Wall Slip Velocity Research Articles

Newtonian flow with slip and pressure-drop predictions in hyperbolic confined geometries

We study theoretically the steady Newtonian flow in confined and hyperbolic long tubes (symmetric channels and axisymmetric pipes) considering slip along the walls. Using a stream function formulation, and the extended (or high-order) lubrication method in terms of the square of the aspect ratio of the tube, ε, the solution for the stream function is found analytically up to twentieth order in ε. At the classic lubrication limit, i.e. i.e. for a vanishing small aspect ratio, and for perfect slip conditions, the analysis predicts a plug-like velocity profile and a constant strain-rate on the midplane/axis of symmetry of the tube. A constant strain-rate is also predicted for the non-slip case. Furthermore, the high order asymptotic results for the stream function and fluid velocity are post-processed with an acceleration technique to investigate the convergence and accuracy of the solution. The results reveal the existence of a boundary layer at the inlet of the tube, the influence of which diminishes in a very short distance from the entrance. We discuss the effect of the contraction ratio of the tube and the dimensionless slip coefficient on the midplane/centerline and wall (slip) velocities, as well as on the average pressure-drop, required to maintain a constant flow-rate. The acceleration of converge technique on the solution for the pressure-drop revealed a remarkable convergence at a value slightly larger (∼1 %) than the value predicted by the classic lubrication theory. Finally, we comment on the common practice in the literature for approaching the velocity profile with the velocity profile at the classic lubrication limit, and we compare the high-order results for the strain rate at the midplane/centerline with the effective strain rate previously derived in the literature by Housiadas & Beris, J. Rheology, 68(3), 327–339, 2024.

Effects of interface friction states on plastic deformation in metal surface and bulk

Interface friction at the tool/die-material interface plays a pivotal role in metal plastic processes, significantly impacting material deformation behavior near the contact surface. This study focuses on understanding friction-induced deformation, particularly the plastic boundary layer and surface expansion behavior, at the tool/die-material interface by employing direct in-situ observations, coupled with high-speed imaging and particle image velocimetry techniques. It proves that interface friction determines the wall-slip behaviors and subsequently results in the non-uniform surface expansion distribution. Moreover, our results indicate that the application of lubricant alters the wall-slip velocity and localized surface expansion by 60% and 76%, respectively, at the contact interface. Based on these observations, a quantitative method for assessing the effectiveness of lubrication is proposed.

Shear layers and plugs in the capillary flow of wormlike micellar gels.

Wormlike micellar solutions formed by long-chained zwitterionic surfactants show gel-like rheology at room temperature and have recently been found to exhibit other complex and interesting rheological features. We study the dynamics of these wormlike micellar gels in a pipe-flow scenario using particle imaging and tracking velocimetry and report the existence of plug flows with strong wall slip and non-parabolic velocity profiles for different surfactant concentrations and imposed flow rates. We rationalize these results as features of a developing transient flow of a viscoelastic solution in space and time. We show that evolution of shear layers is governed by intermittent flows, asymmetric velocity profiles and flow induced heterogeneity. Our experiments shed light on the transient fluid dynamics of wormlike micelles in simple geometries and highlight the complexity of flows involving wormlike micellar gels and similar soft matter systems in canonical flows.

Toward a continuum description of lubrication in highly pressurized nanometer-wide constrictions: The importance of accurate slip laws.

The Reynolds lubrication equation (RLE) is widely used to design sliding contacts in mechanical machinery. While providing an excellent description of hydrodynamic lubrication, friction in boundary lubrication regions is usually considered by empirical laws, because continuum theories are expected to fail for lubricant film heights h0 ≪ 10 nm, especially in highly loaded tribosystems with normal pressures pn ≫ 0.1 GPa. Here, the performance of RLEs is validated by molecular dynamics simulations of pressurized (with pn = 0.2 to 1 GPa) hexadecane in a gold converging-diverging channel with minimum gap heights h0 = 1.4 to 9.7 nm. For pn ≤ 0.4 GPa and h0 ≥ 5 nm, agreement with the RLE requires accurate constitutive laws for pressure-dependent density and viscosity. An additional nonlinear wall slip law relating wall slip velocities to local shear stresses extends the RLE's validity to even the most severe loading condition pn = 1 GPa and h0 = 1.4 nm. Our results demonstrate an innovative route for continuum modeling of highly loaded tribological contacts under boundary lubrication.

