Disjoining Pressure Research Articles

The role of disjoining pressure on the drying shrinkage of cementitious materials

The role of disjoining pressure on the drying shrinkage of cementitious materials

Sliding and merging of strongly sheared droplets

A mathematical and numerical framework is proposed to compute the displacement and merging dynamics of sliding droplets under the action of a constant shear exerted by a gas flow. An augmented formulation is implemented to model surface tension including the full curvature of the free surface. A set of shallow-water evolution equations is obtained for the film thickness, the averaged velocity, an additional quantity (with dimension of a velocity) taking into account the capillary effects and a tensor called enstrophy. The enstrophy accounts for the deviation of the velocity profile from a constant velocity distribution. The formulation is consistent with the long-wave expansion of the basic equations with a conservative part and source terms including the effect of viscosity, in the form of a viscous friction and the effect of the shear stress. The model is hyperbolic with generalised diffusion terms due to capillarity. Finally, our model is completed with a disjoining pressure formulation that is able to account for the hysteresis of the static contact angle. In this formulation, the advancing or receding nature of the contact line is assessed by the accumulation or reduction of mass of the droplet at the contact line. Simulations of sliding water droplets are performed with periodic boundary conditions in a domain of limited size. Hysteresis of the static contact angle causes a slowdown of the drops and a delay in the sequence of coalescence of the drops.

Probing the surface forces between air bubbles and bitumen via direct force Measurements: Effects of aqueous chemistry

The surface interactions of air bubbles and other components (e.g., particles, oil droplets) significantly influence the operation efficiency of a variety of engineering processes such as oily water treatment, bitumen extraction and flotation. Herein, the surface interactions of air bubbles with two types of Athabasca bitumen samples in aqueous solutions of varying pH, salinity, type of cations and in the presence of surfactants have been systematically characterized using a bubble probe atomic force microscope (AFM) technique. AFM imaging has revealed that exposure to high concentrations of NaCl and CaCl2 solutions or alkaline environments causes roughening of the bitumen surfaces. The results of surface force measurements demonstrate that the interaction and attachment behaviors between bubbles and bitumen are significantly affected by ionic strength, solution pH, and the presence of surfactants. The experimental force measurement results could be accurately described by a theoretical model that incorporates Reynolds lubrication theory and augmented Young-Laplace equation, with the inclusion of disjoining pressure. In low-salinity conditions, the bubble-bitumen interaction is dominated by electric double layer (EDL) repulsion, which prevents surface attachment. This effect is more pronounced at elevated pH conditions. In high-salinity solutions, however, the EDL interactions are significantly reduced, and the hydrophobic interaction becomes the dominant factor, overcoming the van der Waals repulsion and leading to the attachment of bubbles to bitumen surfaces. Raising aqueous pH weakens the bubble-bitumen hydrophobic interaction, whereas the introduction of calcium ions strengthens this interaction, resulting in enhanced surface attachment. Interestingly, even in high-salinity conditions, the presence of a small number of surfactants can inhibit bubble-bitumen contact, mainly caused by reduced hydrophobic attraction and increased steric repulsion. This work provides valuable nanoscale insights into how bubbles and bitumen interact in intricate aqueous environments, and the results show practical implications for controlling similar interfacial phenomena in various engineering processes.

Rimming flow in a rotating horizontal cylinder with phase change at the interface

The two-dimensional solutions and stability analysis are presented for an evaporating thin viscous liquid film flowing inside a uniformly heated rotating horizontal cylinder. A non-linear, fourth-order, partial differential evolution equation is obtained by simplifying mass, momentum, and energy conservation equations within the lubrication approximation. The effect of evaporation, gravity, viscous drag, surface tension, thermocapillary stress, and intermolecular forces has been taken into account. The numerical solutions of the model are validated against the existing experimental as well as the numerical results, along with the analytical result for the limiting cases of the present model. The film thickness model is solved to elucidate two-dimensional spatiotemporal solutions and their stability for a wide range of thermal and other parameters. The evaporative mass flux at the liquid–air interface results in unsteady solutions which are oscillatory in nature, and the amplitude of the oscillations increases with an increase in the evaporative flux. The film ruptures after some time and the rupture time is found to be inversely proportional to the evaporation number, a non-dimensional number quantifying the rate of evaporation. The linear stability analysis shows that the thermocapillary stresses as well as the long-range molecular forces destabilize the film. A negative disjoining pressure is shown to reduce the rupture time and vice versa. Evaporation (condensation) plays a destabilizing (stabilizing) role in the thin film flow. Non-linear computations are carried out for the steady profiles, validating the growth rates obtained from the linear stability analysis.

