CALCULATION OF THE DYNAMICS OF GRAVITY-INDUCED DENSITY PROFILES NEAR A LIQUID-VAPOR CRITICAL-POINT

We develop one-dimensional equations that describe the dynamics of a highly compressible fluid in the presence of gravity. We apply these equations to a fluid near its liquid-vapor critical point and discuss how the coupling between gravity and compressibility affects the fluid bulk response to temperature changes. To illustrate the effect of this coupling on the equilibration process, we present numerical solutions for a one-phase critical fluid in the earth's gravity subjected to a sudden temperature step at the boundaries. We find that the adiabatic effect is responsible for accomplishing most of the temperature change in the fluid, within seconds, a rate far faster than that of thermal diffusion. On the other hand, the stratification of density under gravity takes hours, although this time is smaller than the diffusion time in the corresponding zero-gravity situation. Unlike the zero-gravity case, the adiabatic effect creates a small but significant temperature gradient immediately after the quench. As a consequence, diffusion in the fluid bulk begins earlier than it would otherwise. This gradient does not induce buoyant convective flow in the bulk, however, because of the fluid's compressibility. In the time range studied, no single exponential mode has emerged to dominate; a long intermediate regime spans a long period of time (many hours), which could lead to erroneous interpretation of experimental results.