Frictional boundary condition for lattice Boltzmann modelling of dense granular flows

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

Novel insights into abrasive flow machining uniformity for SLM channels

Selective laser melting (SLM) has emerged as a transformative technology for fabricating intricate parts. However, a deteriorated as-built surface remains an Achilles’ heel due to the inherent layer-wise building features, driving the demand for post-finishing processes like abrasive flow machining (AFM) for internal channel refinement. Despite AFM's potential to improve surfaces, a significant research gap exists in ensuring uniform material removal and consistent surface quality. This challenge is accentuated by the complex geometry of SLM channels and the lack of a detailed material removal model considering wall slip velocity and interaction forces. To address this challenge, this study delves deep into the post-finishing process uniformity of AFM for internal channels made by SLM. Investigating the impacts of building orientation angle, abrasive media viscosity, and internal channel geometry on finishing uniformity, the nuances of material removal, surface morphology, and roughness were explored with specially designed rectangular right-angle tubes as samples. The proposed method introduced a CFD simulation model that captures complex abrasive media behaviors, including wall slip and shear thinning. Furthermore, the innovative approach of the study is highlighted by the development of a modified Preston material removal model, which for the first time utilizes the concentrated suspensions theory to reveal the physical mechanisms underlying material removal in AFM. Our exhaustive research demonstrates that experimental outcomes harmoniously resonated with our modified Preston model's predictions, offering robust validation. This significant finding reveals a direct positive correlation between material removal and several parameters, notably particle phase normal stress but not pressure effects. Moreover, geometric variations in the flow channel significantly impact non-uniform removal in AFM, with the challenge escalating as abrasive media viscosity increases. Contrarily, the role of the building orientation angle is less pronounced. Insights into surface quality indicate that a steeper build orientation angle diminishes the initial surface quality of SLM channels. However, this disparity lessens as AFM progresses, underscoring AFM's potential to achieve uniform surfaces of high quality. Therefore, this study offers exceptional insights into AFM uniformity for SLM channels, highlighting pivotal parameters and their effects.

Mapping surface defects in highly-filled wood fiber polymer composite extrusion from inline spectral analysis

Surface defects in highly-filled wood polymer composites (WPCs) are mapped in single-screw extrusion via inline optical spectral analysis for the first time. The effects of wood fiber content and drying on the dynamics of surface defects are spatio-temporally resolved via space–time inline optical imaging. Surface tearing appeared from the lowest shear rates investigated followed by a gradual decay in spectral intensity with increasing shear rates/slip velocities. This is accompanied by broadening of the surface tearing characteristic frequency while the average wavelength is estimated to remain constant within the experimental conditions. Increasing shear rates, drying and increasing wood fiber content showed mitigating effects on surface tearing. However, surface tearing in undried samples was still present even at the highest shear rates and high wall slip velocities. A regime where the extrudate surface is dominated by bubbles at high shear rates and low wood fiber contents in undried WPCs was identified.

Significance of Navier’s slip and Arrhenius energy function in MHD flow of Casson nanofluid over a Riga plate with thermal radiation and nonuniform heat source

Riga plate is known to create a crossing electric and magnetic field to generate a wall-parallel Lorentz force. The significance of Casson nanofluid flow past a Riga plate is observed in the sphere of engineering, such as polymer extrusion, food manufacturing, plastic films, oil reserves and geothermal manufacturing. Researchers are interested in this model because of its potential use in biological rheological models. As Casson nanofluid flows are of great interest, this study aims to investigate the three-dimensional magnetohydrodynamics (MHD) flow with heat and mass transport of Casson nanofluid over a flat Riga plate. As a novelty, this study also includes the effectiveness of wall velocity slip, activation energy, nonlinear radiation, and temperature and space-dependent heat source/sink. Suitable similarity transformations have been employed to generate the dimensionless ordinary differential equations (ODEs) from the partial differential equations (PDEs) regulating the fluid flow problem. The transformed nonlinear boundary value problem is then solved numerically using the in-built routine “bvp4c” in MATLAB. The visual demonstrations are provided for the effects of various significant physical factors on the flow, heat and mass distributions. On the other hand, wall shear stress and rates of heat and mass transport at the surface are measured and displayed numerically in tabular form. The findings indicate that the fluid velocity in both directions slows as the velocity slip parameter increases. However, the velocity profile is escalated with the boost of modified Hartmann number. An increase in heat source parameters leads to decrease the heat transmission rate at the wall. The higher values of the radiation parameter result in a better wall heat transmission rate. Further, the rate of mass transport drops when the activation energy parameter is hiked.

