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Titolo: Twodimensional Stokes and HeleShaw 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:
 09567925(199912)10:<635:TSAHFW>2.0.ZU;2W
 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, 2429 St Giles, Oxford OX1 3LB, England Math Inst 2429 St Giles Oxford England OX1 3LB 3LB, England



 Citazione:
 L.J. Cummings et al., "Twodimensional Stokes and HeleShaw flows with free surfaces", EUR J AP MA, 10, 1999, pp. 635680
Abstract
We discuss the application of complex variable methods to HeleShaw flows and twodimensional 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 HeleShaw hows, the principal consequence being that for HeleShaw 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 HeleShaw flows. We also discuss blowup of zerosurfacetension Stokes flows, and consider a class of weak solutions, valid beyond blowup, which are obtained as the zerosurfacetension 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 26/01/21 alle ore 20:31:13