Slip Length Research Articles

Avalanches and Extreme Value Statistics of a Mesoscale Moving Contact Line.

We report direct atomic force microscopy measurements of pinning-depinning dynamics of a circular moving contact line (CL) over the rough surface of a micron-sized vertical hanging glass fiber, which intersects a liquid-air interface. The measured capillary force acting on the CL exhibits sawtoothlike fluctuations, with a linear accumulation of force of slope k (stick) followed by a sharp release of force δf, which is proportional to the CL slip length. From a thorough analysis of a large volume of the stick-slip events, we find that the local maximal force F_{c} needed for CL depinning follows the extreme value statistics and the measured δf follows the avalanche dynamics with a power law distribution in good agreement with the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. The experiment provides an accurate statistical description of the CL dynamics at mesoscale, which has important implications to a common class of problems involving stick-slip motion in a random defect or roughness landscape.

Enhanced flow in deformable carbon nanotubes

Many researchers observed enhanced water flow through carbon nanotubes (CNTs) and attributed the reason to large slips. Even after taking significant slip effects into account, there remain unaddressed observations of significant improvements in flow rates. As CNTS are deformable, we represent nanotubes with a deformable-wall using a linear pressure–area relationship. We assume lubrication assumption, and using the properties of nanoconfined water, we derive the model for deformable-nanotubes. We validated our derived model in its limiting cases with the previously reported results in the literature. We compare the predictions by our deformable-wall and rigid-wall model with the experimental results and the MD-simulation predictions by multiple literature studies. Many studies were well-predicted by the rigid-wall model with slips. However, we find that there are many studies with high porosity and thin wall tubes, where elasticity or deformability of the tube is essential in modeling, which is well-predicted by our deformable-wall model with slips. In our study, we focus on investigating the impact of two key factors: the deformability, and the slip length on the flow rate. We find that the flow rate inside the tube increases as the deformability increases or the thickness T and elastic modulus E of the tube-wall decrease). We also find that the flow rate in deformable tubes scales as m˙deformable∼1/α0 for (Δp/αAo)≪1, m˙deformable∼1/α for (Δp/αAo)∼O(10−1) and m˙deformable∼α2 for (Δp/αAo)∼O(1). Further, for a given deformability, the percentage change in flow rate in the smaller diameter of the tube is much larger than the larger diameter. As the tube diameter decreases for the given pressure, Δm˙/m˙ increases. We find that for rigid-tube, the flow rate varies m˙rigid∼Δp, whereas for the deformable-tubes, the flow rate scales as m˙deformable∼Δp2 for (Δp/αAo)∼O(10−1), and finally to m˙deformable∼Δp3 for (Δp/αAo)∼O(1). We further find that slip also significantly increases flow rate, but, deformability has more substantial effect.

Fluid Slip and Drag Reduction on Liquid-Infused Surfaces under High Static Pressure.

Liquid-infused surfaces (LIS) have been shown to reduce the huge frictional drag affecting microfluidic flow and are expected to be more robust than superhydrophobic surfaces when exposed to external pressure as the lubricant in LIS is incompressible. Here, we investigate the effect of applying static pressure on the effective slip length measured on Teflon wrinkled surfaces infused with silicone oil through pressure measurements in microfluidic devices. The effect of static pressure on LIS was found to depend on air content in the flowing water: for degassed water, the average effective slip length was beff = 2.16 ± 0.90 μm, irrespective of applied pressure. In gassed water, the average effective slip length was beff = 4.32 ± 1.06 μm at zero applied pressure, decreased by 55% to 2.37 ± 0.90 μm when the pressure was increased to 50 kPa, and then remained constant up to 200 kPa. The result is due to nanobubbles present on LIS, which are compressed or partially dissolved under pressure, and the effect is more evident when the size and portion of surface nanobubbles are higher. In contrast, on superhydrophobic wrinkles, the decline in beff was more sensitive to applied pressure, with beff = 6.8 ± 1.4 μm at 0 kPa and, on average, beff = -1 ± 3 μm for pressures higher than 50 kPa for both gassed and degassed water. Large fluctuations in the experimental measurements were observed on superhydrophobic wrinkles, suggesting the nucleation of large bubbles on the surface. The same pressure increase did not affect the flow on smooth substrates, on which gas nanobubbles were not observed. Contrary to expectations, we observed that drag reduction in LIS is affected by applied pressure, which we conclude is because, in a similar manner to superhydrophobic surfaces, they lose the interfacial gas, which lubricates the flow.