Mesoscopic Model for Disjoining Pressure Effects in Nanoscale Thin Liquid Films and Evaporating Extended Meniscuses.

Disjoining pressure effect is the key to describe contact line dynamics, micro/nanoscale liquid-vapor phase change heat transfer, and liquid transport in nanopores. In this paper, by combining a mesoscopic approach for nanoscale liquid-vapor interfacial transport and a mean-field approximation of the long-range solid-fluid molecular interaction, a mesoscopic model for the disjoining pressure effect in nanoscale thin liquid films is proposed. The capability of this model to delineate the disjoining pressure effect is validated. We demonstrate that the Hamaker constant determined from our model agrees very well with molecular dynamics (MD) simulation and that the transient evaporation/condensation mass flux predicted by this mesoscopic model is also consistent with the kinetic theory. Using this model, we investigate the characteristics of the evaporating extended meniscus in a nanochannel. The nonevaporating film region, the evaporating thin-film region, and the intrinsic meniscus region are successfully captured by our model. Our results suggest that the apparent contact angle and thickness of the nonevaporating liquid film are self-tuned according to the evaporation rate, and a higher evaporation rate results a in larger apparent contact angle and thinner nonevaporating liquid film. We also show that disjoining pressure plays a dominant role in the nonevaporating film region and suppresses the evaporation in this region, while capillary pressure dominates the intrinsic meniscus region. Strong evaporation takes place in the thin-film region, and both the disjoining pressure and capillary pressure contribute to the total pressure difference that delivers the liquid from the intrinsic meniscus region to the evaporating thin-film region, compensating for the liquid mass loss due to strong evaporation. Our work provides a new avenue for investigating thin liquid film spreading, liquid transport in nanopores, and microscopic liquid-vapor phase change heat/mass transfer mechanisms near the three-phase contact line region.

Dielectric Mismatch Effects on Polyelectrolyte Solutions in Electrified Nanopores: Insights from Mean-Field Theory

We utilize the self-consistent field theory to explore the mechanical and electrical properties of charged surfaces immersed in polyelectrolyte solutions that could be potentially useful for electrochemical applications. Our research focuses on how the dielectric heterogeneity of the solution could affect the disjoining pressure and differential capacitance of the electric double layer. Relying on the developed theoretical framework, based on the Noether’s theorem, we calculate the stress tensor, containing the term, arising from the conformational entropy of the polymer chains. With its help we compute the disjoining pressure in polyelectrolyte solution confined between two parallel charged surfaces and analyze its behavior as a function of separation between the surfaces for different values of dielectric mismatch parameter. We also calculate the differential capacitance of the electric double layer and discuss how dielectric heterogeneity of the polyelectrolyte solution influences its values.

Effect of substrate roughness on dynamics of wetting and decay of an ultrathin liquid film

In this study, we analyze the dynamics of wetting and decay of an ultrathin liquid film on a rough substrate. The dependence of disjoining pressure on liquid film thickness is derived by the direct numerical calculation for the Lennard-Jones pair interaction potential and 3D rough substrate with a random relief. It is shown that disjoining pressure for a rough substrate can be approximated by a similar function for a smooth one with highly fluctuating parameters over the substrate surface. The equation describing wetting and decay of 3D liquid film is modified, accounting for the calculated coordinate dependence of disjoining pressure the general form of capillary pressure depending on substrate relief. The approach is used for the simulation of drop formation from a nanosized liquid film for substrates with various roughness parameters. It is demonstrated that substrate roughness is responsible for accelerated film rupture and formation of “detectable” drops, increase in their number density, and decrease in average size. At the later stage, liquid film transformation is described by the power-law dependences of number density, average height and size with the exponents depending on substrate roughness. The blocking point of the size distribution function shifts to a larger value for a substrate with a more fine-grained structure. These changes in the growth rate and size distribution function of drops are associated with the change in conditions of liquid flow, which becomes inhomogeneous due to substrate roughness.

