Finite Pressure Gradient Research Articles

Behavior of the Central Region of a Collapsing Star with Spherical Symmetry and Pressure Gradient

The behavior oi the central region of a collapsing star with spherical symmetry and a finite pressure gradient is studied from the standpoint of boundary conditions at the center r=O. In the case of adiabatic collapse, Einstein's equations supplemented by an equation of state are reduced to four independent equations for five unknown functions of the time variable t only. This arbitrariness is analogous to that in the selection of initial Cauchy data at t=O in the Misner-Sharp approach and it enables us to construct a variety of models for the central region regular at all times. W c also touch upon the case of non-adiabatic collapse by introducing a suitable parameter whose n:~ciprocal stands for the time-scale of the energy flow near r=O.

Stability of Frictionally-Heated Flow

Extended results relative to the existence of a critical stress (a finite shear stress or pressure gradient above which fully-developed steady solutions do not exist) in Couette and Poiseuille motions are reported. The results apply to liquids under general thermal boundary conditions including a conduction-convection balance at the boundaries. A bound which gives a close a priori estimate of the value of the critical stress is developed. Stability characteristics of frictionally-heated Couette flow in the inviscid limit are specified. Below the critical stress the steady solutions are double-valued. The stress parameter first increases, then decreases, with increasing temperature. To the previously reported temperature instability on the second branch can be added a corresponding (inviscid) instability of the motion. On the first branch of the double-valued solution the flow is stable despite the presence of a single vorticity maximum at the channel center.

Significance of pressure gradients in porous materials: Part II. Diffusion and flow in porous catalysts

AbstractDiffusion and flow rates through porous catalysts were measured under the conditions of finite pressure gradients for single‐ and two‐component systems. For large pore (low density) alumina pellets the diffusion rate counter to the pressure gradient was severely depressed, while for small pore Vycor the pressure gradient had little effect.The equations developed in Part I for flow and diffusion in a single capillary were extended to porous catalysts. The resulting prediction methods contain no parameters which require transport data for their evaluation, but pore size and void fraction information is needed. For the catalysts investigated, both the permeability and diffusion rates varied several thousand‐fold. The calculated results predict the same extensive range and show the same effects of pressure gradient and pore properties. Also the quantitative agreement between calculated and experimental results is such that the theory provides a useful method of predicting transport rates through certain types of porous media.

Fluid Distributions Characterizing Gas-Liquid Flow

It is the purpose of this note to call attention to the circumstancecomplicating the attainment of uniform gas-liquid distributions in multi-phaseflow systems, and especially in those of the so-called Hassler type. Althoughthe complication arises directly as a consequence of gas compressibility andthe dependence of fluid distributions on interfacial curvature phenomena, little reference to the problem has yet appeared in the literature. In fact, itis only the paper of Geffen et al. which gives any experimental evidence that aproblem exists. On the other hand, previous authors have made the tacit, albeitfallaceous assumption that uniform gas-liquid distributions automatically areestablished in linear flow systems by the expedient of maintaining the pressuregradients equal in the flowing gas and liquid phases. Such a device, it can beshown, will succeed only if the immiscible fluids are both equally compressibleor both essentially non-compressible. Another necessary condition requiredbefore uniform fluid-fluid distributions can be achieved is that the porousmatrix is isotropic. Uniform fluid saturation distribution conditions obtain in isotropic mediaonly when the curvature of each interface of contact between wetting andnon-wetting fluids is everywhere the same throughout the interspaces. This is anecessary condition which follows from the consideration that variation ininterfacial curvature gives rise to finite capillary pressure gradients andtherefore to variation in the saturation distribution. That this is not asufficient condition follows from the consideration that hysteric possibilitiesallow for different saturations even though the capillary pressure gradient iszero. In any event, it will be recalled that it is the intent in the Hasslerscheme of relative permeability determination to obtain initially (by thecapillary pressure drainage or imbibition process) uniform conditions of fluiddistribution in the core sample, and then to maintain this uniformity duringmixture flow so that the resultant fluid mobilities which are calculated willrefer to steady-state transfer under fixed conditions of uniformsaturation. T.N. 66