Viscoplastic flows in superhydrophobic channels with oriented grooves: From anisotropic slip to secondary flow

In this work, Poiseuille flows of viscoplastic fluids in typically thin channels equipped with a superhydrophobic groovy wall are numerically studied. The orientation of the groove relative to the applied pressure gradient can vary, and this orientation is measured via the groove orientation angle (θ). In particular, longitudinal (θ=0), oblique (0<θ<90∘), and transverse (θ=90∘) flow configurations are considered. The Bingham constitutive equation is employed to model the viscoplastic rheology, within the framework of the Papanastasiou regularization method. Assuming that air (gas) fills the groove completely and that the formed liquid/air interface remains flat while pinned at the groove edges, the viscoplastic fluid slippage is modeled on the liquid/air interface using the Navier slip law. Due to the anisotropic slip dynamics for the oblique flow configuration, a secondary flow is generated normal to the direction of the pressure gradient, offering unique flow features. Our work systematically analyzes the effects of the flow parameters, i.e., the groove orientation angle (θ), the Bingham (B) and slip (b) numbers, the groove periodicity length (ℓ), and the slip area fraction (φ) on the flow variables of interest, i.e., the main and secondary velocity fields, the unyielded center plug zone, the effective slip length tensor (χ), the secondary flow index (IS), the slip angle difference (θ−s), and the pressure drop (ΔP). It is demonstrated that χ’s shear component, IS, and θ−s are maximum at intermediate θ, the value of which generally decreases with B. In addition, the center plug is unbroken for the longitudinal flow while it breaks with an increase in θ for sufficiently large b.

Vorticity dynamics at partial-slip boundaries

In this paper we discuss the dynamics of vorticity at partial-slip boundaries. We consider the total vector circulation, which includes both the total vorticity of the fluid and the slip velocity at the boundary (the interface vortex sheet). The generation of vector circulation is an inviscid process, which does not depend on either viscosity or the slip length at the boundary. Vector circulation is generated by the inviscid relative acceleration between the fluid and the solid, due to either tangential pressure gradients or tangential acceleration of the partial-slip wall. While the slip length does not affect the creation of vector circulation, it governs how vector circulation is distributed between the total vorticity of the fluid and the interface vortex sheet. Specifically, the partial-slip boundary condition prescribes the ratio between boundary vorticity and the strength of the interface vortex sheet, and the viscous boundary flux transfers vector circulation between the interface vortex sheet and the fluid interior to maintain this condition. The interaction between a vortex ring and a partial-slip wall is examined to highlight various aspects of this formulation. For the head-on collision, the quantity of vector circulation diffused into the fluid as secondary vorticity increases as the slip length is decreased, resulting in a stronger secondary vortex and increased rebound of the vortex ring. For the oblique interaction, the extent to which the vortex ring connects to the boundary increases as the slip length is increased.

Boundary slip and lubrication mechanisms of organic friction modifiers with effect of surface moisture

Surface moisture or humidity impacting the lubrication property is a ubiquitous phenomenon in tribological systems, which is demonstrated by a combination of molecular dynamics (MD) simulation and experiment for the organic friction modifier (OFM)-containing lubricant. The stearic acid and poly-α-olefin 4cSt (PAO4) were chosen as the OFM and base oil molecules, respectively. The physical adsorption indicates that on the moist surface water molecules are preferentially adsorbed on friction surface, and even make OFM adsorption film thoroughly leave surface and mix with base oil. In shear process, the adsorption of water film and desorption OFM film are further enhanced, particularly under higher shear rate. The simulated friction coefficient (that is proportional to shear rate) increases firstly and then decreases with thickening water film, in good agreement with experiments, while the slip length shows a contrary change. The wear increases with humidity due to tribochemistry revealing the continuous formation and removal of Si-O-Si network. The tribological discrepancy of OFM-containing lubricant in dry and humid conditions is attributed to the slip plane’s transformation from the interface between OFM adsorption film and lubricant bulk to the interface between adsorbed water films. This work provides a new thought to understand the boundary lubrication and failure of lubricant in humid environments, likely water is not always harmful in oil lubrication systems.

