Multiscale Dynamics of Roughness-Driven Flow in Soft Interfaces

TL;DR

The paper develops a modular, two-dimensional fluid–structure interaction framework to model soft, rough lubricated interfaces across boundary to full-film regimes. It combines Reynolds-flow dynamics with multiscale roughness representations (Persson theory and CG–FFT) and introduces the Reduced Stiffness Method to capture finite-body elasticity, integrated through Boundary–Mixed Lubrication and Mixed–Elastohydrodynamic Lubrication solvers. Key contributions include efficient coupling of microscale roughness with macroscale hydrodynamics via interpolation functions, and experimental validation against rough elastomer–glass contacts demonstrating accurate Stribeck curves and film-thickness predictions. The framework enables robust analysis of soft interfacial systems with applications in biomechanics, soft robotics, and microfluidics, and provides a path toward extensions to nonlinear, viscoelastic, 3D, and non-Newtonian lubrication scenarios.

Abstract

Soft lubricated contacts exhibit complex interfacial behaviours governed by the coupled effects of multiscale surface roughness and non-linear fluid-solid interactions. Accurately capturing this interplay across thin-film flows is challenging due to the strong synergy between contact mechanics and hydrodynamic flow, spanning over various spatiotemporal scales. Here, we develop a rigorous computational framework to simulate the frictional behaviour of soft lubricated interfaces; its modularity and the use of optimal solvers provides solutions for realistic configurations in lubrication regimes ranging from direct solid contact to complete fluid separation. Surface roughness is described via Persson's statistical theory as well as a deterministic Conjugate Gradient with Fast Fourier Transform (CG-FFT) approach, while limitations associated with classical half-space models are addressed by developing the Reduced Stiffness Method (RSM) to rigorously model pressure-induced surface responses. The integrated framework captures the full evolution of frictional behaviour, validated against experiments on rough elastomer-glass interfaces, revealing how surface roughness and material compliance together drive the transition from solid contact to fluid-mediated sliding. The developed approach establishes a robust and versatile simulation tool for analysing a plethora of soft interfacial systems shaped by fluid-solid interactions, with potential applications including but not limited to biomechanics, soft robotics and microfluidic systems.

Figures (11)

• Figure 1: The modularity and robustness of the developed computational framework enable the modelling of diverse soft lubricated contacts and conditions. (A) Examples of soft lubricated interfaces, including wiper-blade and lip-seal configurations, exhibiting mixed lubrication between a compliant rubber lip and a rigid surface through coupled deformation and fluid entrainment; the wiper-blade system is investigated in this study as a representative case. (B) Simplified geometric model used for numerical analysis, where the complex wiper-blade profile is reduced to an elastomer specimen sliding against a rigid glass substrate. (C) Conceptual lubrication map showing the transition from full-film to boundary lubrication.
• Figure 2: Experimental setup and surface characterisation for friction assessment. (A) The UMT2 tribometer with mounted elastomer specimen in contact with the glass slide. (B) Elastometer surface topography measured using Atomic Force Microscopy (AFM). (C) Glass substrate roughness map obtained via White Light Interferometry (WLI). (D) Power spectral density (PSD) of the elastomer surface, with the fitted roughness power spectrum $C({q})$ (in red) corresponding to a Hurst exponent of 0.8.
• Figure 3: Evolution of the interfacial response of a rough elastic solid under increasing external load. Profiles along the central line show: (A) contact pressure and (B) interfacial separation. The material is characterised by a Young’s modulus of 3.3 MPa and a Poisson’s ratio of 0.499. Applied pressures are 0.03 MPa, 0.23 MPa, 0.6 MPa and 1.6 MPa.
• Figure 4: Functional relationships governing rough surface contact under varying load conditions. (A) Dimensionless load–separation curve extracted using the Conjugate Gradient with Fast Fourier Transform (CG-FFT) approach. (B) Contact area evolution with increasing normalised pressure, used in the construction of interpolation functions for pressure estimation and asperity-level stress evaluation.
• Figure 5: Schematic of the model reduction process involved in the Reduced Stiffness Matrix (RSM) method. (A) The full continuum geometry. (B) The corresponding finite element mesh with adaptive refinement. (C) The resulting reduced model containing retained nodes (in red) that define external degrees of freedom during substructure generation.