Modeling and numerical simulation of flow processes of wood‐polymer composites

AbstractThe combination of natural fibers and polymers is finding expanding application in a range of industrial branches, and knowledge of the material behavior is essential for further improving the products and the processing procedure. In this work, the material behavior of wood‐polymer composites (WPC) will be modeled and numerical simulations will be used to investigate the flow behavior. By means of rheological measurements, a shear thinning flow behavior of the composite can be determined, which is also often taken into account in the numerical simulation of WPC processing tools. Increasing shear viscosity and a formation of a yield point with increasing wood content can be observed. However, in addition to the shear‐dominant deformation states, noticeable strain deformations also occur due to cross‐sectional changes. In order to experimentally investigate and model the behavior of WPC under strain, this work involves measurements on hyperbolic dies in which a uniaxial strain state is present and extensional viscosity can be derived from this. Different boundary conditions such as noSlip, navierSlip and full slip are investigated in the simulations. In addition, during the extrusion of WPC, wall shear stresses of about 0.1 MPa and above can be observed. Measurements in a high‐pressure capillary rheometer allow the wall slip velocity to be measured as a function of the wall shear stress at different wood contents. The wall slip behavior is modeled and taken into account accordingly as a boundary condition in the numerical simulations using OpenFOAM [8].

Lie-group method solutions for a viscous flow in a dilating-squeezing permeable channel with velocity slip

The investigation focuses on the effects of wall velocity slip on the solution of a viscous, laminar, incompressible channel flow subjected to small-scaled contraction and expansion of the weakly permeable walls. The study of such flow systems is often contextual for fluid transport in biological organisms. In the considered flow configuration, the vertically moving porous walls enable the fluid to enter or exit with a constant rate. The tangential slip velocity of the flow at the porous walls is modeled with the Navier slip boundary condition. The flow dynamics inside the channel is governed by the full Navier–Stokes equations. The Lie symmetry analysis and the invariant method are adopted to reduce the number of independent variables in the system of governing equations. Consequently, a single fourth-order ordinary differential equation is obtained, which is solved analytically by the double perturbation method and the variation of iteration method. The solutions are compared for different arrangements. Furthermore, the approximated analytical solutions are likened to the numerical solutions obtained from a fourth-order Runge–Kutta solver embedding the Shooting method to check the accuracy. It is observed that the boundary layers are formed, and the flow rapidly turns near the walls, when suction and wall contraction coexist. Alternatively, if injection and wall expansion are paired, the flow adjacent to the walls is delayed. The existence of wall velocity slip advances the near-wall velocity and cuts down the speed of centerline velocity. It results in a change in the volumetric flow rate and shear rate. The overall pressure is also varied by higher wall velocity slip. The results are explored for different values of the permeation Reynold number and the dimensionless wall dilation rate to capture all possible impacts of the flow parameters. The current analysis rectifies the existing errors in the work of Boutros et al. [“Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability,”Appl. Math. Model. 31(6), 1092–1108 (2007)] with the no-slip boundary condition and discusses the overall influences of slip boundary condition on the Lie symmetry solution of the flow system.

Controlling rheology via boundary conditions in dense granular flows.

Boundary shape, particularly roughness, strongly controls the amount of wall slip in dense granular flows. In this paper, we aim to quantify and understand which aspects of a dense granular flow are controlled by the boundary conditions, and to incorporate these observations into a cooperative nonlocal model characterizing slow granular flows. To examine the influence of boundary properties, we perform experiments on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall; the latter is selected among 6 walls with various roughnesses, local concavity, and compliance. We find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observe how the internal stresses fluctuate more for rougher boundaries, corresponding to a lower wall slip, and connect this observation to the propagation of nonlocal effects originating from the wall. Our measurements indicate a universal relationship between dimensionless fluidity and velocity.

