Hydrodynamic Slip Research Articles

Effect of hydrodynamic slip on thermoelectric response in negatively-charged nanofluidic channels

Nanofluidic thermoelectrics has attracted significant interest recently due to its potential for low-grade heat recovery. However, the impact of hydrodynamic slippage on power generation performance in nanofluidic channels has generally been ignored in previous studies, although slip velocity boundary conditions are relevant at the nanoscale. To fill this research gap, this study conducted two-dimensional (2D) numerical simulations based on non-isothermal Poisson, Nernst–Planck, Navier–Stokes, and energy equations to investigate the thermoelectric response, including Seebeck coefficient, thermoelectric current, power factor, and normalized maximum power density, within a nanochannel with slippage at the channel walls. The simulations considered three thermal-driven ion transport mechanisms: temperature-dependent ion electrophoretic mobility (TDIEM), Soret-type ion thermodiffusion, and thermoosmosis. The results showed that TDIEM and thermoosmosis primarily dominate the thermoelectric response of electrolyte confined in slip nanochannels in the presence of the overlapping electrical double layer. The study also found that the impact of access resistance on the thermoelectric response must be considered. The slip-enhancement of the Seebeck coefficient, i.e., the thermoelectric voltage at open-circuit condition, is not significant due to the increase in surface conductivity caused by slip-amplified electroosmosis, especially at low electrolyte concentrations. However, slip-amplified thermoosmosis greatly enhances the thermoelectric current at short-circuit condition, in the absence of the access resistance effect, leading to a significant improvement in the performance of ionic thermoelectricity in nanochannels with hydrodynamic slippage. At a moderate slip length ranging from 10 to 50 nm, it was found that the normalized maximum power density in a 2 nm nanochannel exceeded 10 mW K−2 m−2, even under a small temperature difference of 10 K, which is one order of magnitude higher than the typical thermionic capacitors and thermocells. Overall, this study provides valuable insights into developing efficient nanofluidic-based thermoelectric generators for low-grade heat energy harvesting by highlighting the importance of considering the effect of hydrodynamic slippage.

Fast Water Transport through Subnanometer Diameter Vertically Aligned Carbon Nanotube Membranes.

Small-diameter carbon nanotubes (CNTs) have outstanding mass-transport properties, especially enhanced water flow. Here, we report on water transport through the first macroscopic membranes with vertically oriented, subnanometer (0.8 nm) CNT pores, made by a scalable, solution-based method with electric-field alignment of bulk-grown single-wall CNTs (SWCNTs). After plasma etching to open pores, vertically aligned CNTs served as the primary pathway for liquid-water transport. The CNT membranes showed fast pressure-driven water transport, with up to 105-fold enhancement compared to no-slip Hagen-Poiseuille flow. Comparing 0.8 and 3 nm CNTs, we found that the hydrodynamic slip lengths increased with decreasing nanotube diameter, reaching 8.5 μm for the smaller-diameter CNTs. The results suggest that pressure-driven water transport in small-diameter CNTs is increasingly dominated by entrance resistance, thus becoming independent of nanotube length. Scalably fabricated membranes incorporating vertically aligned subnanometer CNT pores could have applications in water filtration, desalination, and energy harvesting.

Significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation

For its applications in nuclear reactors, food processing, chemical engineering, water emulsions and thermal power generating systems, the significance of irregular heat source and Arrhenius energy on electro-magnetohydrodynamic hybrid nanofluid flow over a rotating stretchable disk with nonlinear radiation have been investigated. The flow problem has been modeled utilizing the modified Buongiorno model and the thermophysical characteristics of water-based Cu − F e 3 O 4 hybrid nanoliquid. Effects like passive control of nanoparticles, hydrodynamic slip and convective boundary conditions are also heeded to boost the realistic nature of this work. Further, engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated which boosts the novelty of this research work. The modeled governing equations are transmuted into a system of first-order ODEs, with the help of apposite similarity transformations, which are then numerically resolved using the finite-difference based bvp5c algorithm. It is noticed that per unit increase in the electric parameter decreases the skin friction coefficient by 41.75% and increases the heat transfer rate by 15.31%. It is also observed that the entrainment velocity is directly proportional to the changes in electric field parameter and is inversely proportional to the changes in volume fraction of copper and magnetite nanoparticles.

