The Effects of Confinement in Active Matter: the Casimir Effect, Partitioning, and Hindered Diffusion

Citation

Kjeldbjerg, Camilla Maria (2022) The Effects of Confinement in Active Matter: the Casimir Effect, Partitioning, and Hindered Diffusion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/avfw-fh81. https://resolver.caltech.edu/CaltechTHESIS:12102021-231944176

Abstract

Active matter describes a class of materials for which constituent "particles" convert chemical energy into mechanical motion leading to self-propulsion (swimming). The origins of this swimming motion for both biological and synthetic constituents is a thriving area of research. However, here we focus on the physical properties and mechanics of the active matter systems. We model active particles using the active Brownian particle (ABP) model that is the simplest model that captures the essential physics, where a particle translates with a swim speed U₀ in a direction q for a characteristic reorientation time τ_R; the average length they move between each reorientation is called the run, or persistence, length ℓ = U₀τ_R. Owing to this persistent swimming, the ABPs distribute non-homogenously near surfaces, accumulating at no-flux boundaries leading to a concentration boundary layer near solid surfaces. Active particles often have an effective size—their run length—which can be much larger than their geometric size such that they experience confinement in geometries whose size is on the order of the run length. Active systems are inherently far from equilibrium, and we cannot appeal to properties of equilibrium thermodynamic such as the chemical potential to predict the partitioning. Fortunately, active particles are still subject to the laws of mechanics, and in this work, we present a simple macroscopic balance that allows one to predict behavior without detailed calculations. We predict the attractive force between two parallel plates in a reservoir (also called the Casimir effect) and find that the average concentration between the plates equals that in the bulk reservoir independent of the degree of confinement (ratio of run length to the spacing between the plates). We then examine the confinement effects in a channel geometry, where the behavior is fundamentally different, and the average concentration grows linearly with the degree of confinement. The understanding of these fundamental geometries motivated us to look into more complex geometries such as porous media. Based on dimensional analysis and our predictive model, we explain the transient behavior and steady-state partitioning of active particles between a fluid reservoir and a porous medium. Lastly, we discuss the hindered diffusion in periodic porous media and how the diffusion depends not only on the porosity of the medium but also on the degree of confinement. We believe that utilizing the insights in effects of confinement for these fundamental geometries and the porous media will be valuable in designing optimal structures for enhancing or isolating active particles.

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