Upstream Swimming in Complex Fluids

We’ve worked on computational and theoretical models for swimming microbes and looked at their dynamics in biologically relevant environments, such as flowing films. Another important consideration is the nature of the fluid that the microbes swim through. An important aspect of many fluids is that they have a dual fluidic and elastic (viscoelastic) nature. Biological examples of such so-called non-Newtonian fluids include cervical mucus, extracellular matrix surrounding biofilms, and flowing blood. To make matters more complicated, microbes such as sperm and other swimming cells must often swim upstream.

With Arnold Mathijssen and Amin Doostmohammadi, we considered a microswimmer swimming in a channel geometry and subjected to a flow. Previous studies with this set-up were done by Zottl and Stark, who established that the mathematics describing the microbe’s swimming are related to the swinging of a pendulum. We built on their work to predict that swimming cells in biological flows naturally reorient toward the centre of channels, where they migrate upstream. This is because of the elasticity in such fluids.

The reorientation also happens because the flow turns the swimmers away from the walls, like in normal, Newtonian fluids (i.e. water). We found that swimmers in fluids that become more viscous when sheared (like cornstarch that thickens when stirred) swim upstream more quickly than in fluids that thin (like ketchup that spills suddenly after slowly creeping). The swimmers move upstream faster in shear-thickening flows because they can spend more time in slower flows near walls, where they have the chance to sneak further upstream.

Figure by Arnold Mathijssen.

Swimming speed is used to assess the fertility of human semen so we suspect that fertility estimates based on speed could be improved by performing these measurements in viscoelastic fluids. The sperm in such a flowing fluid would swim upstream along the centreline where they can have a fair race, without some cheating by sneaking up along the walls.

This work will soon appear in the journal Physical Review Letters.