2026/01/31 by C. Rajarshi, C Rajarshi, Rama Govindarajan
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Particle Dynamics in Fluid Flows #Pickering emulsions and particle stabilization #Point processes and geometric inequalities #cond-mat.stat-mech #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/fwkk-s3w4
17 pages, and 9 figures. Revised version after publication
openalex publication_date 2026/06/16 · openalex created_date 2026/06/17 · arxiv created 2026/07/30 · arxiv updated 2026/07/31 · openalex updated_date 2026/07/31
Estimating collision rates is of immense importance in particle-laden flows. An economical way of doing this is to directly identify incidences of caustics, or extreme clustering, by tracking particle velocity gradients in the neighborhoods of individual particles. The objective of this work is two-fold. (i) We find conditions under which caustics form, in point-vortex flow and in two-dimensional turbulence. While caustics are known to form in regions of strain, we show that the velocity alignment with strain directions is key. Particles must remain in compressional strain throughout the process to form caustics, whereas survivor particles: which visit high strain but do not form caustics, briefly go through extensional strain during the early part of the process. This enables survivor particles to attain significantly straighter paths, and to move faster, whereas caustics particles follow paths of high curvature and move slower. As a result, caustics particles stay longer in high-strain regions than survivors. (ii) We ask about the effect of finite particle density, where the particle is denser than the background fluid. We show that finite-density particles need to sample stronger background strain than infinite-density ones to trigger caustics, but our other findings are universal across particle density.