Kinetic theory of discontinuous rheological phase transition for a dilute inertial suspension

Abstract A kinetic theory for a dilute inertial suspension under a simple shear is developed. With the aid of the corresponding Boltzmann equation, it is found that the flow curves (the relations between the stress and the strain rate) exhibit the crossovers from the Newtonian to the Bagnoldian for a granular suspension and from the Newtonian to a fluid having a viscosity proportional to the square of the shear rate for a suspension consisting of elastic particles, respectively. The existence of the negative slope in the flow curve directly leads to a discontinuous shear thickening (DST). This DST corresponds to the discontinuous transition of the kinetic temperature between a quenched state and an ignited state. The results of the event-driven Langevin simulation of hard spheres perfectly agree with the theoretical results without any fitting parameter. The introduction of an attractive interaction between particles is also another source of the DST in dilute suspensions. Namely, there are two discontinuous jumps in the flow curve if the suspension particles have the attractive interaction.