arXiv subjects

Thomas Dombrowski

Publications and source records attributed to Thomas Dombrowski.

4 recordsLinked to original sources

arXiv2022

Reciprocal swimming at intermediate Reynolds number

In Stokes flow, Purcell's scallop theorem forbids objects with time-reversible (reciprocal) swimming strokes from moving. In the presence of inertia, this restriction is eased and reciprocally deforming bodies can swim. A number of recent works have investigated dimer models that swim reciprocally at intermediate Reynolds numbers Re ~ 1-1000. These show interesting results (e.g. switches of the swim direction as a function of inertia) but the results vary and seem to be case-specific. Here, we introduce a general model and investigate the behaviour of an asymmetric spherical dimer of oscillating length for small-amplitude motion at intermediate Re. In our analysis we make the important distinction between particle and fluid inertia, both of which need to be considered separately. We asymptotically expand the Navier-Stokes equations in the small amplitude limit to obtain a system of linear PDEs. Using a combination of numerical (Finite Element) and analytical (reciprocal theorem, method of reflections) methods we solve the system to obtain the dimer's swim speed and show that there are two mechanisms that give rise to motion: boundary conditions (an effective slip velocity) and Reynolds stresses. Each mechanism is driven by two classes of sphere-sphere interactions, between one sphere's motion and 1) the oscillating background flow induced by the other's motion, and 2) a geometric asymmetry induced by the other's presence. We can thus unify and explain behaviours observed in other works. Our results show how sensitive, counter-intuitive and rich motility is in the parameter space of finite inertia of particles and fluid.

physics.flu-dyn↗

arXiv2021

Pairwise and collective behavior between model swimmers at intermediate Reynolds numbers

We computationally studied the pair interactions and collective behavior of asymmetric, dumbbell swimmers over a range of intermediate Reynolds numbers and initial configurations. Depending on the initial positions and the Re, we found that two swimmers either repelled and swum away from one another or assembled one of four stable pairs: in-line and in-tandem, both parallel and anti-parallel. When in these stable pairs, swimmers were coordinated, swum together, and generated fluid flows as one. We compared the stable pairs' speeds, swim direction and fluid flows to those of the single swimmer. The in-line stable pairs behaved much like the single swimmer transitioning from puller-like to pusher-like stroke-averaged flow fields. In contrast, for the in-tandem pairs we discovered differences in the swim direction transition, as well as the stroke-averaged fluid flow directions. Notably, the in-tandem V pair switched its swim direction at a higher $\text{Re}$ than the single swimmer while the in-tandem orbiting pair switched at a lower $\text{Re}$. We also studied a system of 122 swimmers and found the collective behavior transitioned from in-line network-like connections to small, transient in-tandem clusters as the Reynolds number increased, consistent with the in-line to in-tandem pairwise behavior. Details in the collective behavior involved the formation of triples and other many-body hydrodynamic interactions that were not captured by either pair or single swimmer behavior. Our findings demonstrate the richness and complexity of the collective behavior of intermediate-$\text{Re}$ swimmers.

physics.flu-dyn↗

arXiv2020

Kinematics of a simple reciprocal model swimmer at intermediate Reynolds numbers

We computationally study the kinematics of a simple model reciprocal swimmer (asymmetric dumbbell) as a function of the Reynolds number (Re) and investigate how the onset and gradual increase of inertia impacts the swimming behavior: a reversal in the swim direction, flow directions, and the swim stroke. We divide the swim stroke into the expansion and compression of the two spheres and relate them to power and recovery strokes. We find that the switch in swim direction also corresponds to a switch in power and recovery strokes. We obtain expressions for the mean swimming velocity by collapsing the net displacement during expansion and compression under power law relationships with respect to Re, the swimmer's amplitude, and the distance between the two spheres. Analyzing the fluid flows, we see the averaged flow field during expansion always resembles a pusher and compression always a puller, but when averaged over the whole cycle, the flow that dominates is the one that occurs during the power stroke. We also relate the power and recovery strokes to the swimming efficiency during times of expansion and compression, and we find that the power stroke is, surprisingly, not always more efficient than the recovery stroke. Our results may have important implications for biology and ultimately the design of artificial swimmers.

cond-mat.soft↗

arXiv2018

Transition in swimming direction in a model self-propelled inertial swimmer

We propose a reciprocal, self-propelled model swimmer at intermediate Reynolds numbers ($Re$). Our swimmer consists of two unequal spheres that oscillate in antiphase generating nonlinear steady streaming (SS) flows. We show computationally that the SS flows enable the swimmer to propel itself, and also switch direction as $Re$ increases. We quantify the transition in the swimming direction by collapsing our data on a critical $Re$ and show that the transition in swimming directions corresponds to the reversal of the SS flows. Based on our findings, we propose that SS can be an important physical mechanism for motility at intermediate $Re$.

physics.flu-dyn↗