Oscillating Forces in Microbial Flows: Steady vs. Unsteady Regimes

Many microorganisms inhabit a world of low Reynolds number, where movement through fluid is dominated by viscosity. To swim or feed, they rely on mechanisms like flagellar beating or metachronal waves of cilia. These actions are often modeled using steady Stokes flow. Yet even without inertia, microorganisms can break the constraints of the “scallop theorem” by carefully tuning the timing and location of the forces they exert.

A conceptual model that captures this is the blinking Stokeslet, which mimics alternating power and recovery strokes by periodically switching the position of a point force. This setup can generate chaotic flows, enhancing transport and mixing—a strategy likely used by filter-feeding ciliates.

But what happens when these oscillations become fast enough for unsteady effects to matter? Understanding this transition may shed light on how microorganisms exploit time-dependent flows to optimize feeding and transport.

Comparing steady and unsteady Stokes regimes in such models helps reveal the limits of quasi-steady assumptions and the potential biological advantages of exploiting unsteady flow dynamics.