Asymmetric droplet evaporation on inclined surfaces

A computational model based on disjoining pressure is developed to study the asymmetric evaporation of droplets on an inclined substrate. In the proposed formulation, the disjoining pressure is combined with the arbitrary Lagrange-Euler method (ALE) to describe the solid-liquid interaction and investigate the contact angle hysteresis during evaporation. This model can be used to simulate the droplet evaporation modes of constant contact radius (CCR), constant contact angle (CCA) and “Stick-Slip” (mix evaporation mode), while the results are in good agreement with the experimental data. The obtained droplet shape for different inclined angles shows an asymmetric variation in contact angle at the front and rear ends, with the mean contact angle decreasing as the tilt angle increases. The evaporation flux is symmetric in the case of a horizontal substrate, however, when the substrate is tilted, the front and rear contact angles are modified, which leads to a larger evaporation flux on the rear contact line. Moreover, the asymmetric droplet morphology leads to asymmetric temperature field and vortex in the initial stage of evaporation; as evaporation proceeds, however, the flow and temperature fields within the droplet exhibit a gradual convergence towards symmetry. Moreover, when droplets evaporate on a pair of substrates with complementary tilt angles, their lifetimes exhibit a remarkable similarity. From the evaporation rate evolution, it yields that the larger the percentage of pinning time on the contact line, the faster the evaporation rate of the droplet. The evaporation rate of droplets was 14.76% higher at a tilt angle of α=0° than the case of α=45°.

Theory of electrolyte solutions in a slit charged pore: Effects of structural interactions and specific adsorption of ions.

In this paper, we present a continuation of our research on modeling electrolyte solutions within charged pores. We make use of the model developed by Blossey et al. [Phys. Rev. E 95, 060602 (2017)], which takes into account the structural interactions between ions through a bilinear form over the gradients of local ionic concentrations in the grand thermodynamic potential, as well as their steric interactions through the lattice gas model. The structural interactions may describe the effects of the molecular structure of ions at a phenomenological level. For example, these effects include steric effects due to non-spherical shapes of ions, their conformational lability, and solvent effects. In addition, we explore their specific interactions with the pore walls by incorporating external attractive potentials. Our primary focus is on observing the behavior of ionic concentration profiles and the disjoining pressure as the pore width changes. By starting with the local mechanical equilibrium condition, we derive a general expression for the disjoining pressure. Our findings indicate that considering the structural interactions of ions leads to a pronounced minimum on the disjoining pressure profiles at small pore widths. We attribute this minimum to the formation of electric double layers on the electrified surfaces of the pore. In addition, our results demonstrate that the inclusion of the attractive interactions of ions with the pore walls enhances this minimum and shifts it to smaller pore thicknesses. Our theoretical discoveries may be useful for those involved in supercapacitor electrochemical engineering, particularly when working with porous electrodes that have been infused with concentrated electrolyte solutions.

Development and numerical implementation of a multiscale constitutive law for double-porosity swelling clayey rocks

The swelling of clayey rocks originates at different scales of the material. Clay mineral swelling is governed by two different phenomena: crystalline and osmotic swellings. In this paper, we adapt a multiscale numerical model that considers both crystalline swelling and interlayer osmotic swelling (four water layers and more) to efficiently implement it in a finite element method code. To this end, we itemize the different interactions arising in the interlayer space with respect to the disjoining pressure, and in the interparticular space considering the capillary effects. The overall model is based on the upscaling of the constitutive law from the nanoscopic scale to the macroscopic scale by adding all the different interactions that appear while upscaling. Additionally, the general model adapted in this paper can be considered as a new definition of the effective stress governing the chemo-hydromechanical behavior of clayey rocks. The numerical model is then implemented in Code_Aster software. The validation of our model is conducted by reproducing constant-volume swelling test. Simulation results for different pore size distributions demonstrate fair agreement between the experimental results and the numerical modeling in comparison with linear elasticity that overestimate the final swelling pressure compared to the model developed herein.

