Self-propulsion of droplets driven by an active permeating gel

  • R. KreeEmail author
  • A. Zippelius
Regular Article


We discuss the flow field and propulsion velocity of active droplets, which are driven by body forces residing on a rigid gel. The latter is modelled as a porous medium which gives rise to permeation forces. In the simplest model, the Brinkman equation, the porous medium is characterised by a single lengthscale \(\ell\) --the square root of the permeability. We compute the flow fields inside and outside of the droplet as well as the energy dissipation as a function of \(\ell\). We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit \(\ell\rightarrow\infty\), corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, \(\ell\rightarrow 0\), corresponding to a space filling gel, is singular and not equivalent to Darcy’s equation, which cannot account for self-propulsion.

Graphical abstract


Living systems: Biomimetic Systems 


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© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Georg-August-Universität Göttingen, Institut für Theoretische PhysikGöttingenGermany

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