Abstract: When the concentration of solid particles in a fluid is high, an approach is known in which the particles are treated as a proper continuum interacting with the fluid phase. There are various theories of the interaction of the two continuums. One of them is known as Landau-Khalatnikov superfluid hydrodynamics, developed to describe superfluid helium II under the assumption that such a medium consists of ordinary and superfluid parts with different velocities. The paper presents a generalization of the Landau-Khalatnikov method to the case when the particle phase is treated as a Cosserat-Bingham fluid, i. e. it is both a micropolar fluid and a viscoplastic material. Micropolarity is is due to the concept of the Cosserat continuum, in which each material particle is treated as a solid body. On the one hand, the material is characterized by micro-rotations, micro-inertia, asymmetry of the stress tensor, the presence of a tensor of angular momentum. On the other hand, the material does not deform if the shear stresses or internal stress moments are sufficiently small. Examples are drilling fluids with cuttings, building concretes, and the like. On the basis of new developed mathematical models, it is possible to explain a number of effects in suspensions, when the rotation of particles plays an important role. It turns out that if you do not take into account the rotation of cuttings particles when drilling a well, then you can significantly err in the assessment of downhole pressure. The S´egre-Silberberg effect (Nature, 1961) was established, which consists in the fact that in a steady flow in a pipe, particles are concentrated mainly in a certain annular region. It was the rotation of the particles that managed to explain the effect of centrifugal sedimentation. The case of suspensions with rodlike particles is studied. It has been established that there is a shear banding effect, when a finite number of layers appear, moving in the same horizontal direction and differing in shear rate. In addition, such a banding is unstable: the number of layers can increase with time. In some layers, the orientation of the particles is more or less the same, which is consistent with the known phase transition from the isotropic to the nematic state. An important result is the horizontal oscillations of the flow velocity, which do not disappear with time even at a constant pressure drop. To this we can add a temporary oscillation of the apparent viscosity. Another property of apparent viscosity has been established, which consists in the fact that it demonstrates shear thinning depending on the shear rate. It is shown that, within the framework of the developed approach, it is possible to detect hysteresis flow regimes. This result is consistent with the data on the operation of oil pipelines, which show that when a given flow regime is reached, the pressure losses due to friction depend on the prehistory of compressor operation. Thanks. This work is supported by the grant No. 20-19-00058 of Russian science foundation. References [1] V. Shelukhin, Rotational particle separation in solutions: micropolar fluid theory approach, Polymers, 13 (2021), 1072. [2] V. Shelukhin, Flows of linear polymer solutions and other suspensions of rodlike particles: anisotropic micropolar-fluid theory approach, Polymers, 13 (2021), 3679.

Cite: Shelukhin V.
Dynamics of suspensions: thermodynamics and micro-structure
Dynamics in Siberia, 2023 27 Feb - 4 Mar 2023