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

AbstractSlip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

NEW AND HIGHLY EFFICIENT METHOD TO MEASURE STEADY SHEAR VISCOSITY AND WALL SLIP OF RUBBER COMPOUNDS: CLOSED-BOUNDARY RHEOMETER (RPA)

ABSTRACT The rubber process analyzer was commercialized by Monsanto Rubber Instrument and Equipment company in the early 1990s. In its initial version, the RPA was able to perform only oscillatory-type tests, which varied in frequency and strain. Later, it offered a controlled strain–stress relaxation test. Only recently and not for all models has a controlled steady shear test been made available. Using this type of test, the instrument has successfully measured steady shear viscosity with high repeatability without correction. The results fit well with other rheometers or viscometers when no-slip conditions are ensured. The closed-boundary configuration prevents edge fracture, as commonly experienced with open-boundary rheometers (DMA) on high-viscosity, high-elasticity materials. A comparison of results using grooved dies (no-slip) and polished dies (slip) readily provides wall slip velocity under constant pressure. The results of wall slip versus shear stress follow a power-law function per the Navier slip law [F(V) = −k(Vr)e]. This method separates the shear rate from pressure effects on wall slip. It questions pressure-driven flow instruments (capillary rheometer), which use pressure measurements for shear stress calculations, and prevents an easy and controlled change of the die surface roughness.

Superhydrophobic SLA 3D printed materials modified with nanoparticles biomimicking the hierarchical structure of a rice leaf

ABSTRACT The rice leaf, combining the surface properties of lotus leaves and shark skin, presents outstanding superhydrophobic properties motivating its biomimesis. We created a novel biomimetic rice-leaf superhydrophobic surface by a three-level hierarchical structure, using for a first time stereolithographic (SLA) 3D printed channels (100µm width) with an intrinsic roughness from the printing filaments (10µm), and coated with TiO2 nanoparticles (22 and 100nm). This structure presents a maximum advancing contact angle of 165° characterized by lower both anisotropy and hysteresis contact angles than other 3D printed surfaces, due to the presence of air pockets at the surface/water interface (Cassie-Baxter state). Dynamic water-drop tests show that the biomimetic surface presents self-cleaning, which is reduced under UV-A irradiation. The biomimetic surface further renders an increased floatability to 3D printed objects meaning a drag-reduction due to reduced water/solid contact area. Numerical simulations of a channel with a biomimetic wall confirm that the presence of air is essential to understand our results since it increases the average velocity and decreases the friction factor due to the presence of a wall-slip velocity. Our findings show that SLA 3D printing is an appropriate approach to develop biomimetic superhydrophobic surfaces for future applications in anti-fouling and drag-reduction devices.

