Aspects of Applicability King - St. Clair Approximation in a Non-Newtonian Fluid Mechanics

Abstract

This studyis a contribution to research on the biomedical and clinical applications of ultrasound. Our research concerns the procedure for the separation of human blood fractions-erythrocytes. Ultrasonic waves can be used for the separation of cells in human blood. From a physical point of view, the human blood is a suspension of liquids and solids (cell elements), and behaves like a non-Newtonian fluid. Our work is devoted to the problem of the motion of red cells in human blood under the influence of ultrasonic wave. It defines a range of the applicability of approximation consisting in neglecting the nonlinear term in the friction force. It also analyzes the general properties of the equation of motion of the cell in the case of large attenuation constants, corresponding to the values of the drift forces for the cells with radii of a few µm. Finally, it defines the applicability criterion of the so-called King-St Clair approximation consisting in the assumption of equilibrium between the drift and the Stokes viscosity forces, neglecting the term representing inertia. This approximation permits analytical estimation of the time constants for the cell transport to points of stable equilibrium in an ultrasonic standing wave field.