Multiscale Dynamics of Roughness-Driven Flow in Soft Interfaces

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.