Theoretical collision model of elongated particles in turbulence

The collisions between elongated particles in turbulence play an important role in various natural and industrial processes. In this study, we establish a theoretical model to estimate the collision kernels of monodisperse elongated passive particles in homogeneous isotropic turbulence. The model is composed of two terms: the collision kernel with fixed relative angles and the angular-volumetric number density of neighbouring pairs, where we first derive under the Gaussian hypothesis of the fluid velocity gradients and then incorporate a non-Gaussianity factor into the formulations. The collision kernels obtained by the present model are in a good agreement with that of direct numerical simulations. Moreover, our model provides insights into the mechanism of the relative alignment between nearby particle pairs and the chain formation in turbulence, from the perspective of particle collisions.