Spreading under variable viscosity and time-dependent boundary conditions: estimate of viscosity from spreading experiments

Abstract

One of the cooling concepts of the high-temperature corium melt which may form in a core meltdown accident relies on sufficiently homogeneous spreading. The conditions under which complete spreading can be expected are the objects of current theoretical and experimental studies. The lubrication approximation for low Reynolds number flows leads to an equation for which self-similar solutions for various conditions have been found by many authors. This paper offers self-similar solutions for the spreading of a volume of liquid which increases as a power law of time. The effect of cooling on the viscosity is represented by the time-dependent viscosity. A variety of spreading experiments have been performed within many international programs. The initial conditions and boundary conditions used are more complex than those for which self-similar solutions are known explicitly. Based on the asymptotic behavior, as t→∞, of solutions of the Cauchy problem for a quite general class of initial data, approximate solutions are given describing the spreading of finite volume with a time dependent flux release, and some of the high-temperature experiments are analyzed. The effect of bubbles on rheology in spreading experiments with water and shear-thinning fluids is investigated.