Transport phenomena in Darcy-Forchheimer flow over a rotating disk with magnetic field and multiple slip effects: modified Buongiorno nanofluid model

The current study focuses on investigating the significance of magnetic field and multiple slip constraints on the water-based graphene Darcy-Forchheimer nanofluid flow over a rotating disk. For a realistic approach, the modified Buongiorno nanofluid model that incorporates the combination of effective thermophysical properties, thermophoretic diffusion, and Brownian diffusion has been utilized. Engineering quantities like moment coefficient and pumping efficiency of the disk are also elucidated. The transmutation of the mathematically modeled nonlinear equations into a system of first-order ODEs are achieved through Von Kármán’s similarity transformations and are then resolved using the shooting technique along with the Runge–Kutta-Fehlberg algorithm. The highest heat transfer rate is experienced for smaller values of magnetic field parameter, Forchheimer number, porosity parameter, and thermal slip constraint. An increment rate of 88.14355% in the azimuthal drag coefficient and a decrement rate of 39.849732% in the radial drag coefficient are noted when the values of hydrodynamic slip constraint are augmented. Further, per unit increase in the volume fraction of graphene nanoparticles descends the moment coefficient and the entrainment velocity by 456.25501% and 12.48875%, respectively. The tidings of this numerical simulation have applications in spin coating, centrifugal filtration, medical equipment, gas turbine rotors, and thermal power generating systems.

Diffusiophoresis of hydrophobic spherical particles in a solution of general electrolyte

The present article deals with the diffusiophoresis of hydrophobic rigid colloids bearing arbitrary ζ-potential. We derived the generic expression for the diffusiophoretic velocity of such a colloid exposed in an externally applied concentration gradient of the general electrolyte solution. The derived expression takes into account the relaxation effect and is applicable for all values of surface ζ-potential and hydrodynamic slip length at large κa (κa≥ca.50), where κ−1 is the thickness of the electric double layer and a is the particle radius. We further derived several closed-form expressions for particle velocity derived under various electrostatic and hydrodynamic conditions when the particle is exposed in an applied concentration gradient of binary symmetric (e.g., z:z), asymmetric (1:2, 2:1, 3:1, 1:3), and a mixed electrolyte (mixture of 1:1 and 2:1 electrolytes). The results for diffusiophoretic velocity are further illustrated graphically to indicate the mutual interaction of chemiphoresis, induced electrophoresis due to unequal mobilities of cations and anions of the electrolyte, and the mechanism by which the sufficiently charged particle migrates opposite to the direction of the applied concentration gradient. The impact of hydrophobicity is further discussed.

Liquid–Liquid Flow at Nanoscale: Slip and Hydrodynamic Boundary Conditions

Nonequilibrium molecular dynamics (NEMD) simulations have been performed to describe the flow of a fluid nanolayer confined by another fluid. The results show that the behavior of liquids can still be described by the Navier-Stokes equation at the nanoscale, i.e., when only few molecular layers are involved. NEMD furthermore gives additional knowledge on flow. Indeed, while a very small slip is evidenced for a solid-liquid interface as, e.g., in lubrication, the slip lengths are significantly larger at the liquid-liquid interface, as encountered, e.g., in droplet coalescence. The slip lengths of the two fluids are linked. The increase in hydrodynamic slip for liquid-liquid interfaces is attributed to the enhancement of fluid diffusion, which reduces friction.

Combined electromagnetohydrodynamic flow in microchannels with consideration of the surface charge-dependent slip

In microscale systems, hydrodynamic slip is considered to significantly influence the fluid flow field. Existing theories of electromagnetohydrodynamic flow in hydrophobic microchannels have postulated a constant slip length and ignored the effect of the surface charge on slip. In this study, we extended prior models by considering a combined pressure-driven and electromagnetohydrodynamic flow in microchannels with consideration of surface charge-dependent slip. An analytical solution for this simple model was derived. After a detailed discussion of the obtained results, we demonstrate that the more realistic surface-charge-dependent case has smaller velocities and flow rates than the surface-charge-independent slip case. Considering the effect of the surface charge on slip, the flow rate can be reduced by up to 7% in the currently selected parameter range. Our results are useful for optimizing electromagnetohydrodynamic flow models in microchannels.