Electroosmosis of viscoelastic fluids in pH-sensitive hydrophobic microchannels: Effect of surface charge-dependent slip length

We analytically investigated the electroosmotic flow characteristics of complex viscoelastic liquids within a charged hydrophobic microchannel, considering the pH and salt concentration-dependent surface charge effects in our analysis. We examined the variation of the electric-double layer (EDL) potential field, the surface charge-dependent slip (SCDS) length, the flow field, the viscosity ratio, and both normal and shear stresses in relation to the bulk pH, bulk salt concentration, and Deborah number of the solution. Our current findings indicate that, under strong flow resistance due to increased electrical attraction on counter ions, a highly basic solution with a high EDL potential magnitude results in a significant decrease in the slip length. Neglecting the effect of SCDS leads to an overestimation of flow velocity, with this overprediction being more pronounced for highly basic solutions. This overestimation diminishes as bulk salt concentration increases, particularly when compared to strongly acidic solutions. Furthermore, a noticeable increase in average velocity is observed as the Deborah number rises for highly basic solutions compared to highly acidic ones. This is attributed to the substantial reduction in apparent viscosity caused by the shear-thinning nature of the liquid at higher shear rates, supported by a larger zeta potential modulated strong electrical force for basic solutions. Additionally, we found that the intensity of shear and normal stresses tends to increase with bulk pH, primarily due to the rise in electric body force at higher zeta potential. These results can potentially inform the design and development of a compact, nonmoving electroosmotic pump for transporting biological species with varying physiological properties, such as solution pH. This technology could be applied in subsequent processes involving mixing, separation, flow-focusing for cell sorting, and other related applications.

Flow past a heated slippery corner

Discussed in this paper is the unsteady, laminar, two-dimensional, viscous flow around a corner subject to Navier-slip conditions characterized by a slip length, γ, with 0 ≤ γ ≤ 1. Comparisons with no-slip (γ = 0) boundary conditions are made to assess the impact of a slippery surface. Both isothermal and heated flows are considered including forced and mixed convection. A numerical solution procedure utilizing boundary-layer coordinates is outlined. Numerous simulations have been compiled for the Reynolds number Re = 100 and Rayleigh numbers Ra = 0, 1, 10. Various results and comparisons are presented and discussed.

Impact of sandpaper grit size on drag reduction and plastron stability of super-hydrophobic surface in turbulent flows

In this work, we experimentally investigated the impact of surface roughness on drag reduction as well as the plastron stability of superhydrophobic surfaces (SHSs) in turbulent flows. A series of SHSs were fabricated by spraying hydrophobic nanoparticles on sandpapers. By changing the grit size of sandpapers from 240 to 1500, the root mean square roughness height (krms) of the SHSs varied from 4 to 14 μm. The experiments were performed in a turbulent channel flow facility, where the mean flow speed (Um) varied from 0.5 to 4.4 m/s, and the Reynolds number (Rem) based on Um and channel height changed from 3400 to 26 400. The drag reduction by SHSs was measured based on pressure drops in the fully developed flow region. The plastron status and gas fraction (φg) were simultaneously monitored by reflected-light microscopy. Our results showed a strong correlation between drag reduction and krms+ = krms/δv, where δv is the viscous length scale. For krms+ &amp;lt; 1, drag reduction was independent of krms+. A maximum 47% drag reduction was observed. For 1 &amp;lt; krms+ &amp;lt; 2, less drag reduction was observed due to the roughness effect. And for krms+ &amp;gt; 2, the SHSs caused an increase in drag. Furthermore, we found that surface roughness influenced the trend of plastron depletion in turbulent flows. As increasing Rem, φg reduced gradually for SHSs with large krms, but reduced rapidly and maintained as a constant for SHSs with small krms. Finally, we found that as increasing Rem, the slip length of SHS reduced, although φg was nearly a constant.

Modeling flow through tubes and annuli with liquid‐infused surfaces for enhanced stability of the fluid‐fluid interface

AbstractSuperhydrophobic (SHS) and liquid‐infused surfaces (LIS) have shown great potential in various engineering applications. Due to their heterogeneous surface properties, a mathematical description of the flow behavior along such surfaces is challenging. Circular textured surfaces are of particular importance. They are modeled as either axially traversed tubes or annuli consisting of no‐slip walls that are padded with rotationally symmetric finite‐shear regions. The latter represents a viscous interaction zone with a second fluid, assumed with layer thickness zero. Zimmermann and Schönecker provide analytical equations that describe the flow field and effective slip length for such geometries. They are applicable to Newtonian fluids of arbitrary viscosity ratio. This article emphasizes the development of principles and guidelines for the design of SHS and LIS to enhance sliding effects, based on these analytical models. The approach presented here facilitates an geometric evaluation of slippery circular surfaces, aiming to offer insights for the design. Through this research, the potential for significant energy savings and enhanced fluid transport performance can be realized, contributing to the development of more efficient fluid engineering systems.

