Systematic parameterizations of minimal models of microswimming

Simple models are used throughout the physical sciences as a means of developing intuition, capturing phenomenology, and qualitatively reproducing observations. In studies of microswimming, simple force-dipole models are commonplace, arising generically as the leading-order, far-field descriptions of a range of complex biological and artificial swimmers. Though many of these swimmers are associated with intricate, time varying flow fields and changing shapes, we often turn to models with constant, averaged parameters for intuition, basic understanding, and back-of-the-envelope prediction. In this brief study, via an elementary multitimescale analysis, we examine whether the standard use of a priori-averaged parameters in minimal microswimmer models is justified, asking if their behavioural predictions qualitatively align with those of models that incorporate rapid temporal variation through simple extensions. In doing so, we find that widespread, seemingly innocuous choices of parameters can give rise to qualitatively incorrect conclusions from simple models, with the potential to alter our intuition for swimming on the microscale. Further, we highlight and exemplify how a straightforward asymptotic analysis of the non-autonomous models can result in effective, systematic parametrizations of minimal models of microswimming.

Automated summary

Simple models are commonly used in the physical sciences to gain intuition, capture phenomena, and qualitatively reproduce observations. In the study of microswimmers, simple force-dipole models are prevalent and serve as far-field descriptions of complex swimmers. However, the use of constant, averaged parameters in these models may lead to qualitatively incorrect conclusions and alter our intuition for microscale swimming. Through a multitimescale analysis, we investigate the validity of a priori-averaged parameters and explore models that incorporate rapid temporal variation through simple extensions. We demonstrate how asymptotic analysis of non-autonomous models can lead to effective parametrizations of minimal microswimmer models.