Non-Axisymmetric Brightness Patterns in Spherical Couette Flow: A Probabilistic Approach to Flaky Particle Orientation

Our research focuses on non-axisymmetric patterns observed in experimental visualizations using infinitesimal flaky particles in axisymmetric spherical Couette flow (SCF). Even if diffusion effects cause a simple broadening in the orientation distribution of the flakes, axisymmetric brightness patterns should still be obtained if their orientations align with deterministic solutions. In fact, deterministic numerical simulations yield axisymmetric patterns. To resolve this discrepancy, we derive an equation for the probability density function (PDF) of flaky particle orientations based on the Fokker–Planck equation.

First, we present the deterministic orientation equation for the flakes and show the resulting visualization patterns from numerical simulations. We then compare these patterns with those observed experimentally to highlight the differences.

Second, we introduce the PDF-based equation and show the simulated visualization patterns that account for diffusion effects.

Finally, we briefly provide a theoretical explanation for why these fundamental different patterns emerge.