Simulation and Experimental on Thermal Behavior of Hydrostatic Thrust Bearing Based on Superhydrophobic/oleophobic Surface

Abstract The temperature rises of oil film in hydrostatic bearings at high-speed lead to a reduction in load capacity, accuracy and stability. In this paper, a superhydrophobic/oleophobic surface with micro-bulges structure is proposed. The surface is prepared by laser cross-scanning and chemical modification. The contact angle (CA) of surface is 138° and the boundary condition of surface modificated from non-slip to slip condition. The relationship between the slip length and the height of the micro-bulges structure is established by rheological experiments. By the simple partial simulations, validity of the temperature rise reduction on the superhydrophobic/oleophobic surface is verified. Then a bearing test rig was set up to measure temperature and load capacity of bearings at multiple points, the performance of smooth primary surface/structured oleophobic surface thrust bearings was compared. Results show that the structured bearing has lower oil film temperature and higher load capacity than the smooth bearing. The prepared oleophobic surface can effectively suppress the temperature rise at high speed conditions, and significantly increase the bearing load capacity.

Effects of variable slip length over induced electric potentials in microchannels

The exploration of new alternatives in renewable energy has embraced several branches: from solar, hydroelectric, and wind energy on the macro scale, up to those more recently such as to harvest power from some electrokinetic phenomenon, for instance, the well-known electric generation by means of the induced streaming potential process. This electric potential is found in micro and nano scales, where the physicochemical properties of surfaces have fundamental importance, such as the slippage effect. Most works oriented to determine induced electric potential in micro and nanochannels assume constant Navier slip length, which quantifies the hydrophobic degree of the surface. This assumption could overestimate the performance of the so-called electrokinetic batteries. For this reason, it is necessary to enlarge the analysis of variable slip over electrokinetics in micro and nanoscale.In the present analysis, we develop an analytical procedure to estimate the electric potentials induced in a microchannel by a flowing laminar solution due to osmotic gradients, whose configuration is better known as an electrokinetic forward osmosis battery. Assuming a non-linear dependence of Navier slip as a function of the pressure, we obtain regular perturbative series solutions for velocity, pressure, and the streaming potential. For this purpose, we use the dimensionless decay parameter ϵ̃, which measures the decrease of slippage due to the pressure at the wall as the perturbation parameter. We conclude that the velocity field has not only a longitudinal component if not also a transverse component normal to the surfaces as a consequence of the variable slippage, showing that the classical assumption of fully developed flow is no longer possible. In addition, our data shows that constant slip overpredicts the electric potentials up to 5% in comparison with the case of exponential slip. Finally, the results show that induced electric potentials are benefited from variable slippage; however, the influence of the decay parameter that appears in the boundary condition (32) associated with the variable slip decreases the induced potentials.

Power-law fluid annular flows between concentric rotating spheres subject to hydrodynamic slip

ABSTRACT We report analytical solutions to the problem of non-Newtonian power-law fluid flows in the annular space between a pair of concentric spherical surfaces rotating at distinct angular velocities with the inner and outer wall boundaries subject to general asymmetric hydrodynamic slip conditions. Analytical solutions are possible because of assuming constant valued apparent hydrodynamic slip lengths in the linearized kinematic slip conditions, and our solutions can be validated against the limiting results of Newtonian fluids, no-slip conditions or a single rotating sphere reported in previous literature. Comprehensive systematic parametric studies show that (additional to the power-law fluid flow behavior index) the degree of hydrodynamic slip at the inner surface is the dominant factor that determines the limiting values of the viscous torque exerted on the inner sphere as the outer-to-inner radius ratio assumes significantly large values. Nonetheless, the flow behavior index and outer slip length prove to be the crucial key parameters responsible for a variety of torque responses, which can be categorized by a compact analytical expression, as the outer-to-inner radius ratio is increased in the small to moderate regime. We propose a criteria which identifies the proper slip length and outer-to-inner radius ratio combinations for a given power-law flow behavior index such that the hydrodynamic slip wall effects of the outer surface can be minimized or eliminated. A simple method is also presented to characterize and quantify the apparent hydrodynamic slip effects by use of the concentric rotating spheres viscometer.