The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics

We study a prototypical example in nonlinear dynamics where transition to self-similarity in a singular limit is fundamentally changed as a parameter is varied. Here, we focus on the complicated dynamics that occur in a generalised unstable thin-film equation that yields finite-time rupture. A parameter, n, is introduced to model more general disjoining pressures. For the standard case of van der Waals intermolecular forces, n=3, it was previously established that a countably infinite number of self-similar solutions exist leading to rupture. Each solution can be indexed by a parameter, ϵ=ϵ1>ϵ2>⋯>0, and the prediction of the discrete set of solutions requires examination of terms beyond-all-orders in ϵ. However, recent numerical results have demonstrated the surprising complexity that exists for general values of n. In particular, the bifurcation structure of self-similar solutions now exhibits branch merging as n is varied. In this work, we shall present key ideas of how branch merging can be interpreted via exponential asymptotics.

Phase field simulation of liquid filling on grooved surfaces for complete, partial, and pseudo-partial wetting cases.

We develop and harness a phase field simulation method to study liquid filling on grooved surfaces. We consider both short-range and long-range liquid-solid interactions, with the latter including purely attractive and repulsive interactions as well as those with short-range attraction and long-range repulsion. This allows us to capture complete, partial, and pseudo-partial wetting states, demonstrating complex disjoining pressure profiles over the full range of possible contact angles as previously proposed in the literature. Applying the simulation method to study liquid filling on grooved surfaces, we compare the filling transition for the three different classes of wetting states as we vary the pressure difference between the liquid and gas phases. The filling and emptying transitions are reversible for the complete wetting case, while significant hysteresis is observed for the partial and pseudo-partial cases. In agreement with previous studies, we also show that the critical pressure for the filling transition follows the Kelvin equation for the complete and partial wetting scenarios. Finally, we find the filling transition can display a number of distinct morphological pathways for the pseudo-partial wetting cases, as we demonstrate here for varying groove dimensions.

Preparation and application of modified carbon black nanofluid as a novel flooding system in ultralow permeability reservoirs

Conventional flooding systems have very low recovery rates in ultralow permeability reservoirs in virtue of the characteristics of high injection pressure, low permeability and small pores in such reservoirs. In this study, a novel surface-modified carbon black (MCB) nanofluid was prepared as a flooding system to resolve this problem. The preparation process of MCB nanoparticles was divided into three stages: (1) oxidation of carbon black (CB) nanoparticles, (2) acyl chlorination of oxidized carbon black (OCB) nanoparticles and (3) grafting of active groups onto the surface of acyl chloride carbon black (ACB) nanoparticles, and the main synthesis conditions, such as modifier concentration and grafting temperature, were optimized. X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) analysis indicated that the factional groups were successfully introduced onto the surface of CB nanoparticles, and the crystallinity of CB nanoparticles decreased gradually during the reaction process. Additionally, the dispersed stability, temperature resistance, salinity tolerance, wettability alteration and oil stripping ability were evaluated so as to obtain the performance of the MCB nanofluid. The results show that the average size of the MCB nanoparticles is approximately 72.3 nm, and the dispersed stability of the MCB nanofluid is much better than that of the CB nanofluid. Compared with the carbon black (CB) nanofluid, the MCB nanofluid shows stronger wettability alteration and oil stripping ability, and can also withstand the high temperature and high salt environment of oil reservoirs. 1 PV of MCB nanofluid can enhance oil recovery by 28.9%. Furthermore, the enhanced oil recovery (EOR) mechanisms for the MCB nanofluid are revealed through analysis of low oil–water IFT (IFT), wettability alteration and Wasan’s theory of structural disjoining pressure. This new type of environment-friendly flooding system injects vitality into the development of ultralow permeability reservoirs.

Experimental and theoretical investigation of the impact of crude-oil on the wettability behavior of calcite and silicate due to low salinity effect

