Complex Fluids and Flows in Mathematical Biology

Monday, June 14 at 5:45pm (PDT)
Tuesday, June 15 at 01:45am (BST)
Tuesday, June 15 09:45am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS03" time block.
Note: this minisymposia has multiple sessions. The second session is MS02-MMPB (click here).

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Calina Copos (University of North Carolina at Chapel Hill, USA), Tony Gao (Michigan State University, USA), On Shun Pak (Santa Clara University, USA), Yuan-nan Young (New Jersey Institute of Technology, USA)


Biological fluid environments often display highly complex characteristics due to the presence of microstructure formed by suspensions of passive and/or active components such as proteins, microtubules, or self-propelled particles that interact with a flow. The complexity of these biological fluids and flows poses challenges to the mathematical description of the physics governing the biological processes. Continuing developments of mathematical and numerical tools have enabled the studies of biological processes involving complex fluid environments. This mini-symposium will focus on recent advances in this vibrant field of research. Topics include the impacts of complex rheology and heterogeneity of the fluid environments on various biological processes (e.g., cell motility, mucus transport) as well as novel emergent dynamics of active fluids. Fundamental insights gained from these complex biological flows will improve human understanding of important biological processes, diseases, and thereby the development of new therapies to improve health outcomes.

Tony Gao

(Michigan State University, USA)
"Q-tensor model for undulatory swimming in a liquid crystal"
Microorganisms may exhibit rich swimming behaviors in anisotropic fluids, such as liquid crystals, that have direction-dependent physical and rheological properties. Here we construct a two-dimensional computation model to study the undulatory swimming mechanisms of microswimmers in a solution of rigid, rodlike liquid-crystalline polymers. We describe the fluid phase using Doi's Q-tensor model, and treat the swimmer as a finite-length flexible fiber with imposed propagating traveling waves on the body curvature. The fluid-structure interactions are resolved via an Immersed Boundary method. Compared to the swimming dynamics in Newtonian fluids, we observe non-Newtonian behaviors that feature both enhanced and retarded swimming motions in lyotropic liquid-crystalline polymers. We reveal the propulsion mechanism by analyzing the near-body flow fields and polymeric force distributions, together with asymptotic analysis for an idealized model of Taylor's swimming sheet.

David Stein

(Simons Foundation, USA)
"The many behaviors of deformable active droplets"
Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motion. In some cases, these phenomena have been well characterized, and theory can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this talk, I will discuss the behavior of droplets of an active nematic fluid. Through a mix of linear stability analysis and nonlinear simulations, we identify parameter regimes where single modes dominate and droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zig-zaggers, washing machines, wanderers, and pulsators.

Herve Nganguia

(Indiana University of Pennsylvania, USA)
"Swimming in a fluid pocket enclosed by a porous medium"
This talk presents a minimal theoretical model to investigate how heterogeneity created by a swimmer affects its own locomotion. As a generic locomotion model, we consider the swimming of a spherical squirmer in a purely viscous fluid pocket (representing the liquified or degelled region) surrounded by a Brinkman porous medium (representing the mucus gel). We obtain analytical expressions for the swimming speed, flow field, and power dissipation of the swimmer. Depending on the details of surface velocities and fluid properties, our results reveal the existence of a minimum threshold size of mucus gel that a swimmer needs to liquify in order to gain any enhancement in swimming speed.

Anup Kanale

(University of Southern California, USA)
"Flow-mediated instabilities in ciliary carpets"
Motile cilia that densely cover epithelial tissues are known to coordinate their beating in metachronal waves to transport fluid. Although hydrodynamic coupling seems to drive this coordination, the exact mechanisms leading to the emergence of ciliary waves remain unclear. Here, we propose a minimal model in which each cilium is a rotating bead driven by a phase-dependent active force, and we accordingly construct a coarse-grained continuum model. Isotropic states are unstable relative equilibria. Perturbations to these equilibria lead, beyond the transient regime, to noisy wave-like patterns that propagate along the direction of the ciliary beating. These noisy patterns seem globally attracting for all initial conditions, and depend only on the nature of the forcing at the level of an individual cilium. We use the continuum model to analyze the linear stability of both the synchronized and isotropic states to perturbations of all wavelengths and show that both states are unstable with growth rates that are in good agreement with the discrete cilia simulations. Our findings demonstrate a set of minimal conditions necessary to create wave-like coordination in ciliary carpets.

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Virtual conference of the Society for Mathematical Biology, 2021.