Blood microcirculation critically depends on the migration of red cells towards the flow centerline. We identify theoretically the ratio of the inner over the outer fluid viscosities lambda as a key parameter. At low lambda, the vesicle deforms into a tank-treading ellipsoid shape far away from the flow centerline. The migration is always towards the flow centerline, unlike drops. Above a critical lambda, the vesicle tumbles or breaths and migration is suppressed. A surprising coexistence of two types of shapes at the centerline, a bulletlike and a parachutelike shape, is predicted.
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Danker et al. (2009) studied this question.
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