Slip and friction at fluid-solid interfaces: Concept of adsorption layer

TL;DR

The paper introduces the adsorption layer (AL) as a finite-thickness interfacial region $\delta l$ in which solid–fluid interactions simultaneously drive adsorption/depletion and interfacial slip. By constructing a total energy functional $\mathcal{L}_{T}=\mathcal{F}+\mathcal{P}+\mathcal{K}+\mathcal{K}_{\text{w}}$ for the AL and applying an energy-minimization principle, the authors derive coupled interfacial equations that account for chemical diffusion, viscous stresses, and solid–fluid friction, with explicit pressure coupling across the interface. This framework recovers and generalizes the generalized Navier boundary condition (GNBC) while highlighting the role of normal pressure gradients $\nabla P_{\text{s}}$ and surface chemical potential gradients $\nabla\mu_{\text{s}}$ in determining slip. The model successfully explains confinement-enhanced water slippage in carbon nanotubes and captures spatial slip variations near moving contact lines in binary fluids, demonstrating that the slip length is an emergent, geometry- and composition-dependent quantity rather than a fixed material constant. Overall, the AL approach provides a physically grounded link between molecular-scale interfacial physics and continuum hydrodynamics with strong implications for microfluidics and surface engineering.

Abstract

When a fluid flows past a solid surface, its macroscopic motion arises from a subtle interplay between microscopic hydrodynamic and thermodynamic effects at the fluid-solid interface. Classical hydrodynamic models often rely on an unphysical no-slip boundary condition or an arbitrarily prescribed slip length, yet both approaches lack a rigorous physical foundation. This work introduces the concept of an Adsorption Layer (AL), an interfacial region of thickness delta l, where fluid-solid molecular interactions regulate both surface adsorption/depletion and interfacial slip. By applying the energy minimization principle, we derive balance equations within the AL that couple fluid-solid friction, viscous stresses, and surface adsorption dynamics. This framework establishes a self-consistent thermodynamic coupling between the AL and the bulk fluid, unlike conventional sharp-interface models. A key finding is the often-overlooked role and coupling of pressure and chemical potential gradients in the direction normal to the interface. This theoretical advance successfully explains the confinement-induced enhancement of water slippage in carbon nanotubes, quantitatively agreeing with molecular dynamics and experimental data -- an effect classical slip models fail to reproduce. Furthermore, when extended to binary liquids, the theory captures spatial variations in slip velocity near moving contact lines, highlighting the role of interfacial friction in shaping local flow. Our results demonstrate that the slip length is not a fixed material constant but rather an emergent, geometry- and composition-dependent property arising from coupled interfacial thermodynamics and hydrodynamics. This framework provides a physically grounded description of interfacial momentum transfer, with significant implications for microfluidics and surface engineering.

Figures (8)

• Figure 1: (I) Fluid velocity distribution $\mathbf{u}(y)$ with no-slip boundary condition at fluid-substrate contacting surface S. (II) Slip boundary condition enables non-zero fluid velocity $\mathbf{u}_{ \text{s}}$ at S. The Navier slip length is mathematically defined as $l_{ \text{s}}=\mathbf{u}_{ \text{s}}/\partial_{\text{n}} \mathbf{u}$.
• Figure 2: (I) Illustration of fluid passing the solid substrate. Solid-fluid molecular interactions form the adsorption layer (AL) above the solid surface S. (II) Solid-fluid molecular interactions perpendicular to S leads to surface depletion/adsorption which modifies surface composition $c_{ \text{s}}$ deviating from the bulk fluid. Interactions parallel to S, such as bond rotation, results in shear/friction which changes the velocity profile $\mathbf{u}$.
• Figure 3: (I) One-dimensional Poiseuille flow through a tube with radius R. (II) Calculated effective slip length $l_{ \text{eff}}$ of water in nanotube with \ref{['eq:slip_l']} shows R-dependent decays, compared with previous molecular dynamic simulations. CNT: carbon nanotube, BNNT: boron nitride nanotube, for both $\delta l = 0.5nm$. (III) Enhanced experimental slip length of KCl (potassium chloride) aqueous solution ($10^{ -3}$M) in CNT deviates from MD, indicating the larger $\delta l \approx 13nm$ associated with the Debye length of KCl solution.
• Figure 4: One-dimensional Poiseuille flow with surface depletion/adsorption. Tube radius $\text{R}=50$, characteristic length $\delta l=0.5$, friction coefficient $\lambda=20$. (I) Depletion/adsorption induced viscosity distribution $\eta(\text{r})=1+\eta_{ 0}e^{ \text{R}/\delta l}\cosh(\text{r}/\delta l)$. $\eta_{ 0}>0$: adsorption increases viscosity; $\eta_{ 0}<0$: depletion reduces viscosity. (II) Flow profile modified by surface depletion/adsorption. Black line: parabolic profile without depletion/adsorption. (III) Effective slip length $l_{ \text{eff}}$ changing with depletion/adsorption; dots: \ref{['eq:slip_l']}, line: linear relation.
• Figure 5: (I) Flow rate of one-dimensional Poiseuille flow with slip influenced by surface depletion/adsorption for different tube radius R. The black dashed line: standard $Q_{ \text{s}}$ by \ref{['eq:qs']}. (II) Viscosity $\eta$ and flow velocity $\text{u}(\text{r})$ deviate from the standard Poiseuille flow without surface adsorption (dashed black lines), for small confinement with $\text{R}=4$, corresponding to the star symbol in (I). The dark blue and light blue regions denote AL and bulk fluid, respectively.