Wettability alteration is recognized as the main responsible mechanism for enhanced oil recovery during low salinity water flooding (LSWF) in both carbonates and sandstones. However, there is still a lack of understanding about the possible role of oil type on rock wettability alteration during LSWF. In the current study, contact angle (CA), interfacial tension (IFT), and zeta potentials for both oil/brine and rock/brine interfaces are measured for rock/brine/crude oil systems in a wide range of salinity of seawater. Two different crude oil samples and both calcite and silicate as good end-members of carbonate and sandstones are investigated. For oil A, the CA decreases with brine dilution; however, for oil B, the CA showed almost the opposite trend vs. salinity. The increased water-wetness of silicate compared to calcite surface was more highlighted in lower salinity. The results of zeta potentials showed that diluting seawater (SW) reduced the zeta potentials of rock/brine and oil/brine in all systems. The changes in zeta potential suggest that more dilution shall lead to more water-wetness, which is not in agreement with the CA behavior of two minerals in the case of crude oil B. Based on the augmented Young-Laplace equation, it was demonstrated that there is a good correlation between the IFT and the wettability, especially for calcite minerals. To shed light on the competition between the IFT and the EDL force, a comprehensive model was created to predict the CA results by coupling the surface complexation model (SCM), the DLVO theory, and the Young-Laplace equation. The coupled model successfully predicted the experimental contact angle for both crude oil and rock samples. Analyzing the disjoining pressure curves showed that due to the attractive EDL forces of calcite rocks, the oil/brine IFT solely controls the calcite wettability behavior with salinity. However, for silicate substrates, the high repulsive EDL forces are the main reason for the rock water-wetness at low salinity brines.

Experimental Investigation of the Effects of the Sizes and Concentrations of SiO2 Nanoparticles on Wettability Alteration and Oil Recovery

The use of silica nanoparticles for enhanced oil recovery has recently attracted the attention of investigators, and the disjoining pressure has been found to be a promising mechanism for removing residual oil. Previous studies have found that decreasing the particle size and increasing the concentration of nanoparticles improves the disjoining pressure, which enables the oil to be removed more easily. However, these studies were not designed for a reservoir environment. In the present work, our goal is to investigate the effects of the sizes and concentrations of nanoparticles by performing experimental wettability tests and core-flooding tests under reservoir conditions and by calculating the disjoining pressure. Our results demonstrate that both wettability alteration and oil recovery are higher with smaller particle sizes. However, we observed no correlation between wettability alteration and concentration. In contrast, the oil-displacement rate was better in the early stages of oil recovery for increased nanoparticle concentrations, suggesting that the disjoining pressure may be more effective then. These results demonstrate that particle sizes and concentrations are essential parameters for enhanced oil recovery using nanoparticles, even in a reservoir environment.

Mesoscopic theory for ionic liquids and concentrated electrolytes in a slit with charged walls

Concentrated electrolytes and ionic liquids confined between parallel charged plates are studied within a theory combining density functional and field-theoretic methods, extended in this work to the slit geometry. We obtain charge- and density profiles, as well as the excess grand potential as a function of the slit width L in the self-consistent Gaussian approximation. For large density of ions, the obtained disjoining pressure exhibits oscillatory asymptotic decay for increasing L, with the decay length that agrees with the results of recent experiments. On a general level, we show that if the charge density decays with a distance from a charged surface in the oscillatory way, then the electrostatic energy of the slit with charged walls also decays with L in an oscillatory way with the same characteristic lengths. The oscillatory decay disagrees with the asymptotic repulsion obtained in the surface force balance experiments. We argue that in the experiment, the lack of the attraction between the confining surfaces for large L may follow from slow ordering of the isotropic fluid absorbed in the expanding slit into layers with alternating charge.

STABILITY OF SOME SILICONE LUBRICATING INTERLAYERS IN LIQUID-INFUSED COATINGS

One of the most actively developing research areas in materials science relevant to polyfunctional coatings is the creation of slippery liquid-infused porous surfaces (SLIPS) based on porous hydrophobic or hydrophilic materials filled with low-volatility viscous liquids (lubricants). In the present work, we have investigated the possibility of using two organosilicon liquids of different polarities, bis(trifluoromethylsulfonyl)imide dicationic ionic liquid and silicone oil, as lubricants for fabricating slippery coatings that reduce the adhesion of solid and liquid aqueous precipitations to aluminium oxide substrates. To calculate the stability of the films of such lubricants, we have employed the theory of van der Waals forces to study the refractive index dispersions and the dielectric properties of the liquids in the region of microwave relaxation. On the basis of experimentally obtained data, the dielectric permittivity spectra have been calculated as functions of imaginary frequency for the entire spectral range, as well as the contribution of the van der Waals forces to the stability of the disjoining pressure isotherms of the lubricant films on the hydrophobic and hydrophilic aluminium oxide substrates. The disjoining pressure isotherms obtained in this work have indicated that the ionic liquid used to prepare slippery coatings is a more durable lubricant than silicone oil, because its films retain their stability when the vapor phase is replaced by an aqueous medium over a wider range of thickness.

