Catalogo Articoli (Spogli Riviste)

OPAC HELP

Titolo:
Two-dimensional Stokes and Hele-Shaw flows with free surfaces
Autore:
Cummings, LJ; Howison, SD; King, JR;
Indirizzi:
Math Inst, Oxford OX1 3LB, England Math Inst Oxford England OX1 3LBMath Inst, Oxford OX1 3LB, England Univ Nottingham, Dept Theoret Mech, Nottingham NG7 2RD, England Univ Nottingham Nottingham England NG7 2RD , Nottingham NG7 2RD, England
Titolo Testata:
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
, volume: 10, anno: 1999,
parte:, 6
pagine: 635 - 680
SICI:
0956-7925(199912)10:<635:TSAHFW>2.0.ZU;2-W
Fonte:
ISI
Lingua:
ENG
Soggetto:
DEPENDENT FREE BOUNDARIES; MOVING BOUNDARY; TENSION MODEL; CLASSIFICATION; INJECTION; BUBBLES; DRIVEN; FLUID; CELL;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Engineering, Computing & Technology
Citazioni:
45
Recensione:
Indirizzi per estratti:
Indirizzo: Cummings, LJ Math Inst, 24-29 St Giles, Oxford OX1 3LB, England Math Inst 24-29 St Giles Oxford England OX1 3LB 3LB, England
Citazione:
L.J. Cummings et al., "Two-dimensional Stokes and Hele-Shaw flows with free surfaces", EUR J AP MA, 10, 1999, pp. 635-680

Abstract

We discuss the application of complex variable methods to Hele-Shaw flows and two-dimensional Stokes flows, both with free boundaries. We outline thetheory for the former, in the case where surface tension effects at the moving boundary are ignored. We review the application of complex variable methods to Stokes flows both with and without surface tension, and we explorethe parallels between the two problems. We give a detailed discussion of conserved quantities for Stokes flows, and relate them to the Schwarz function of the moving boundary and to the Baiocchi transform of the Airy stress function. We compare the results with the corresponding results for Hele-Shaw hows, the principal consequence being that for Hele-Shaw flows the singularities of the Schwarz function are controlled in the physical plane, while for Stokes flow they are controlled in an auxiliary mapping plane. We illustrate the results with the explicit solutions to specific initial value problems. The results shed light on the construction of solutions to Stokes flows with more than one driving singularity, and on the closely related issue of momentum conservation, which is important in Stokes flows, although it does not arise in Hele-Shaw flows. We also discuss blow-up of zero-surface-tension Stokes flows, and consider a class of weak solutions, valid beyond blow-up, which are obtained as the zero-surface-tension limit of flows with positive surface tension.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 25/11/20 alle ore 18:44:15