Experimental study of rheological behavior of foam flow in capillary tubes

• Rheological behavior of the pre-generated foam was studied in capillary tubes • Tube materials were: PTFE and FEP (hydrophobic) and glass tubes (hydrophilic) • Foam behaves as shear-thinning fluid in all capillary tubes • Transition foam quality in tubes depends on the material type and tube diameter • Foam's apparent viscosity is higher in hydrophobic tubes than in hydrophilic tube due to wall-slip velocity • Wall-slip velocity depends on the tube material type and diameter • Foam texture in tubes is highly dependent on foam quality and flow rate Studies of foam flow in highly permeable porous media are still limited due to foam's complex behavior and discrepancies in foam research. Specifically, it is still unclear how foam flows in capillary tubes and what the effects of material and tube diameter are. We have investigated the rheology of pre-generated foam in capillary tubes. Experiments were carried out using two types of capillary tubes: hydrophobic (PTFE – polytetrafluoroethylene; FEP – fluorinated ethylene propylene) and hydrophilic (GT – glass tubes). The foam was previously formed in the sand-pack by co-injecting a surfactant solution and nitrogen gas. We investigated the effect of material and tube size on foam rheology versus gas fraction (for a fixed flow rate) and flow rate (for a fixed gas fraction). A three-parameter Herschel-Bulkley model was used to describe foam rheology in capillary tubes. Pictures of foam flow in GT and FEP tubes were taken to determine the mean bubble area using image analysis. We estimated wall-slip velocity in capillary tubes and compared the results with the bulk-foam rheology using an analytical expression of the Herschel-Bulkley model for volumetric flow through the circular tubes. We observed shear-thinning behavior in all capillary tubes (FEP, PTFE, GT), and the Herschel-Bulkley model successfully fitted its behavior. The foam in PTFE tubes behaved as a yield-stress fluid, while yield stress was not observed in GT and FEP tubes. We also found that transition foam quality depends on the material type and tube diameter. The results show that foam's apparent viscosity is higher in hydrophobic tubes (FEP and PTFE tubes) than in hydrophilic glass tubes. This was explained by the wall-slip velocity being higher in glass tubes than in FEP and PTFE tubes because of the difference in surface roughness. The corrected flow rate without wall slip matches the flow rate calculated using the measured bulk foam viscosity better. Therefore we conclude that considering wall-slip velocity is important when studying foam flow in porous media.

Entropy analysis of thermally radiating MHD slip flow of hybrid nanoparticles (Au-Al2O3/Blood) through a tapered multi-stenosed artery

This paper deals with the heat transfer and entropy generation analysis of unsteady blood flow through a tapered multi-stenosed artery incorporating hybrid nanoparticles (gold and alumina) with Joule heating, viscous dissipation, radiation, and inclined magnetic field. For the realistic behavior of blood, Reynold’s viscosity model is considered in this study. The Crank-Nicolson scheme is applied to solve the continuity, momentum, and energy equations with appropriate initial and boundary conditions. The important findings are represented graphically and have been analyzed for different values of the dimensionless parameters. The velocity contours for several emerging parameters are presented to study the overall behavior of blood flow patterns. It is observed that the axial flow accelerates with increasing wall slip velocity (ws) due to the presence of the hydrodynamic wall slip effect. The velocity profile increases as the concentration of Au nanoparticles increases, while the reverse effect is noted for the concentration of Al2O3 nanoparticles. The current findings may be helpful for biomedical scientists who are interested in investigating the treatment of various cardiovascular diseases.

Unsteady MHD radiative-dissipative flow of Cu-Al[formula omitted]O[formula omitted]/H[formula omitted]O hybrid nanofluid past a stretching sheet with slip and convective conditions: A regression analysis

The current investigation is concerned with the study of unsteady laminar flow with heat and mass transfer of an incompressible and hydromagnetic Cu-Al2O3/H2O hybrid nanofluid near a nonlinearly permeable stretching sheet in the presence of nonlinear thermal radiation, viscous-Ohmic dissipation and velocity slip. Further, the impacts of heat generation/absorption, chemical reaction, convective heat and mass conditions at the boundary are also considered. The prevailing model equations are converted into dimensionless form with the implementation of some suitable similarity transformations. A shooting technique along with Runge–Kutta–Fehlberg method is used to develop the solutions for momentum, thermal and mass fields. The impingements of several controlling parameters on the velocity as well as heat and mass distributions are demonstrated and exhibited graphically. Also, the variations in the physical quantities like skin-friction coefficient, Nusselt and Sherwood numbers are delineated with the help of graphs. The analysis reveals that Hartree pressure gradient and wall velocity slip have the tendency to slow down the flow. On the other side, the velocity ratio parameter, thermal radiation and Biot number boost the fluid temperature. Furthermore, the regression analysis presents that skin-friction is more prone to the suction parameter than the Hartree pressure gradient while the Nusselt number is much sensitive to the radiation parameter as compared to the Eckert number. However, the Sherwood number is dominated by the solutal Biot number.

