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 h ighly compressible fluid in the presence of gravity. We apply these eq uations to a fluid near its liquid-vapor critical point and discuss ho w the coupling between gravity and compressibility affects the fluid b ulk 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 s udden temperature step at the boundaries. We find that the adiabatic e ffect is responsible for accomplishing most of the temperature change in the fluid, within seconds, a rate far faster than that of thermal d iffusion. On the other hand, the stratification of density under gravi ty takes hours, although this time is smaller than the diffusion time in the corresponding zero-gravity situation. Unlike the zero-gravity c ase, 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 d oes not induce buoyant convective flow in the bulk, however, because o f the fluid's compressibility. In the time range studied, no single ex ponential mode has emerged to dominate; a long intermediate regime spa ns a long period of time (many hours), which could lead to erroneous i nterpretation of experimental results.