Model of two-phase fluid flow with non-uniform effective viscosity

Title	Model of two-phase fluid flow with non-uniform effective viscosity
Authors	S. I. Martynov¹ ¹Ulyanovsk State University
Annotation	The paper considers flows of fluid with particles along a flat wall with a given stress on the free surface and in a circular pipe with a given pressure gradient based on a continuous medium model with effective viscosity. It is assumed that the effective viscosity changes with distance from the walls. The equations of the dynamics of the medium under consideration in this case contain terms with a gradient of effective viscosity. However, for the considered inhomogeneity of effective viscosity, the obtained equations have exact solutions, which allows us to estimate the flow rate and the effect of the two-phase medium under consideration on the walls.
Keywords	numerical simulation, viscous liquid, collective interaction of particles, chain, deformation.
Citation	Martynov S. I. ''Model of two-phase fluid flow with non-uniform effective viscosity'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 163-169. Available at: https://conf.svmo.ru/files/2025/papers/paper33.pdf. - Date of access: 30.08.2025.