Title:

A mathematical analysis of the hydromechanics associated with the Vitros Immunodiagnostic System

A description of the Vitros Immunodiagnostic System is given in Chapter 1. In Chapter 2, a mathematical model is developed to describe the structure of the mixture within the well. In Chapter 3, dynamical equations are formulated with respect to a moving frame of reference at rest relative to the well. In particular, with reference to two especial states of motion: that of a 'sweep' at constant angular velocity of the outer carousel ring, and that of a 'jiggle' at rapidly fluctuating angular velocity. In the former the equations admit a solution in which the fluid moves as if it were rigid. Whereas, in the latter the equations admit an axially symmetric motion of the mixture. In Chapter 4, the equations describing the primary flow and the (incipient) secondary flow are solved exactly for a hemispherical shaped well. This analytic solution gives a powerful description of the flow, being valid for the whole spectrum of values of the Reynolds number. The analysis shows that for large values of the Reynolds number the flow varies rapidly in the region immediately adjacent to the boundary wall, but elsewhere the flow is approximately a rigid body rotation. In Chapter 5, a similar type analysis is carried out for a cylindrical shaped well. Chapter 6 is concerned with the problem of determining the way in which the suspended reagents drift through the patient sample, and of ascertaining the pattern they create when becoming entrapped on the boundary wall.
