Porous squeeze-film flow

Abstract

The squeeze-film flow of a thin layer of Newtonian fluid filling the gap between a flat impermeable surface moving under a prescribed constant load and a flat thin porous bed coating a stationary flat impermeable surface is considered. Unlike in the classical case of an impermeable bed, in which an infinite time is required for the two surfaces to touch, for a porous bed contact occurs in a finite contact time. Using a lubrication approximation an implicit expression for the fluid layer thickness and an explicit expression for the contact time are obtained and analysed. In addition, the fluid particle paths are calculated, and the penetration depths of fluid particles into the porous bed are determined. In particular, the behaviour in the asymptotic limit of small permeability, in which the contact time is large but finite, is investigated. Finally, the results are interpreted in the context of lubrication in the human knee joint, and some conclusions are drawn about the contact time of the cartilage-coated femoral condyles and tibial plateau and the penetration of nutrients into the cartilage.

Gas-cushioned droplet impacts with a thin layer of porous media

“…However, the non-dimensional Beavers-Joseph equation (30) will be adopted here. Following the approach developed by Knox et al [21] for the coupled squeeze film and porous substrate flow driven by an approaching flat plate, the pressure in the substrate is expanded as…”

Viscous backflow from a model fracture network: influence of a permeable boundary

“…Knox et al. (2015) and Venerus (2018), have considered the addition of a porous boundary. Figure 6 shows the difference between our model and one considering a constant force on the boundary rather then the relaxation of a linear elastic one.…”

“…knee and hip, Knox et al. 2015; Karmakar & Raja-Sekhar 2018), soft robotics (Matia & Gat 2015) and various microfluidic applications (Christov et al. 2018; Wang & Christov 2019).…”

A lubrication replenishment theory for hydrogels

“…7b illustrates the two lubricant loss mechanisms that are suggested for the hydrogel contact: squeeze-out of lubricant from the contact region and loss due to fluid flow into the porous hydrogel structure. 43,44 This resembles the mechanism of squeeze film lubrication, where a lubricating film initially forms due to the fast approach of two surfaces, thus 'trapping' the lubricant. Since the fluorescent profiles show an initial presence of the lubricant, such a film was likely formed in the contact.…”

“…The film subsequently diminishes because of the squeezeout flow from contact and fluid flow into the porous material. 43,44 This loss of lubricant can explain the rapid increase in friction in the first few seconds of a test.…”