Quantification of shear viscosity and wall slip velocity of highly concentrated suspensions with non-Newtonian matrices in pressure driven flows

The rheological characterization of concentrated suspensions is complicated by the heterogeneous nature of their flow. In this contribution, the shear viscosity and wall slip velocity are quantified for highly concentrated suspensions (solid volume fractions of 0.55–0.60, D4,3 ~ 5 µm). The shear viscosity was determined using a high-pressure capillary rheometer equipped with a 3D-printed die that has a grooved surface of the internal flow channel. The wall slip velocity was then calculated from the difference between the apparent shear rates through a rough and smooth die, at identical wall shear stress. The influence of liquid phase rheology on the wall slip velocity was investigated by using different thickeners, resulting in different degrees of shear rate dependency, i.e. the flow indices varied between 0.20 and 1.00. The wall slip velocity scaled with the flow index of the liquid phase at a solid volume fraction of 0.60 and showed increasingly large deviations with decreasing solid volume fraction. It is hypothesized that these deviations are related to shear-induced migration of solids and macromolecules due to the large shear stress and shear rate gradients.

Energy efficiency analysis of mass transport enhancement in time-periodic oscillatory electroosmosis

The streamwise mass transport of passive, neutral non-reacting solutes in oscillatory electroosmotic microchannel flows is theoretically investigated from an energy consumption and efficiency perspective for general asymmetric wall zeta potentials and slip velocities. Analytical solutions to the averaged mass transport and total power input (consisting of Joule heating, viscous dissipation, and sliding friction) are obtained and expressed in terms of the relevant parameters governing the system. Particularly, we define a “χg-parameter” to quantify the mass transport gained (excluding pure diffusion) per total power input in our analysis and discussions. While the no-slip, symmetric potential χg-performances agree with the mass transport results reported in previous literature, a “resonance like” behavior in the χg-performances is identified for large enough Womersley numbers and symmetric slip lengths despite the extra sliding friction, viscous dissipation, and Joule heating consumptions in the symmetric zeta potential configuration. When favorable asymmetries in the wall potentials and slip lengths are introduced, the χg-performances are not only considerably improved, but also highly correlated with the magnitudes of the velocity gradients in the oscillatory velocity profiles, hence reinforcing the physical picture of Taylor–Aris dispersion. Geometric symmetry can be identified among distinct velocity profiles which yield the same χg-performance. These profiles are generally associated with particular families of wall potential and/or slip length combinations also exhibiting symmetry among one another. Finally, the aspect ratio of the slit microchannel (width divided by length) is found to play a crucial role in significantly improving the χg-energy efficiency of mass transport in time-periodic electroosmosis.

Effect of imposed shear on the dynamics of a contaminated two-layer film flow down a slippery incline

The linear instability of a surfactant-laden two-layer falling film over an inclined slippery wall is analyzed under the influence of external shear, which is imposed on the top surface of the flow. The free surface of the flow and the interface among the fluids are contaminated by insoluble surfactants. Dynamics of the fluid layers are governed by the Navier–Stokes equations, and the surfactant transport equations regulate the motion of the insoluble surfactants at the interface and free surface. Instability mechanisms are compared by imposing the external shear along and opposite to the flow direction. A coupled Orr–Sommerfeld system of equations is derived using the perturbation technique and normal mode analysis. The eigenmodes corresponding to the Orr–Sommerfeld eigenvalue problem are obtained by employing the spectral collocation method. The numerical results imply that the stronger external shear destabilizes the interface mode instability. However, a stabilizing impact of the external shear on the surface mode is noticed if the shear is imposed in the flow direction, which is in contrast to the role of imposed external shear on the surface mode for a surfactant-laden single layer falling film. Furthermore, in the presence of strong imposed shear, the overall stabilization of the surface mode by wall velocity slip for the stratified two-fluid flow is also contrary to that of the single fluid case. The interface mode behaves differently in the two zones at the moderate Reynolds numbers, and higher external shear magnifies the interfacial instability in both zones. An opposite trend is observed in the case of surface instability. Moreover, the impression of shear mode on the primary instability is analyzed in the high Reynolds number regime with sufficiently low inclination angle. Under such configuration, dominance of the shear mode over the surface mode is observed due to the weaker impact of the gravitational force on the surface instability. The shear mode can also be stabilized by applying the external shear in the counter direction of the streamwise flow. Conclusively, the extra imposed shear on the stratified two-layer falling film plays an active role in the control of the attitude of the instabilities.