Dynamics of growing interfaces from the simulation of unstable flow in random media
- Department of Physics, West Virginia University, P.O. Box 6315, Morgantown, West Virginia 26506-6315 (United States)
- U.S. Department of Energy, Morgantown Energy Technology Center, Morgantown, West Virginia 26507-0880 (United States)
Viscous fingering in random porous media is encountered in many applications of two-phase flow, where the interface is unstable because the ratio of the viscosity of the displaced fluid to that of the injected fluid is large. In these applications, including enhanced oil recovery, characterization of the width of the interface is an important concern. In the limit of stable flow, the interfacial width had been found to grow as [ital w][approx][ital t][sup [beta]], where [beta][approx]0.66, approximately independent of capillary number. To study the same behavior for the unstable case, we have simulated flow in two-dimensional random porous media using a standard model with different viscosity ratios and zero capillary pressure. When the injected fluid has zero viscosity, viscosity ratio [ital M]=[infinity], the interfacial width has the expected self-similar diffusion-limited-aggregation-like behavior. For smaller viscosity ratios, the flow is self-affine with [beta]=0.66[plus minus]0.04, which is the same value that had been observed in studies of stable flow. Furthermore, the crossover from self-similar fractal flow to self-affine fractal flow is observed to scale with the same characteristic'' time, [tau]=[ital M][sup 0.17], that had been found to scale the average interface position. This fractal'' scaling of the crossover leads to definite predictions about the viscosity-ratio dependence of the amplitudes associated with interfacial position and interfacial width.
- OSTI ID:
- 7207349
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Vol. 49:5; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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POROUS MATERIALS
TWO-PHASE FLOW
DYNAMICS
CAPILLARIES
COMPUTERIZED SIMULATION
FRACTALS
GROWTH FACTORS
VISCOUS FLOW
BLOOD VESSELS
BODY
CARDIOVASCULAR SYSTEM
FLUID FLOW
MATERIALS
MECHANICS
MITOGENS
ORGANIC COMPOUNDS
ORGANS
PROTEINS
SIMULATION
420400* - Engineering- Heat Transfer & Fluid Flow