Analytical models for pressure-driven Stokes flow through superhydrophobic and liquid-infused tubes and annular pipes

Analytical expressions for the velocity field and the effective slip length of pressure-driven Stokes flow through slippery pipes and annuli with rotationally symmetrical longitudinal slits are derived. Specifically, the developed models incorporate a finite local slip length and constant shear stress along the slits, and thus go beyond the assumption of perfect slip employed commonly for superhydrophobic surfaces. Thereby, they provide the possibility to assess the influence of both the viscosity of the air or other fluid that is modelled to fill the slits as well as the influence of the micro-geometry of these slits. First, expressions for tubes and annular pipes with superhydrophobic or slippery walls are provided. Second, these solutions are combined to a tube-within-a circular-pipe scenario, where one fluid domain provides a slip to the other. This scenario is interesting as an application to achieve stable fluid–fluid interfaces. With respect to modelling, it illustrates the specification of the local slip length depending on a linked flow field. The comparison of the analytically calculated solutions with numerical simulations shows excellent agreement. The results of this paper thus represent an important instrument for the design and optimization of slippage along surfaces in circular geometries.

Electrokinetic energy conversion efficiency in a nanochannel with slip-dependent zeta potential

Abstract Electrokinetic energy conversion in hydrophobic nanochannels has been studied by many scholars because of its high estimated conversion efficiency. However, these studies mainly focued on the the case of slip-independent zeta potential, ignoring the effect of slip length on zeta potential. In the paper, we study the energy conversion of pressure-driven flow in plane nanochannel with slip-dependent (S.D.) zeta potential. Through the derived analytical expression and schematic analysis of electrokinetic energy conversion efficiency, it can be observed that, within specific parameter ranges, when taking into account the S.D. zeta potential, the conversion efficiency is improved. The maximum conversion efficiency obtained is approximately 23%, which is an improvement of 5.9% compared to the slip-independent (S.I.) zeta potential. This study may have a positive impact on achieving more efficient energy collection and play a important role in the energy field.

Hydrodynamic drag reduction in ribbed microchannel with infused non-Newtonian lubricants

Liquid-infused surfaces have recently gained prominence in engineering applications owing to their versatile characteristics such as self-cleaning, anti-fogging, drag reduction, and enhanced heat transfer. In this article, a numerical analysis of pressure-driven flow past a periodic array of rectangular transverse grooves infused with non-Newtonian immiscible lubricants is performed. The volume of fluid method is employed to capture the interface between primary and secondary fluids, and the power-law model is deployed to mimic the non-Newtonian lubricant. The drag reduction capability of the microchannel is examined for various parameters such as Reynolds number, liquid fraction, viscosity ratio, viscosity index, and contact angle. It is observed that the introduction of a non-Newtonian fluid (shear-thickening or shear-thinning) drastically modifies the interface velocity and hydrodynamic resistance. In particular, a shear-thinning lubricant enhances the slip length as the viscosity index (n) is reduced owing to the reduced viscosity at the interface. Note that, for a lubricant having n = 0.7, the percentage improvement in the slip length is 382% in comparison with a Newtonian counterpart having the same viscosity ratio, N = 0.1. Importantly, the introduction of a shear-thinning lubricant with a viscosity ratio N = 5, a liquid fraction of 0.8, and a behavior index n = 0.7 yielded a pressure drag reduction of 63.6% with respect to a classical no-slip channel and of 23% with reference to a microchannel with the Newtonian lubricant. Moreover, at high Reynolds numbers, Re→50, the drag mitigation is slightly lowered due to the primary vortex shift in the cavity. Furthermore, the effect of the interface contact angle (θc) is investigated, as θc drops from 90° (flat) to 45° (convex); the meniscus curvature is enhanced, and the effective slip length is reduced. These observations suggest that a shear-thinning lubricant-infused microchannel is a promising candidate for drag reduction in lab-on-chip applications.

