Role of surface charge on boundary slip in fluid flow

Effect of the Surface Charge-Dependent Boundary Slip on the Electrophoresis of a Hydrophobic Polarizable Rigid Colloid

The electrophoresis of a hydrophobic charged rigid colloid is studied by considering the lateral movement of the adsorbed surface charge. The slip velocity condition at the hydrophobic surface is modified to take into account the impact of the frictional and electric forces created by the adsorbed laterally mobile surface charge. Though the dependency of the surface charge on the slip velocity in the context of electrophoresis has been addressed before, the effect of the laterally mobile adsorbed surface charge on the electrophoresis of hydrophobic colloids has not been studied. The dielectric colloid is considered to polarize and create an induced immobile surface charge when subjected to an imposed electric field. The impact of the mobile surface charge along with the immobile induced surface charge on electrophoresis of a hydrophobic colloid is elucidated by numerically solving the governing electrokinetic equations in their full form. We have also developed a simplified model under a weak applied field consideration, which can be further reduced to a closed-form analytic expression for the mobility under the Debye-Hückel approximation. This analytic model for mobility is in excellent agreement with the exact numerical solution for an entire range of the Debye length when the ζ-potential is in the order of the thermal potential. One of the notable features of this closed-form mobility expression is that it accounts for the mobile adsorbed surface charge on the hydrodynamic slip condition and the dielectric polarization of the particle. We find that the mobility of the surface charge decreases the electrophoretic mobility of the hydrophobic dielectric colloid. However, the mobile surface charge enhances the mobility of a conducting hydrophobic colloid.

Slip Effects on Ionic Current of Viscoelectric Electroviscous Flows through Different Length Nanofluidic Channels

The pressure driven slip flow of an electrolyte solution is studied through different nanofluidic channel lengths at varying salt concentrations. The viscous-thickening due to the electrostatic interactions within the electric double layer and the reverse ionic transport due to the streaming potential are developed. The influence of the Navier slip boundary condition is described under both electroviscous and viscoelectric effects with a surface charge regulation (CR) model while the observed behavior is compared and validated with molecular dynamic (MD) calculations from multiple studies. Results show that electroviscous and viscoelectric effects decrease transport. Earlier studies at the no slip boundary presented an increase of ionic current by increasing salt concentration and decreasing channel length. In contrast, our study found that the ionic current occurred almost independent of both salt concentration and channel length, except for very short channels and very low salt concentrations, when electroviscous and viscoelectric effects were considered. In the case of the constant slip length condition, ionic conduction was enhanced, but velocity slip developing on surfaces showed significant variation based on the salt concentration and channel length. This is due to the natural CR behavior enhancing the surface charge and consequential near surface electrohydrodynamics as a result of increase in salt concentration and/or decrease of channel length. Considering that the electroviscous effect alone creates up to 70% lower velocity slips than Poiseuille flow predictions, while further including the viscoelectric effect, results in an almost no-slip condition at high salt concentrations and/or short channels. As a result, the ionic current of a viscoelectric electroviscous slip flow is found to be equal to 1/3 of an electroviscous slip flow and to decrease with a decrease in the channel length.

Self-Propulsion of Janus Particles near a Brush-Functionalized Substrate

Thermophoresis is a common mechanism that can drive autonomous motion of Janus particles under the right environment. Despite recent efforts to investigate the mechanism underlying the self-propulsion of thermophoretic particles, the interaction of particles with the substrate underneath the particle has remained unclear. In this work, we explore the impact of poly(N-isopropylacrylamide) (PNIPAM)-functionalized substrate with various chain lengths on the active motion of a single polystyrene particle half-coated with gold (Au-PS). We show how the modification of the substrate with polymer brushes enhances the particle velocity, where brush chain length plays a significant role as well. The results demonstrate the intrinsic dependence of particle velocity on the flow boundary condition and the thermo-osmotic slip at the interface.

Liquid-Solid Slip on Charged Walls: The Dramatic Impact of Charge Distribution

Nanofluidic systems show great promise for applications in energy conversion, where their performance can be enhanced by nanoscale liquid-solid slip. However, efficiency is also controlled by surface charge, which is known to reduce slip. Combining molecular dynamics simulations and analytical developments, we show the dramatic impact of surface charge distribution on the slip-charge coupling. Homogeneously charged graphene exhibits a very favorable slip-charge relation (rationalized with a new theoretical model correcting some weaknesses of the existing ones), leading to giant electrokinetic energy conversion. In contrast, slip is strongly affected on heterogeneously charged surfaces, due to the viscous drag induced by counterions trapped on the surface. In that case slip should depend on the detailed physical chemistry of the interface controlling the fraction of bound ions. Our numerical results and theoretical models provide new fundamental insight into the molecular mechanisms of liquid-solid slip, and practical guidelines for searching new functional interfaces with optimal energy conversion properties, e.g., for blue energy or waste heat harvesting.

Effects of surface charge and boundary slip on time-periodic pressure-driven flow and electrokinetic energy conversion in a nanotube

Time-periodic pressure-driven slip flow and electrokinetic energy conversion efficiency in a nanotube are studied analytically. The slip length depends on the surface charge density. Electric potential, velocity and streaming electric field are obtained analytically under the Debye-Hückel approximation. The electrokinetic energy conversion efficiency is computed using these results. The effects of surface charge-dependent slip and electroviscous effect on velocity and electrokinetic energy conversion efficiency are discussed. The main results show that the velocity amplitude and the electrokinetic energy conversion efficiency of the surface charge-dependent slip flow are reduced compared with those of the surface charge-independent slip flow.

Establishment of a Standard Method for Boundary Slip Measurement on Smooth Surfaces Based on AFM

Typically, it is difficult to analyze and design a micro/nanofluid system, and the design process cannot follow the traditional law of hydrodynamics. The boundary condition is very important in the applications of a micro/nanofluid system. The existence of boundary slip can reduce the hydrodynamic resistance and enhance fluid flow. How to accurately determine the dynamic boundary conditions is increasingly concerned by researchers. Atomic force microscope (AFM) is proven to be the most advanced experimental instrument for studying the characteristics of the surface and the interaction interface. Most studies on the application of atomic force microscopy to the measurement of the boundary slip do not describe a systematic standard process, leading to many differences in the measurement results. In this paper, a standard process of measuring slip on smooth and flat surfaces is developed, including the data processing methods that minimize the interference factors in the original data as well as simplify the data expression. Thus, the boundary slip can be obtained more easily and accurately.

Electrophoresis of a polarizable charged colloid with hydrophobic surface: A numerical study

We consider the electrophoresis of a charged colloid for a generalized situation in which the particle is considered to be polarizable and the surface exhibits hydrophobicity. The dielectric polarization of the particle creates a nonlinear dependence of the electrophoretic velocity on the applied electric field, and the core hydrophobicity amplifies the fluid convection in the Debye layer. Thus, a linear analysis is no longer applicable for this situation. The present analysis is based on the numerical solution of the nonlinear electrokinetic equations based on the Navier-Stokes-Nernst-Planck-Poisson equations coupled with the Laplace equation for the electric field within the dielectric particle. The hydrophobicity of the particle may influence its electric polarization by enhancing the convective transport of ions. The nonlinear effects, such as double-layer polarization and relaxation, are also influenced by the hydrophobicity of the particle surface. The present results compare well for a lower range of the applied electric field and surface charge density with the existing results for a perfectly dielectric particle with a hydrophobic surface based on the first-order perturbation analysis due to Khair and Squires [Phys. Fluids 21, 042001 (2009)PHFLE61070-663110.1063/1.3116664]. Dielectric polarization creates a reduction in particle electrophoretic velocity, and its impact is strong for a moderate range of Debye length. A quantitative measure of the nonlinear effects is demonstrated by comparing the electrophoretic velocity with an existing linear model.

Effect of Surface Charge on the Nanofriction and Its Velocity Dependence in an Electrolyte Based on Lateral Force Microscopy

The nanofriction between a silicon nitride probe and both a silicon wafer and an octadecyltrichlorosilane (OTS)-coated surface is studied in saline solution by using lateral force microscopy (LFM). The effects of surface charge on the nanofriction in an electrolyte as well as its velocity dependence are studied, while the surface charge at the solid-liquid interface is adjusted by changing the pH value of the electrolyte. The results show that the nanofrictional behavior between the probe and the samples in an electrolyte depends strongly on the surface charge at the solid-liquid interface. When the probe and the sample in the electrolyte are charged with the same sign, a repulsive electrostatic interaction between the probe and the sample is produced, leading to a reduction in nanofriction. In contrast, when the two surfaces are charged with the opposite sign, nanofriction is enhanced by the attractive electrostatic interaction between the probe and the sample. The velocity dependence of nanofriction in an electrolyte is believed to be tied to charge regulation referring to a decreasing trend in surface charge densities for the two approaching charged surfaces in an electrolyte. When the probe slides on the sample at a low velocity, charge regulation occurs and weakens the electrostatic interaction between the probe and the sample. As a result, nanofriction is reduced for surfaces charged with the opposite sign, and it is enhanced for surfaces charged with the same sign. When the sliding velocity between the probe and the sample is high, there is insufficient time for charge regulation to occur. Thus, the friction pair shows a larger nanofriction when the surfaces are charged with the opposite sign and a smaller nanofriction when the surfaces are charged with the same sign when compared to the case of a lower sliding velocity.

