Analysis of KATS experiments

In many applications the cooling process will lead to variable flow properties, e. g. variable viscosity and, consequently, to a coupled system of the temperature and flow equations. It is impossible to satisfactorily treat this problem analytically. The lubrication approximation leads to an equation for which similarity solutions for various conditions have been found by many authors (Zel'dovich and Kompaneets, 1950; Sakimoto, 1995; Huppert, 1982; Foit, 1997). Bercovici (1994) developed a model for an axisymmetric gravity current which accounts for thermoviscous effects, i. e., the spatial variation of the viscosity. The numerical results showed significant deviations from the similarity profiles of the constant viscosity (Huppert, 1982) as well as the time-dependent viscosity (Foit, 1997) case. A variety of experiments have been carried out to determine the effects of cooling on the flow of fluids with different properties. The influence of the crust formation rates on the fluid flow was explored experimentally by Fink and Griffiths (1993) with the aim of understanding and classifying small-scale flow surface morphology for a fluid with weakly temperature dependent viscosity (polythylene glycol 600). This study indicated that a crust does not greatly affect the fluid flow except for very high crust formation rates. Experiments which used a fluid with strongly temperature dependent viscosity (glucose syrup) were performed by M. V. Stasluk et al. (1993). In this case the cold, viscous fluid accumulated at the leading edge, altering the flow shape and thickness and slowing the spreading. The front became steeper and the surface behind the front was nearly horizontal. All performed experiments evolved to a stage at which the overall spreading behaviour of the flow can be approximated by a constant bulk viscosity. (orig.)