https://doi.org/10.1140/epje/i2018-11729-1
Regular Article
Self-propulsion of droplets driven by an active permeating gel
Georg-August-Universität Göttingen, Institut für Theoretische Physik, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany
* e-mail: kree@theorie.physik.uni-goettingen.de
Received:
22
March
2018
Accepted:
7
September
2018
Published online:
11
October
2018
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 
--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 . We furthermore show that there are optimal gel fractions, giving rise to maximal linear and rotational velocities. In the limit 
, corresponding to a very dilute gel, we recover Stokes flow. The opposite limit, 
, corresponding to a space filling gel, is singular and not equivalent to Darcy’s equation, which cannot account for self-propulsion.
Key words: Living systems: Biomimetic Systems
© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature, 2018