Study of the Relationship between Boundary Slip and Nanobubbles on a Smooth Hydrophobic Surface

Surface nanobubbles, which are nanoscopic or microscopic gaseous domains forming at the solid/liquid interface, have a strong impact on the interface by changing the two-phase contact to a three-phase contact. Therefore, they are believed to affect the boundary condition and liquid flow. However, there are still disputes in the theoretical studies as to whether the nanobubbles can increase the slip length effectively. Furthermore, there are still no direct experimental studies to support either side. Therefore, an intensive study on the effective slip length for flows over bare surfaces with nanobubbles is essential for establishing the relation between nanobubbles and slip length. Here, we study the effect of nanobubbles on the slippage experimentally and theoretically. Our experimental results reveal an increase from 8 to 512 nm in slip length by increasing the surface coverage of nanobubbles from 1.7 to 50.8% and by decreasing the contact angle of nanobubbles from 42.8 to 16.6°. This is in good agreement with theoretical results. Our results indicate that nanobubbles could always act as a lubricant and significantly increase the slip length. The surface coverage, height, and contact angle are key factors for nanobubbles to reduce wall friction.

Rapid capillary filling via ion-water interactions over the nanoscale

Giant frictional resistances are grand challenges against the rapid filling of nanoscale capillaries, as encountered in a wide variety of applications ranging from nature to energy. It is commonly believed that partially wettable charged nanocapillaries fill up considerably slower, compared to completely wettable ones, under the influence of a complex interplay between interfacial tension and electrical interactions. In sharp contrast to this common belief, here we discover a new non-intuitive regime of rapid filling of charged capillaries over the nanometer scale, by virtue of which a partially wettable capillary may fill up comparatively faster than a completely wettable one. We attribute the fundamental origin of this remarkable behavior to ion-water interactions over interfacial scales. The underlying novel electro-hydrodynamic mechanism, as unveiled here, may provide deeper insights into the physico-chemical interactions leading to augmentations in the rates of nanocapillary filling over hydrophobic regimes, bearing far-reaching implications in the transport of biological fluids, enhanced oil recovery, and miniaturized energy harvesting applications.

The effect of surface charge on the boundary slip of various oleophilic/phobic surfaces immersed in liquids

The reduction of fluid drag is an important issue in many fluid flow applications at the micro/nanoscale. Boundary slip is believed to affect fluid drag. Slip length has been measured on various surfaces with different degrees of hydrophobicity and oleophobicity immersed in various liquids of scientific interest. Surface charge has been found to affect slip length in water and electrolytes. However, there are no studies on the effect of surface charge on slip at solid-oil interfaces. This study focuses on the effect of surface charge on the boundary slip of superoleophilic, oleophilic, oleophobic, and superoleophobic surfaces immersed in deionized (DI) water and hexadecane and ethylene glycol, based on atomic force microscopy (AFM). The surface charge was changed by applying a positive electric field to the solid-liquid interface, and by using liquids with different pH values. The results show that slip length increases with an increase in applied positive electric field voltage. Slip length also increases with a decrease in the pH of the solutions. The change in slip length is dependent on the absolute value of the surface charge, and a larger surface charge density results in a smaller slip length. In addition, the surface charge density at different solid-liquid interfaces is related to the dielectric properties of the surface. The underlying mechanisms are analyzed.

Effect of surface modification on interfacial nanobubble morphology and contact line tension

Past research has confirmed the existence of surface nanobubbles on various hydrophobic substrates (static contact angle >90°) when imaged in air-equilibrated water. Additionally, the use of solvent exchange techniques (based on the difference in saturation levels of air in various solvents) also introduced surface nanobubbles on hydrophilic substrates (static contact angle <90°). In this work, tapping mode atomic force microscopy was used to image interfacial nanobubbles formed on bulk polycarbonate (static contact angle of 81.1°), bromo-terminated silica (BTS; static contact angle of 85.5°), and fluoro-terminated silica (FTS; static contact angle of 105.3°) surfaces when immersed in air-equilibrated water without solvent exchange. Nanobubbles formed on the above three substrates were characterized on the basis of Laplace pressure, bubble density, and contact line tension. Results reported here show that (1) the Laplace pressures of all nanobubbles formed on both BTS and polycarbonate were an order of magnitude higher than those of FTS, (2) the nanobubble number density per unit area decreased with an increase in substrate contact angle, and (3) the contact line tension of the nanobubbles was calculated to be positive for both BTS and polycarbonate (lateral radius, Rs < 50 nm for all nanobubbles), and negative for FTS (Rs > 50 nm for all nanobubbles). The nanobubble morphology and distribution before and after using the solvent exchange method (ethanol-water), on the bulk polycarbonate substrate was also characterized. Analysis for these polycarbonate surface nanobubbles showed that both the Laplace pressure and nanobubble density reduced by ≈98% after ethanol-water exchange, accompanied by a flip in the magnitude of contact line tension from positive (0.19 nN) to negative (-0.11 nN).

