Modeling of microswimmers for drug delivery

Many types of motile cells, such as bacteria in our guts and sperms in the female reproductive tract, need to push themselves through tight spaces filled with viscous fluid. In recent years, the movement of these “micro swimmers” has been mimicked in the design of micro- and nanoscale self-propelled machines for applications including targeted drug delivery. Optimizing the design of these machines requires detailed mathematical knowledge of microswimmers in these environments. A large international group of physicists led by Abdallah Daddi-Moussa-Ider of Heinrich-Heine-Universität Düsseldorf, Germany, has now generated mathematical models of micro-swimmers in clean, viscous, surfactant-coated droplets, demonstrating that surfactant alters significantly the behavior of swimmers. They published their work in EPJ E.

The dynamics of microswimmers moving within a viscous liquid drop depends on many things, including the shape and size of the drop, the number of microswimmers, and the liquid’s Reynolds number. This is a measure of viscosity; Liquids with a low Reynolds number are more viscous and flow linearly with little turbulence. The flow of such a liquid can be modeled by solving a series of partial differential equations known as Navier-Stokes equations. In this case, the microswimmer itself was considered to be a force dipole confined within the droplet and located at a set point. The presence of a surfactant layer surrounding the drop containing the microswimmer was modeled using boundary conditions.

By solving these equations under a series of conditions – drops with or without surfactant layers, fixed and free-moving, and with different Reynolds numbers and rays – he gave Daddi-Moussa-Ider and his collaborators a series of flow fields. subtly different, from which the dynamics of the microswimmer could be defined. They note that these models of swimmer dynamics can prove useful in the design of micro-machines for material assembly, biosensing and microsurgery, as well as drug delivery.

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Reference

AR Sprenger, VA Shaik, AM Ardekani, M. Lisicki, AJTM Mathijssen, F. Guzmán-Lastra, H. Löwen, AM Menzel and A. Daddi-Moussa-Ider (2020), Towards an analytical description of active microswimmers in clean environment and in drops covered with surfactant, EUR. Phys. J. E 43:58. https: //doi.org /10.1140 /flexibility /i2020-11980-9

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