| This dissertation explores two problems, all related to modeling and analysis of hydrodynamic interactions between microswimmers, most common example of which are swimming microorganisms, e.g. Bacillus subtilis. Results for both problems were published in peer-reviewed journals.;In Chapter 1 we introduce the subject of the study, its origins and goals, as well as its current state of development.;In Chapter 2 we present the first problem, in which we study the dynamics and interaction of two microswimmers, modeled by self-propelled dumbbell-type structures. We focus on alignment dynamics of a coplanar pair of elongated swimmers, which propel themselves either by "pushing" or "pulling" both in three- and quasi-two-dimensional geometries of space. We derive asymptotic expressions for the dynamics of the pair, which, complemented by numerical experiments, indicate that the tendency of bacteria to align with one another strongly depends on the position of the propulsion force. In particular, we observe that positioning of the effective propulsion force inside the dumbbell results in qualitative agreement with the dynamics observed in experiments, such as mutual alignment of converging bacteria.;In Chapter 3 we present the second problem, where we develop a 2D model for a suspension of microswimmers in a fluid and analyze it analytically in the dilute regime when swimmer-swimmer interactions can be neglected and numerically in the moderate concentration regime accounting for all hydrodynamic interactions, using a Mimetic Finite Difference method -- efficient method for problems with complex geometries. Our analysis shows that in the dilute regime (in the absence of rotational diffusion) the effective shear viscosity is not affected by self-propulsion. But at the moderate concentrations (due to swimmer-swimmer interactions) the effective viscosity decreases linearly as a function of the propulsion strength of the swimmers. These results prove that ( i) a physically observable decrease of viscosity for a suspension of self-propelled microswimmers can be explained purely from the view of hydrodynamics, i.e. "higher order" phenomena such as chemotaxis and chemical constitution of fluid can be neglected (ii) self-propulsion and interactions among swimmers are both essential to the reduction of the effective shear viscosity.;In Chapter 3 we also present a number of numerical experiments for the dynamics of swimmers resulting from pairwise interactions at moderate distances from one another. The numerical results agree with the physically observed phenomena (e.g., attraction of swimmer to swimmer and swimmer to the wall). This is viewed as an additional validation of the model and the numerical scheme. |
