A Non-inertial Model for Particle Aggregation Under Turbulence
Year: 2025
Type: book-chapter
Abstract: We consider an abstract non-inertial model of aggregation under the influence of a Gaussian white noise with prescribed space-covariance, and prove a formula for the mean collision rate R, per unit of time and volume. Specializing the abstract theory to a non-inertial model obtained by an inertial one, with physical constants, in the limit of infinitesimal relaxation time of the particles, and the white noise obtained as an approximation of a Gaussian noise with correlation time $$\tau _{\eta }$$ τ η , up to approximations the formula reads $$R\sim \tau _{\eta }\left\langle \left| \Delta _{a}u\right| ^{2}\right\rangle a\cdot n^{2}$$ R ∼ τ η Δ a u 2 a · n 2 where n is the particle number per unit of volume and $$\left\langle \left| \Delta _{a}u\right| ^{2}\right\rangle $$ Δ a u 2 is the square-average of the increment of random velocity field u between points at distance a, the particle radius. If we choose the Kolmogorov time scale $$\tau _{\eta }\sim \left( \frac{\nu }{\varepsilon }\right) ^{1/2}$$ τ η ∼ ν ε 1 / 2 and we assume that a is in the dissipative range where $$\left\langle \left| \Delta _{a}u\right| ^{2}\right\rangle \sim \left( \frac{\varepsilon }{\nu }\right) a^{2}$$ Δ a u 2 ∼ ε ν a 2 , we get Saffman–Turner formula for the collision rate R.
Source: Journal of Statistical Physics
Authors: Franco Flandoli, Ruojun Huang
Institutions: Scuola Normale Superiore, University of Münster
Language: English
Subfield: Ocean Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4408894547