Solid–liquid interface disjoining pressure of frozen clay and its effect on water transport

To account for the influence mechanism of solid–liquid interface disjoining pressure on water migration during clay freezing, this study first provides a theoretical calculation model of solid–liquid interface disjoining pressure by combining the thermodynamic equilibrium relation of solid–liquid interface with the parallel plate capacitor model. This is done at the molecular level. An implicit equation for calculating the film thickness d of unfrozen water is also given and the accuracy of the model verified. Secondly, considering that unfrozen water film is anisotropic, the concept of tensor is introduced to show the distribution characteristics and functions of solid–liquid interface disjoining pressure in unfrozen water film. Finally, the effects of solution concentration and undercooling degree on film thickness d of unfrozen water are discussed. The results show that solid–liquid interface disjoining pressure can be expressed by the excess free energy on the surface of charged media, and it is a single-valued function of unfrozen water film thickness. Solid–liquid interface disjoining pressure not only provides an effective driving force for water migration, but also provides growth space for ice lenses; the thickness of unfrozen water film d is negatively correlated with solution concentration and undercooling degree. The research results can provide a theoretical reference for the study of frost heave mechanism in clay soils.

Ultrathin Micellar Foam Films of Sodium Caseinate Protein Solutions

Sodium caseinates (NaCas), derived from milk proteins called caseins, are often added to food formulations as emulsifiers, foaming agents, and ingredients for producing dairy products. In this contribution, we contrast the drainage behavior of single foam films made with micellar NaCas solutions with well-established features of stratification observed for the micellar sodium dodecyl sulfate (SDS) foam films. In reflected light microscopy, the stratified SDS foam films display regions with distinct gray colors due to differences in interference intensity from coexisting thick-thin regions. Using IDIOM (interferometry digital imaging optical microscopy) protocols we pioneered for mapping nanotopography of foam films, we showed that drainage via stratification in SDS films proceeds by the expansion of flat domains that are thinner than surrounding by a concentration-dependent step-size, and nonflat features (nanoridges and mesas) form at the moving front. Furthermore, stratifying SDS foam films show stepwise thinning, such that the step-size and terminal film thickness decrease with concentration. Here we visualize the nanotopography in protein films with high spatiotemporal resolution using IDIOM protocols to address two long-standing questions. Do protein foam films formulated with NaCas undergo drainage via stratification? Are thickness transitions and variations in protein foam films determined by intermicellar interactions and supramolecular oscillatory disjoining pressure? In contrast with foam films containing micellar SDS, we find that micellar NaCas foam films display just one step, nonflat and noncircular domains that expand without forming nanoridges and a terminal thickness that increases with NaCas concentration. We infer that the differences in adsorbing and self-assembling unimers triumph over any similarities in the structure and interactions of their micelles.

Single bubble nucleation in water-filled 59-nm nanochannel

Bubble nucleation, by surface heating, is simulated in a water-filled 59 nm height silicon-dioxide nanochannel using computational fluid dynamics. Disjoining pressure of water is integrated in the continuum-level simulations to capture the molecular effects of nanoscale confinement. Input parameters of imposed heat flux and phase-transition coefficient are widely varied to perform a set of 50 simulations. Bubble nucleation occurs within a narrow temperature range of 124.7 ± 2.5 °C, and in excellent agreement with prior experimental finding. Onset of bubble nucleation occurs at the center of the channel rather than at the surface due to the presence of disjoining pressure, i.e., no three-phase contact line forms and a water film is present between the bubble and the surface. Post nucleation, three distinct paths of bubble collapse, steady-state, and continuous growth are observed, with the last case leading to formation of three-phase contact line. Such behavior is attributed to a critical thickness of the water film and associated disjoining pressure. The present work sheds light on the importance of disjoining pressure and its dominance in governing the bubble onset and growth behavior. Such fundamental understanding can potentially advance the development of future thermal management devices, such as heat pipes.