Two-phase Hele-Shaw flow with a moving contact line

Conference · Fri Jan 01 00:00:00 EST 1988

OSTI ID:5534306

Weinstein, S J; Ungar, L H ^[1]; Dussan, E B ^[2]

---

1. Pennsylvania Univ., Philadelphia, PA (USA). Dept. of Chemical Engineering
2. Schlumberger-Doll Research Center, Ridgefield, CT (USA)

An asymptotic analysis is presented for Hele-Shaw viscous fingering with a moving contact line at flow rates. As in problems where a thin film is present instead of a contact line, the narrow gap limit is nonuniform, and interfacial boundary conditions valid for the Hele-Shaw equations must be determined in order to predict the flow field and interface shape. Many well-posed boundary-value problems can be identified, each corresponding to a different flow regime characterized by the relative sizes of the capillary number (dimensionless velocity) and the dimensionless gap width. These problems incorporate terms corresponding to the gapwise component of the interfacial curvature (the curvature in the cross-sectional view of the Hele-Shaw cell) and spanwise curvature (seen in the top view of the cell) in different ways. Nonunique interface solutions typically arise as in the analogous thin film problems. The relationships between the curvature terms, the spectra of allowable solutions, and the implications for stability are discussed.

• OSTI ID: 5534306
• Report Number(s): CONF-881143-
• Resource Relation: Conference: American Institute of Chemical Engineers annual meeting, Washington, DC (USA), 27 Nov - 2 Dec 1988; Other Information: Technical Paper 154C
• Country of Publication: United States
• Language: English

Related Subjects

02 PETROLEUM
42 ENGINEERING
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
POROUS MATERIALS
TWO-PHASE FLOW
ASYMPTOTIC SOLUTIONS
BOUNDARY-VALUE PROBLEMS
FLOW RATE
FLUID FLOW
POROSITY
VISCOUS FLOW
MATERIALS
020300* - Petroleum- Drilling & Production
420400 - Engineering- Heat Transfer & Fluid Flow
990230 - Mathematics & Mathematical Models- (1987-1989)