Abstract: The thermodynamics of a two-phase granular liquid is developed by the Khalatnikov-Landau method, which makes it possible to generalize the Navier-Stokes equations to the case of particle suspension flow. The new mathematical model explains a number of known experimental effects. These include the Boycott effect (Nature 1920), according to which erythrocytes in the blood in an inclined test tube are deposited more intensively than in a vertical one [1]. Fig. 1 depicts how rapidly the upper zone of a pure liquid without particles increases with time. This result was established by numerical methods. Another phenomenon is known as the Segre-Silberberg effect (Nature, 1961). It consists in the fact that in a steady flow along a pipe, particles accumulate not on the axis and not near the walls, but in a concentric annular region with an average radius r=0.6 R, where R is the radius of the pipe. The developed theory explains this effect by the rotation of particles, the angular velocity of which is taken into account in the law of conservation of internal angular momentum by using the Cosserat continuum. Experiments show that in the case of a channel branching into two branches, the particles “prefer” the branch in which the liquid flow rate is higher. This Zweifach-Fung (1968, 1973) effect can also be explained in terms of the formulated equations.

Cite: Shelukhin V.
Generalization of Navier-Stokes equations for two-phase flows and applications
Days on diffraction 2023 05-09 июн. 2023