Universality in statistics of Stokes flow over no-slip wall with random roughness

TL;DR

This paper investigates how random surface roughness affects low-Reynolds Stokes flows near no-slip walls, exploring the universality of velocity fluctuation statistics and potential flow control applications in microfluidics.

Contribution

It provides a theoretical analysis of velocity fluctuation statistics caused by surface roughness and examines their universal properties in Stokes flow.

Findings

Velocity fluctuations depend on surface roughness statistics.

Universal behavior observed in fluctuation distributions.

Implications for microfluidic flow control.

Abstract

Stochastic roughness is widespread feature of natural surfaces and is an inherent by-product of most fabrication techniques. In view of rapid development of microfluidics, the important question is how this inevitable evil affects the low-Reynolds flows which are common for micro-devices. Moreover, one could potentially turn the flaw into a virtue and control the flow properties by means of specially "tuned" random roughness. In this paper we investigate theoretically the statistics of fluctuations in fluid velocity produced by the waviness irregularities at the surface of a no-slip wall. Particular emphasis is laid on the issue of the universality of our findings.