A laser study of the motion of particles suspended in a slow viscous shear flow

Abstract

Theoretical and experimental techniques are developed which show the feasibility of using a laser to study the statistics pertaining to the orientation of small axisymmetric particles with fore-aft symmetry suspended in a slow viscous shear flow. The Rayleigh-Gans theory of light scattering is used to calculate the angular intensity distribution of light scattered from both a single particle and a collection of particles. A form factor which accounts for the size, shape, and orientation effects is calculated for the actual bi-concave disk geometry of the red blood cell, and theoretical results are given for the scattering from a single cell with a discrete orientation and also for a collection of cells with random orientations. The influence of the motion of blood cells on their light scattering properties is considered in detail. The statistics of their orientation is determined from the equations of their motion based on the theory of Jeffery. Integral relations are established which relate the distribution of particle orbit constants to the angular intensity distribution. Theoretical light scattering curves are given for several distributions of orbit constants of interest. Experiments are performed which verify the applicability of the Rayleigh-Gans theory to dilute suspensions of erythrocytes. Light scattered from suspensions sheared in a cylindrical Couette flow apparatus shows a progressive decrease in scattering at small angles compared to the random suspension. Light scattering data indicates an equilibrium orientation of the blood cells occurs with the axis of revolution of the blood cell parallel to the vorticity vector of the undisturbed flow field. This orientation corresponds to a maximum rate of energy dissipation. The relaxation time for this equilibrium configuration is found to be inversely proportional to the square of the rate of shear.