Effects of hydrophobic slips in non-uniform electrokinetic transport of charged viscous fluid in nozzle-diffuser

The mixing efficiency and electro-osmotic flow enhancement over a hydrophobic structured microchannel with nozzle-diffuser under an external electric field is studied. The interfacial surface zeta potential is varied to generate a strong convection effect between two injecting fluids from the reservoirs for a wide range of Reynolds numbers. The Poisson–Nernst–Plank model is incorporated to deal with thick and thin diffuse layers formed by a non-Newtonian electrolyte solution for the numerical simulation of the mobility of ions. To avoid the high-pressure drop complications in the computation, we have scaled the mixing efficiency with the average pressure drop. The analytical validation of the velocity and potential for thin and thick electric double layer with the existing experimental results corroborated and bridged the performance of the present model to achieve faster mixing by reducing pressure gradient. It is demonstrated that hydrodynamic slip increases the flow velocity producing larger mobility; however, the heterogeneous zeta potential generates a backflow that prevents the driving fluids leading to higher mixing efficiency, discussed in the first phase of the work. It is found that the mixing performance of Newtonian fluid is maximum for a nozzle-diffuser-shaped microchannel when all other physical parameters are constant. In the next phase, the mixing performance of shear thickening, shear thinning, and Newtonian fluid has been discussed for various physio-chemical parameters, i.e., slip length, Debye parameter, channel conical angle/slope, and heterogeneous zeta potential strength. The mixing efficiency and the pressure gradient decrease with the increase in the Debye parameter and the slip length. It is observed that the mixing efficiency can further be enhanced by increasing the heterogeneity of zeta potential strength and channel conical angle. This study can be used as a benchmark model for fabrication of chaotic mixers in hydrophobic slips with wall-mounted heterogeneous zeta potential and can be suitable for handling the power-law fluids.

Analysis of pulsatile combined electroosmotic and shear-driven flow of generalized Maxwell fluids in a microchannel with slip-dependent zeta potential

The present study investigates the flow characteristics for a pulsatile, combined electroosmotic and shear-driven flow of generalized Maxwell fluid through a straight planar microchannel including the effect of hydrodynamic slippage on asymmetric zeta potential. Mathematical expressions have been obtained in dimensionless form for the electrical potential distribution of the electrical double layer (EDL), velocity distribution and the volumetric flow rate after analytically solving the Poisson-Boltzmann and momentum equations. Critical values and critical ranges of time period of oscillating electric field have been obtained for no-slip and slip cases respectively where anomalous behaviour of dimensionless volumetric flow rate is observed. Flow rate magnitude sensitivity on hydrodynamic slippage is also analyzed. Moreover, critical values of the time period of oscillating electric field are obtained where the sensitivity of flow rate magnitude on the relaxation time of Maxwell fluid vanishes. Similarly, pivotal values of the time period of oscillating electric field are obtained at which the sensitivity of flow rate magnitude on the relaxation time of Maxwell fluid becomes invariant with the lower wall velocity.

Analysis of dissipative non‐Newtonian magnetic polymer flow from a curved stretching surface with slip and radiative effects

AbstractThe convective–radiative magnetohydrodynamic non‐Newtonian second‐grade fluid boundary layer flow from a curved stretching surface has been scrutinized in the present study. The Reiner–Rivlin second‐grade viscoelastic model is deployed which provides a good approximation for certain magnetic polymers. High temperature invokes the presence of radiative heat transfer, which is simulated with the Rosseland diffusion approximation. Viscous dissipation and Joule heating are also featured in the model and hydrodynamic (velocity) slip at the wall is also incorporated in the boundary conditions. The emerging nonlinear coupled dimensionless transport equations are solved with a Runge–Kutta method and a shooting numerical scheme. The influence of emerging multiphysical flow parameters on the dimensionless profiles is examined with the help of plots for comparative analysis of both non‐Newtonian fluid and Newtonian fluid. The numerical solutions are validated for special cases with existing works. The velocity declines for a higher magnetic field, whereas the reverse trend is noted for the temperature function. The augmentation in the thermal field is noted with increments in radiation parameters. Furthermore, the fluid temperature of the second‐grade fluid is higher with increasing Brinkmann number. The wall slip induces deceleration. Contour plots for streamlines and isotherms are also visualized and analyzed.

