Effects of small surface tension in Hele-Shaw multifinger dynamics: An analytical and numerical study

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 4, 2002, Pages 13-

  Paune E ^a   Siegel, M ^b   Casademunt, J ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

^b NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY PROBLEMS; PHASE-SPACE FLOW; SOLVABILITY; UNSTABLE FLOW;

FLOW PATTERNS; FLUID DYNAMICS; FUNCTIONS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; SOLUTIONS;

SURFACE TENSION;

ARTICLE;

EID: 41349107347     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.046205     Document Type: Article

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37. For interfaces symmetric with respect to the central axis of the channel our formulation also describes periodic boundary conditions, that is, an infinite array of fingers.
38. This region can move differently from the (Formula presented) (zero) once the second inner region discussed below has impacted the unit disk. We do not consider this possibility here.
39. Although the daughter singularity is said to impact the unit disk when (Formula presented) the singularities comprising the cluster do not actually impinge upon the unit disk. However, at (Formula presented) the singularities are close enough to influence the interface shape, in the sense that (Formula presented)
40. The steady state with (Formula presented) is unstable to tip splitting modes, although specifying the initial value problem in the extended complex plane precludes the presence of noise needed to activate the instability.
41. It is noted that the (Formula presented) interfacial profile and the projection profile do differ significantly in small scale features. This is another indication of the difficulties in using zero-surface-tension solutions to describe, even qualitatively, the finite surface tension dynamics.