A note on the two-phase Hele-Shaw problem

Journal of Fluid Mechanics

Volumn 409, Issue , 2000, Pages 243-249

  Howison, Sam D ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

IMMISCIBLE FLUIDS; MATHEMATICAL METHOD; TWO-PHASE FLOW;

EID: 0033911790     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112099007740     Document Type: Article

References (8)

1. CUMMINGS, L., HOWISON, S. D. & KING, J. R. 1999 Two-dimensional Stokes and Hele-Shaw flow with free surfaces. Eur. J. Appl. Maths 10, 681-706.
2. DAVIS, P. J. 1974 The Schwarz Function and its Applications. Carus Mathematical Monographs, vol. 17. Math. Assoc. of America.
3. ELLIOTT, C. M. & JANOVSKY, V. 1981 A variational inequality approach to Hele-Shaw flow with a moving boundary. Proc. R. Soc. Edinb. A 88, 93-107.
4. JACQUARD, P. & SÉGUIER, P. 1962 Mouvement de deux fluides en contact dans un milieu poreux. J. de Méc. 1, 367-394.
5. OTTO, F. F. 1997 Viscous fingering: an optimal bound on the growth rate of the mixing zone. SIAM J. Appl. Maths 57, 982-990.
6. OTTO, F. F. 1999 Evolution of microstructure in unstable porous media flow: a relaxational approach. Commun. Pure Appl. Maths 52, 873-915.
7. SAFFMAN, P. G. 1959 Exact solutions for the growth of fingers from a flat interface between two fluids in a porous medium or Hele-Shaw cell. Q. J. Mech. Appl. Maths 12, 146-150.
8. SAFFMAN, P. G. & TAYLOR, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312-329.