A meshless scheme on the electrokinetically driven flow of power-law fluid through nanochannel considering dual effects of heterogeneity in wall charge and surface wettability

The present article deals with the development of a meshless scheme to study the electrokinetically driven flow of non-Newtonian fluid through narrow confinement. Combined impact of patterned charge and hydrodynamic slip length along the channel walls is considered. The widely employed power-law model is adopted to consider non-Newtonian behaviour of the background electrolytic medium. The mathematical model to study the transport of ionized liquid consists of the Poisson equation for electrostatic potential, Nernst–Planck equations for conservation of mass of mobile electrolyte ions and the Cauchy momentum equations along with equations of continuity for the flow field. We further delineated the impact of complex flow physics on the mixing efficiency of the uncharged solute injected from the inlet. The present study has two different aspects, on one hand, the successful implementation of meshless scheme based on radial basis functions and on the other hand, to dictate the impact of patterned charge and hydrodynamic slip length on the overall electrokinetic transport of ionized liquid and its effect on the mixing of injected uncharged solute. Going beyond the widely employed Debye-Hückel approximation, we simulate the governing equations using meshless scheme based on Radial Basis Functions (RBF). The numerical results are found to be in close agreement with the available theoretical and experimental results. The computational results are further presented to indicate the impact of pertinent parameters on the flow modulation and mixing of uncharged solutes. • Combined impact of patterned charge and hydrodynamic slip length of channel walls on the electrokinetic flow modulation is considered. • Power-law model is adopted to consider the non-Newtonian rheology of the fluidic medium. • Radial basis function based meshless scheme is employed for the numerical simulation. • Impact of variable surface charge and slip length on flow modulation is analysed for maximum throughput. • Impact of modulated flow field on the mixing efficiency of injected uncharged solutes is further illustrated.

Electrical Conductance of Charged Nanopores.

A nanopore’s response to an electrical potential drop is characterized by its electrical conductance, . For the last two decades, it has been thought that at low electrolyte concentrations, , the conductance is concentration-independent such that . It has been recently demonstrated that surface charge regulation changes the dependency to , whereby the slope typically takes the values α = 1/3 or 1/2. However, experiments have observed slopes of 2/3 and 1 suggesting that additional mechanisms, such as convection and slip-lengths, appear. Here, we elucidate the interplay between three mechanisms: surface charge regulation, convection, and slip lengths. We show that the inclusion of convection does not change the slope, and when the effects of hydrodynamic slip are included, the slope is doubled. We show that when all effects are accounted for, α can take any value between 0 and 1 where the exact value of the slope depends on the material properties. This result is of utmost importance in designing any electro-kinetically driven nanofluidic system characterized by its conductance.

Effect of hydrodynamic slip on the electrophoresis of hydrophobic spherical particles in a solution of general electrolytes

Effect of hydrodynamic slip on the electrophoresis of hydrophobic spherical particles in a solution of general electrolytes

