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Stokes flow through a two-dimensional channel with a linear expansion

TitleStokes flow through a two-dimensional channel with a linear expansion
Publication TypeJournal Article
Year of Publication2018
AuthorsLuca E., Smith SGL
JournalQuarterly Journal of Mechanics and Applied Mathematics
Date Published2018/11
Type of ArticleArticle
ISBN Number0033-5614
Accession NumberWOS:000454979200004
Keywordsequation; Mathematics; mechanics; slow viscous-flow; transform method

Motivated by various applications in microfluidics, we consider low-Reynolds-number flow in a two-dimensional channel with different widths in the upstream and downstream directions. The channel geometry consists of a polygonal domain with angled edges at transition points. The polygonal nature of the geometry makes it amenable to analysis via the Unified Transform Method, providing quasi-analytical solutions which can be used to compute all the physical quantities of interest. We compute the pressure drop between the ends of the expansion or constriction region as a function of the channel width ratio and the orientation of the angled edges and compare our results to extended lubrication theory.

Short TitleQ. J. Mech. Appl. Math.
Student Publication: