Izbrane teme sodobne fizike in matematike
The study of microswimmers in low Reynolds number environments plays a crucial role in the understanding of biological locomotion. This article investigates the hydrodynamics governing microscale swimming, with a focus on the squirmer model - a canonical representation of self-propulsion driven by surface distortions. It begins with an overview of the fundamental principles of low Reynolds number hydrodynamics, including the Stokes equation and key concepts such as rate independence and the scallop theorem. The squirmer model is then derived, and its swimming velocity is calculated using both direct solutions of the flow field and the Lorentz reciprocal theorem. Squirmers are further classified into pushers and pullers according to their flow field characteristics, and their interactions with solid boundaries are examined. Theoretical predictions are finally compared with experimental data for Volvox carteri, demonstrating the model’s effectiveness in capturing the behaviour of biological swimmers.
Študij mikroplavalcev v okolju z nizkim Reynoldsovim številom ima ključno vlogo pri razumevanju biološkega samopogona. Članek obravnava hidrodinamiko, ki določa gibanje na mikroskali, s poudarkom na modelu zvijača (angl. squirmer), kanoničnem opisu samopogona, ki izhaja iz površinskih deformacij. Članek začne s pregledom temeljnih načel hidrodinamike pri nizkem Reynoldsovem številu, vključno s Stokesovo enačbo ter ključnimi pojmi, kot sta neodvisnost od hitrosti in teorem školjke. Nato je izpeljan model zvijača, njegova hitrost plavanja pa izračunana z uporabo neposrednih rešitev tokovnega polja ter Lorentzovega izreka o recipročnosti. Zvijači so nadalje razvrščeni na potiskače in vlečnike glede na značilnosti njihovih tokovnih polj, pri čemer so analizirane tudi njihove interakcije s togimi mejami. Teoretične napovedi so na koncu primerjane z eksperimentalnimi podatki za Volvox carteri, kar potrjuje učinkovitost modela pri opisu obnašanja bioloških plavalcev.