Abstract
In addition to enabling movement towards environments with favourable living conditions, swimming by microorganisms has also been linked to enhanced mixing and improved nutrient uptake by their populations. Experimental studies have shown that Brownian tracer particles exhibit enhanced diffusion due to the swimmers, while theoretical models have linked this increase in diffusion to the flows generated by the swimming microorganisms, as well as collisions with the swimmers. In this study, we perform detailed simulations based on the force-coupling method and its recent extensions to the swimming and Brownian particles to examine tracer displacements and effective tracer diffusivity in squirmer suspensions. By isolating effects such as hydrodynamic or steric interactions, we provide physical insight into experimental measurements of the tracer displacement distribution. In addition, we extend results to the semi-dilute regime where the swimmer–swimmer interactions affect tracer transport and the effective tracer diffusivity no longer scales linearly with the swimmer volume fraction.
Highlights
Active suspensions of micro-swimmers such as spermatozoa (Creppy et al, 2015), bacteria (Wensink et al, 2012) or microalgae are common both in the natural environment, such as oceans (Durham et al, 2013; Pedley & Kessler, 1992; Stocker, 2012), lakes and ponds, and within living organisms, such as the human body
Our squirmer simulations adequately capture the Gaussian core of the distributions
That the larger, but rarer, displacement events related to the tails are slightly underestimated by the model. This is consistent with similar findings of tracer displacements by squirmers (Thiffeault, 2014). We attribute this to the fact that in the near-field the squirmer does not replicate the flow induced by swimming C. reinhardtii and the tails of the Probability Density Function (PDF) for short-time tracer
Summary
Active suspensions of micro-swimmers such as spermatozoa (Creppy et al, 2015), bacteria (Wensink et al, 2012) or microalgae are common both in the natural environment, such as oceans (Durham et al, 2013; Pedley & Kessler, 1992; Stocker, 2012), lakes and ponds, and within living organisms, such as the human body. In the dilute limit, where swimmers move along straight paths and the interactions between tracers and swimmers are well characterized, the effective diffusion coefficient can be computed (Burkholder & Brady, 2017; Kasyap et al, 2014; Lin et al, 2011; Mio et al, 2011; Pushkin et al, 2013; Pushkin & Yeomans, 2013; Thiffeault, 2014) by averaging the displacements of a single particle due to repeated interactions with swimmers that move independently of one another In many of these studies, the swimmers are modelled as spherical squirmers. Recent experiments (Jeanneret et al, 2016) in the dilute regime have shown that the front-mounted flagella of C. reinhardtii can trap such micron-sized particles and generate very large displacements through direct entrainment Such dramatic events are due to near-field interactions and are strongly related to swimmer geometry, as well as actuation mechanism.
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