Numerical investigation of the natural transition in boundary layers on underwater axisymmetric bodies with superhydrophobic surfaces

The natural transition in boundary layers on axisymmetric bodies with superhydrophobic surfaces is studied using numerical methods. By boundary layer, we mean the boundary layer around the forebody and around the parallel body of an underwater vehicle. A method of calculating basic laminar flows on axisymmetric bodies with superhydrophobic curved surfaces is proposed, and a method of linear stability analysis for the boundary layers that considers the slip-velocity boundary condition for small disturbances is established. The eN method is used to predict the transition locations of the boundary layers. On a superhydrophobic surface, the slip velocity on the wall increases and then decreases along the streamwise direction, resulting in a maximum value at the forebody. The boundary layer thickness on a superhydrophobic surface becomes smaller than that on an ordinary surface. The superhydrophobic surface stabilizes the boundary layer and thus delays the natural transition. As the slip length on the superhydrophobic surface increases, the unstable zone shrinks, and the transition location moves further downstream, indicating that the delay effect of the superhydrophobic surfaces becomes stronger. As the oncoming flow velocity increases, the transition location on the superhydrophobic surface moves upstream and then downstream, leading to a “dangerous” velocity, at which the transition location is closest to the leading edge. The underlying mechanism of the dangerous velocity phenomenon is discussed: An increasing velocity has both stabilizing effect and destabilizing effect on the boundary layer.

Heat and mass transfer of water flow in graphene nanochannels: effect of pressure and interfacial interaction.

The low-resistance transport of water within graphene nanochannels makes it promising for electronic cooling applications. However, how the water pressure and the water-graphene interaction strength affect the flow field and the thermal transfer, including velocity slip, friction coefficient, Nusselt number, temperature slip, interfacial thermal resistance, and variation of physical properties, is still not clearly understood. In this paper, we employ molecular dynamics (MD) simulations to investigate qualitatively the heat transfer of water flow in graphene nanochannels. Our results reveal that the water peak density near the wall increases approximately linearly with water pressure and water-graphene interaction strength. The water peak density near the water-graphene interface is a key factor in regulating interfacial flow and heat transfer characteristics. Under constant inlet temperature, the relationship between velocity slip length and peak density follows a consistent power function, simply modifying the pressure or the interaction strength doesn't bring a specific effect. The Nusselt number and interfacial thermal resistance are not solely dependent on water peak density; at the same water peak density, increasing interaction strength results in lower interfacial thermal resistance compared to increasing pressure. Increasing pressure improves both interfacial heat transfer and internal heat transfer of water. Furthermore, the convection heat transfer coefficient increases approximately linearly with flow resistance when pressure and interaction strength vary moderately. Finally, we notice that pressure and interaction strength hardly affect the variation range of viscosity and thermal conductivity at a channel height of 10-12 nm. These qualitative insights could lead to the development of more efficient cooling systems for electronic devices.

Slip Backflow of Polymers in Elastic Fractures for Subsurface Heat Recovery

This research delves into the complexities of backflow phenomena in finite-length and flat-walled fractures with elastic walls, specifically focusing on power-law fluids, whose shear-thinning behavior distinguishes them from Newtonian fluids. We model the backflow process under the lubrication approximation and by incorporating the linear Navier slip law. We numerically examine the influence of parameters such as slip length, fluid rheology, and external pressure on the backflow propagation of the carrier fluid. Our findings underscore the significant role played by the rheological index in determining the fracture closure rate. Additionally, our investigations highlight the marked effect of external pressure variations on pressure distribution within the fracture. Notably, the friction coefficient at the fracture walls, as denoted by a dimensionless slip number, exhibits limited influence on the fundamental dynamics of the problem. These insights advance our understanding of power-law fluid backflow and have wide-ranging applications across various engineering disciplines.

Diode-like response of conical-shaped nanochannels to external stimuli: The importance of slip length

The present study reports the effect of slip length on the ionic current rectification and ion selectivity in conical-shaped electrolyte-loaded nanochannels with and without a coated polyelectrolyte layer (PEL). The electrolyte was considered a salted incompressible Newtonian fluid. The polyelectrolyte layer was also modeled as a rigid and charged porous solid saturated with a salted Newtonian fluid. The electrolyte-polyelectrolyte layer interface was modeled as a surface, considering ion partitioning with distinct physical properties across the interface. The results demonstrated that the relationship between the slip length and the rectification factor depended on the surface charge density, the concentration of the electrolyte solution, and the type of nanochannel. Moreover, the effect of slip length on the ion selectivity factor is remarkably higher in the solid-state nanochannel compared to the PEL-coated nanochannel. Furthermore, the slip length considerably enhances the ion selectivity factor in the solid-state nanochannel. Considering a bulk concentration of 100 mM, a charge density of 60 mol m−3, and a surface charge density of −20 mC m−2, the ionic rectification factor was degraded by 49% and enhanced by 43%, respectively, for the solid-state and PEL-coated nanochannels when the slip length is taken into account.