Dewetting acceleration by evaporation

Dewetting of a substrate, i.e. the liquid film retraction under partial wetting conditions, has been studied extensively over the past decades. This theoretical work deals with the dewetting phenomenon in the presence of liquid evaporation into the pure vapour atmosphere driven by substrate superheating with respect to the saturation temperature corresponding to the vapour pressure. The dynamic profile of the vapour–liquid interface is analysed numerically by using the generalised lubrication approximation that can be applied to an interface slope larger than its conventional counterpart. This approximation uses a phenomenological argument to increase the precision of calculations. For small slopes, it reduces to the conventional lubrication approach. Several nanoscale effects are included in the theory to obtain more precise results: the Kelvin effect, the hydrodynamic slip, the Marangoni effect, the vapour recoil and the interfacial thermal resistance. Their relative importance is discussed. The results include the film shape evolution, the apparent contact angle and the contact line speed, all defined by the substrate superheating and its wetting properties. These dependencies agree with existing experimental results. It is found that the dewetting is accelerated by evaporation. The numerical results are compared to those of the multiscale theory that uses two main parameters, the Voinov angle (the apparent angle obtained within the microregion problem) and the Voinov length. The latter is studied for several fluids as a function of superheating, and an approximate expression for it is proposed. A good agreement between the numerics and the multiscale theory shows the validity of the latter. This means that the dewetting speed in the presence of evaporation can be calculated with an analytical expression that requires only the Voinov angle as a numerical input. Such results are important for many applications, for instance, bubble growth in boiling or film dynamics in heat pipes.

Hydrodynamic slip significantly alters chaotic advection and scattering of small particles

We present a computational study of the effect of hydrodynamic slip at the surface of a particle on the statistical behavior of an ensemble of spherical particles in a two-dimensional von Karman flow in the wake of a cylinder. We predict that slip can lead to significant differences in escape rates, more initial positions that lead to vortex trapping at long times, and a greater uncertainty in scattering predictions. Thus, our work highlights that hydrodynamic slip significantly affects particle trajectories in unsteady flows.

QCM-D Investigations of Anisotropic Particle Deposition Kinetics: Evidences of the Hydrodynamic Slip Mechanisms.

Deposition kinetics of positively charged polymer microparticles, characterized by prolate spheroid shape, at silica and gold sensors was investigated using the quartz microbalance (QCM) technique. Reference measurements were also performed for positively charged polymer particles of spherical shape and the same mass as the spheroids. Primarily, the frequency and bandwidth shifts for various overtones were measured as a function of time. It is shown that the ratio of these signals is close to unity for all overtones. These results were converted to the dependence of the frequency shift on the particle coverage, directly determined by atomic force microscopy and theoretically interpreted in terms of the hydrodynamic model. A quantitative agreement with experiments was attained considering particle slip relative to the ambient oscillating flow. In contrast, the theoretical results pertinent to the rigid contact model proved inadequate. The particle deposition kinetics derived from the QCM method was compared with theoretical modeling performed according to the random sequential adsorption approach. This allowed to assess the feasibility of the QCM technique to furnish proper deposition kinetics for anisotropic particles. It is argued that the hydrodynamic slip effect should be considered in the interpretation of QCM kinetic results acquired for bioparticles, especially viruses.

Water Flow in Single-Wall Nanotubes: Oxygen Makes It Slip, Hydrogen Makes It Stick.

Experimental measurements have reported ultrafast and radius-dependent water transport in carbon nanotubes which are absent in boron nitride nanotubes. Despite considerable effort, the origin of this contrasting (and fascinating) behavior is not understood. Here, with the aid of machine learning-based molecular dynamics simulations that deliver first-principles accuracy, we investigate water transport in single-wall carbon and boron nitride nanotubes. Our simulations reveal a large, radius-dependent hydrodynamic slippage on both materials, with water experiencing indeed a ≈5 times lower friction on carbon surfaces compared to boron nitride. Analysis of the diffusion mechanisms across the two materials reveals that the fast water transport on carbon is governed by facile oxygen motion, whereas the higher friction on boron nitride arises from specific hydrogen–nitrogen interactions. This work not only delivers a clear reference of quantum mechanical accuracy for water flow in single-wall nanotubes but also provides detailed mechanistic insight into its radius and material dependence for future technological application.

