz) is converted to higher frequencies (2–6 Hz) by partially saturated reservoirs.

Unified framework for mapping shape and stability of pendant drops including the effect of contact angle hysteresis

Solution of the Young-Laplace equation for fluid-fluid interface shapes is crucial in several applications related to colloids, capillarity, and surfaces. Despite significant progress in analysis and computation, the solution framework in literature is quite sparse with different norms for non-dimensionalisation and often limited to simplistic boundary conditions. These problems can be overcome and a unified solution framework can be developed if the relevant parameters are non-dimensionalised with respect to the capillary length, and collapsed onto a single graphical chart in the form of axes and contours. Here we use vector parameterized cubic splines to represent axisymmetric droplet profiles, which are then evolved quasi-statically to get to the equilibrium shapes using a novel thermodynamic free energy minimization-based algorithm. The generated dataset for a wide range of geometric and surface parameters is validated and then compiled in the form of a graphical chart. The chart traces the complete profile of axisymmetric pendant drops, predicts their evolution and stability on any surface, all without running any computer simulation. Most importantly, the contact angle contours on this chart offer the capability to incorporate the effect of contact angle hysteresis, a situation which is practically relevant, but has yet not been modelled.

Effects of contact angle hysteresis on drop manipulation using surface acoustic waves

Surface acoustic waves have gained much attention in flow control given the effects arising from acoustic streaming. In this study, the hydrodynamic interference of a drop under surface acoustic waves is comprehensively investigated and the contact angle hysteresis effects are considered, too. This paper reveals the effects of some control parameters such as wave amplitude and wave frequency on the dynamical behaviors of drop. For these purposes, a multiple-relaxation-time color-gradient model lattice Boltzmann method is developed. In these case studies, wave frequency and amplitude were in the ranges of 20–60 MHz and 0.5–2 nm, respectively. In addition, the density ratio of 1000, the kinematic viscosity ratio of 15, Reynolds numbers of 4–24, Capillary numbers of 0.0003–0.0008 and Weber numbers of 0–0.4 were considered. Results show that drop would not move, but would incline in the direction of wave propagation equal to radiation angle when the wave amplitude is low. However, the drop will initiate to move as wave amplitude is progressively augmented. Meanwhile, the increase in frequency leads to an increment of required power to change the modes of the system from streaming to pumping or jetting states. The obtained results clearly show that a reduction in viscosity and an increase in surface tension coefficient significantly influence the flow control system and enhance its sensitivity. Also, the contact angle hysteresis modeling can improve the numerical results by up to 20%.