Deryagin–Landau–Verwey–Overbeek Colloids in Poiseuille Liquid Flow

Abstract

The properties of a dilute Deryagin–Landau–Verwey–Overbeek colloidal solution, a solution flowing in a long tube of finite cross section (Poiseuille flow), are discussed. Such colloids entering the channel are likely to adsorb at the metal-electrolyte interface (see the main text for details). In this case, their motion along the walls of the metal tube cannot be considered to be stokes (a rectilinear motion without signs of rotation motion of a trial sphere of radius \({{R}_{0}}\) relative to a stationary, viscous liquid is called the stokes motion). For a trial sphere located near the wall-viscous fluid boundary, motion along the channel axis without signs of rotation is impossible. A set of colloids adsorbed on the walls of the channel is forced to roll along its sides, coherently changing the hydrodynamic boundary conditions of the Poiseuille problem by its translational-rotational motion. As a consequence, the content of the formulas defining the regularities of the flow of viscous suspensions in a long tube of the finite cross section (Poiseuille flow) is noticeably modified. As a suitable example of the influence of finite colloid density on Poiseuille hydrodynamics in long channels, the details of the law of dispersion of sound oscillations in long, flat, or cylindrically symmetric tubes are discus-sed.