Probability theory of active suspensions

A new approach to studying active suspensions is presented. They exhibit a specific behavior pattern, sometimes referred as turbulence. Starting from first principles, we establish description for an suspension, consisting of Newtonian fluid and Janus particles. The phase described by Navier–Stokes equations the particles Newton–Euler equations. level set used separate two phases, well-known representation sharp interfaces in various numerical schemes. By introducing multi-point probability density function (PDF)-approach known hydrodynamic turbulence, obtain hierarchical ordered infinite linear statistical However, K-point PDF depend on K + 1 2-point PDF, exposing closure problem As all moments can be formed latter already includes every model suspensions. To illustrate this, derive Eulerian spatial averaging theory hierarchy PDF-equations.