Abstract
.I discuss fluid flow at the interface between solids with anisotropic roughness. I show that the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity. This shows that, in most cases, the surface roughness observed at high magnification is irrelevant for fluid flow problems such as the leakage of static seals, and fluid squeeze-out. The effective medium theory predicts that the fluid flow conductivity vanishes at the relative contact area A/A0 = 0.5 independent of the anisotropy. However, the effective medium theory does not solve the elastic contact mechanics problem but is based on a purely geometric argument. Thus, for anisotropic roughness the contact area may percolate at different values of A/A0 depending on the direction. We discuss how this may be taken into account in the effective medium and critical junction theories.Graphical abstract
Highlights
Fluid flow at the interface between elastic solids is a complicated topic, in general involving elastic deformations, complex fluid rheology and interfacial fluid slip [1]
The effective medium theory predicts that the fluid flow conductivity vanishes at the relative contact area A/A0 = 0.5 independent of the anisotropy
For anisotropic roughness the contact area may percolate at different values of A/A0 depending on the direction
Summary
Fluid flow at the interface between elastic solids is a complicated topic, in general involving elastic deformations, complex fluid rheology and interfacial fluid slip [1]. We consider the simplest fluid flow problems, which include the leakage of static seals [11, 12] and the squeeze-out of fluids [13] between elastic solids For these applications the roughness enter only via one function, namely the pressure flow factor φp(u) (in general a 2 × 2 tensor) or, equivalently, the (effective) fluid flow conductivity σeff defined by the equation. I show that, unless the applied pressure is very small, the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity (and the fluid pressure flow factor) This shows that for applications which involve only the flow conductivity (or, equivalently, the pressure flow factor), such as the leakage of static seals and fluid squeeze-out, in most cases the (short wavelength) surface roughness observed at high magnification is irrelevant
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