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Dilute emulsions with surface tension
Worcester Polytechnic Institute, USA.ORCID iD: 0000-0002-4403-6908
Worcester Polytechnic Institute, USA.
2016 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485, Vol. 74, no 1, p. 89-111Article in journal (Refereed) Published
Abstract [en]

We consider an emulsion formed by two newtonian fluids in which one fluid is dispersed under the form of droplets of arbitrary shape in the presence of surface tension. We consider both cases of droplets with fixed centers of mass and of convected droplets. In the non-dilute case, for spherical droplets of radius aϵ of the same order as the period length $ϵ$, the two models were studied by Lipton-Avellaneda (1990) and Lipton-Vernescu (1994). Here we are interested in the time-dependent, dilute case when the characteristic size of the droplets aϵ, of arbitrary shape, is much smaller than ϵ. We study the limit behavior when $ϵ→0$ in each of these two models. We establish a Brinkman type law for the critical size $a_ϵ=O⁡(ϵ^3)$ in the first case, whereas in the second case there is no “strange” term, and in the limit the flow is unperturbed by the droplets.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2016. Vol. 74, no 1, p. 89-111
Keywords [en]
Stokes flow, Brinkman equations, surface tension, G-convergence, Mosco-convergence, emulsions
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-88399DOI: 10.1090/qam/1403ISI: 000372755600005OAI: oai:DiVA.org:kau-88399DiVA, id: diva2:1635169
Available from: 2022-02-04 Created: 2022-02-04 Last updated: 2022-09-13Bibliographically approved

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Nika, Grigor

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