Regression analysis on MHD Darcy-Forchheimer hybrid nanoliquid flow over an elongated permeable sheet in a porous medium with hydrodynamic slip constraint: a realistic two-phase modified Buongiorno model

Injection and suction effects play a crucial role in astronomical disciplines, fuel injection, solar collector plate, thermal protection, and aerodynamics. Therefore, the dynamics of hydromagnetic Darcy-Forchheimer hybrid nanoliquid flow over an elongated permeable sheet in the presence of hydrodynamic slip and Newtonian boundary constraints is investigated. A realistic model considering the passive control of nanoparticles and the modified Buongiorno nanoliquid model has been utilised. The modelled partial differential equations are transmuted into a system of nonlinear ordinary differential equations with the aid of apposite similarity transformations which are then resolved numerically using the finite-difference based bvp5c routine. Regression analysis is employed to statistically scrutinise the relationship between the pertinent parameters and the drag coefficients. It is observed that the -directional velocity descends with the Forchheimer number and hydrodynamic slip parameter whereas the -directional velocity ascends with the stretching parameter. It is also noted that the Biot number and the volume fraction of copper nanoparticles have a constructive effect on the hybrid nanoliquid temperature. Furthermore, lower temperature and velocity profiles were exhibited by the suction case when compared with the injection case. An improved heat transfer rate is observed for higher values of Biot number and volume fraction of copper nanoparticles.

Theoretical analysis of close-contact melting on superhydrophobic surfaces

The present study deals with close-contact melting of a vertical cylinder on a horizontal isothermal superhydrophobic surface with an array of circular posts. A new numerical model for this phenomenon is formulated under several simplifying assumptions. For the limiting case of perfect slip and thermal contact, based on the model assumptions, it is demonstrated that superhydrophobic surfaces can enhance the melting time by no more than 30 %. Numerical solution of the new model reveals that the effect of superhydrophobic hydrodynamic slip can decrease the molten layer thickness. However, due to the dominant effect of thermal slip, the heat transfer rate can be decreased significantly, and the melting time can be roughly doubled. An approximate analytical model is developed for understanding the problem dynamics better. The analytical model predictions are compared extensively against the numerical model results. For sufficiently low surface volume fractions, the analytical model provides excellent estimations of the numerical model predictions. Dimensional analysis reveals that according to the analytical model, the ratio between the melting times for superhydrophobic and regular surfaces is governed by a single dimensionless group. Moreover, according to the analytical model, the melting time on a superhydrophobic surface is always longer than on a regular surface, which agrees qualitatively with the numerical model results. Based on this analysis, a dimensionless condition for the analytical model range of validity is formulated. Finally, a conservative criterion for the liquid–gas interface stability under a close-contact melting process is established.

Asymmetric Electrokinetic Energy Conversion in Slip Conical Nanopores.

Ion current rectification (ICR) phenomena in asymmetric nanofluidic structures, such as conical-shaped nanopores and funnel-shaped nanochannels, have been widely investigated in recent decades. To date, the effect of asymmetric nanofluidic structures on electrokinetic power generation driven by the streaming current/potential has not been explored. Accordingly, this study employed a numerical model based on the Poisson equation, Nernst–Planck equation, and Navier–Stokes equation to investigate the electrokinetic energy conversion (EKEC) in a conical nanopore while considering hydrodynamic slippage. The results indicated that the asymmetric characteristics of streaming current (short-circuit current), streaming potential (open-circuit voltage), maximum power generation, maximum conversion efficiency, and flow rate were observed in conical nanopores under the forward pressure bias (tip-to-base direction) and reverse pressure bias (base-to-tip direction) once the nonequilibrium ion concentration polarization (ICP) became considerable. The rectification behaviors in the streaming current, maximum power, and maximum conversion efficiency were all shown to be opposite to those of the well-known ICR in conical nanopores. In other words, the reverse pressure bias revealed a higher EKEC performance than the forward pressure bias. It was concluded that the asymmetric behavior in EKEC is attributed to the asymmetric electrical resistance resulting from asymmetric ion depletion and ion enrichment. Particularly, it was found that the decrease in electrical resistance (i.e., the change in electrical resistance dominated by the ion enrichment) observed in the reverse pressure bias enhanced the maximum power and maximum conversion efficiency. The asymmetric EKEC characteristics became more significant with increasing slip length, surface charge density, cone angle, and pressure bias, especially at lower salt concentrations. The present findings provide useful information for the future development of EKEC in engineered membranes with asymmetric nanopores.