The coupling of surface charge and boundary slip at the solid-liquid interface and their combined effect on fluid drag: A review

Fluid drag of micro/nano fluidic systems has inspired wide scientific interest. Surface charge and boundary slip at the solid-liquid interface are believed to affect fluid drag. This review summarizes the recent studies on the coupling of surface charge and slip, and their combined effect on fluid drag at micro/nano scale. The effect of pH on surface charge of borosilicate glass and silica surfaces in deionized (DI) water and saline solution is discussed using a method based on colloidal probe atomic force microscopy (AFM). The boundary slip of various oil-solid interfaces are discussed for samples with different degrees of oleophobicity prepared by nanoparticle-binder system. By changing the pH of solution or applying an electric field, effect of surface charge on slip of a smooth hydrophobic octadecyltrichlorosilane (OTS) in DI water and saline solution is studied. A theoretical model incorporating the coupling relationship between surface charge and slip is used to discuss the combined effect of surface charge-induced electric double layer (EDL) and slip on fluid drag of pressure-driven flow in a one-dimensional parallel-plates microchannel. A theoretical method is used to reduce the fluid drag. The studies show that the increasing magnitude of surface charge density leads to a decrease in slip length. The surface charge results in a larger fluid drag, and the coupling of surface charge and slip can further increase the fluid drag. Surface charge-induced EDLs with asymmetric zeta potentials can effectively reduce the fluid drag.

The study of surface wetting, nanobubbles and boundary slip with an applied voltage: A review

The drag of fluid flow at the solid-liquid interface in the micro/nanoscale is an important issue in micro/nanofluidic systems. Drag depends on the surface wetting, nanobubbles, surface charge and boundary slip. Some researchers have focused on the relationship between these interface properties. In this review, the influence of an applied voltage on the surface wettability, nanobubbles, surface charge density and slip length are discussed. The contact angle (CA) and contact angle hysteresis (CAH) of a droplet of deionized (DI) water on a hydrophobic polystyrene (PS) surface were measured with applied direct current (DC) and alternating current (AC) voltages. The nanobubbles in DI water and three kinds of saline solution on a PS surface were imaged when a voltage was applied. The influence of the surface charge density on the nanobubbles was analyzed. Then the slip length and the electrostatic force on the probe were measured on an octadecyltrichlorosilane (OTS) surface with applied voltage. The influence of the surface charge on the boundary slip and drag of fluid flow has been discussed. Finally, the influence of the applied voltage on the surface wetting, nanobubbles, surface charge, boundary slip and the drag of liquid flow are summarized. With a smaller surface charge density which could be achieved by applying a voltage on the surface, larger and fewer nanobubbles, a larger slip length and a smaller drag of liquid flow could be found.

Quantification of surface charge density and its effect on boundary slip

Reduction of fluid drag is important in the micro-/nanofluidic systems. Surface charge and boundary slip can affect the fluid drag, and surface charge is also believed to affect boundary slip. The quantification of surface charge and boundary slip at a solid-liquid interface has been widely studied, but there is a lack of understanding of the effect of surface charge on boundary slip. In this paper, the surface charge density of borosilicate glass and octadecyltrichlorosilane (OTS) surfaces immersed in saline solutions with two ionic concentrations and deionized (DI) water with different pH values and electric field values is quantified by fitting experimental atomic force microscopy (AFM) electrostatic force data using a theoretical model relating the surface charge density and electrostatic force. Results show that pH and electric field can affect the surface charge density of glass and OTS surfaces immersed in saline solutions and DI water. The mechanisms of the effect of pH and electric field on the surface charge density are discussed. The slip length of the OTS surface immersed in saline solutions with two ionic concentrations and DI water with different pH values and electric field values is measured, and their effects on the slip length are analyzed from the point of surface charge. Results show that a larger absolute value of surface charge density leads to a smaller slip length for the OTS surface.