Role of linear viscoelasticity and rotational diffusivity on the collective behavior of active particles

Abstract

A linear dynamics scheme has been used to quantify the impact of viscoelasticity of the suspending fluid on the collective structure of active particles, including rotational diffusivity. The linear stability examines the response near an isotropic state using a mean-field theory including far-field hydrodynamic interactions of the swimmers. The kinetic model uses three possible constitutive models, the Oldroyd-B, Maxwell, and generalized linear viscoelastic models inspired by fluids like saliva, mucus, and biological gels. The perturbation growth rate has been quantified in terms of wavenumber, translational diffusivity, rotational diffusivity, and material properties of the fluids. A key dimensionless group is the Deborah number, which compares the relaxation time of the fluid with the characteristic timescale of the instability. An advantage of the model formalism is the ability to calculate some properties analytically and others efficiently numerically in the presence of rotational diffusion. The different constitutive equations examined help illustrate when and why the dispersion relation can have a peak at a particular wavenumber. The fluid properties can also change the role of rotational diffusion; diffusion always stabilizes a system in a Newtonian fluid but can destabilize a system in a Maxwell fluid. V

Theory of Locomotion Through Complex Fluids

“…9). Recent studies have adapted the mean-field theories for suspensions in Newtonian fluids [68][69][70][71] to quantify the impact of the addition of viscoelasticity [72,73]. Specifically a polymeric stress is incorporated into the mean-field description of the flow which is forced by a configurational average of the force dipoles exerted by the swimmers on the fluid.…”

Viscoelastic and elastomeric active matter: Linear instability and nonlinear dynamics

“…Because this quantity generally exhibits significant fluctuations in time, particularly in the chaotic regime, we define our criterion for significant or net throughput as being when the mean of the throughput time series μ exceeds the standard deviation σ : 4 There are several differences between our study and Ref. [18]. In that work (i) the stability analysis is about an isotropic base state, (ii) liquid-crystalline stresses are not included, (iii) the active particles are self-propelled, and (iv) the concentration field can vary in space (we assume a homogeneous concentration).…”

“…One related study did however consider the linear stability of the bulk isotropic phase in an Oldroyd-B fluid [18]. While the specifics of that model differ from the one presented here, 4 both studies find (i) that increasing η C at fixed τ C will always eventually suppress the spontaneous flow instability, (ii) that at small τ C the polymer simply renormalizes the solvent viscosity (this is our viscous limit), and (iii) a region at large τ C where unstable oscillatory behavior is predicted (this is our elastomeric limit).…”

“…The effect of a viscoelastic polymeric background is also likely to play an important role in modifying active flows and diffusion [18] at a supracellular level. Indeed, long-chain molecules are present in mucus, saliva, and many other viscoelastic fluids both inside and outside the body that are susceptible to colonization by swarms of motile bacteria.…”

Active Viscoelastic Matter: From Bacterial Drag Reduction to Turbulent Solids

“…These slow relaxations should couple to the orientational order, strongly modifying the effects of activity. Polymers could also play a strong role in modifying diffusion [16] and active flows at the supracellular level: they are present in mucus, saliva, and other viscoelastic fluids in which swarms of motile bacteria reside. Notably, many bacteria excrete their own polymers [17], suggesting an advantage in controlling the viscoelasticity of their surroundings.…”