Large-amplitude oscillatory shear rheology of dilute active suspensions

Abstract

Suspensions of swimming microorganisms are a class of active suspensions that show an interesting rheological response in steady shear flow. In particular, the particle contribution to the viscosity can be negative, which has been calculated from models and measured experimentally. In this article, the material functions in large-amplitude oscillatory shear (LAOS) flow are calculated. In addition to the linear material functions, the nonlinearities are quantified analytically using the intrinsic nonlinear material functions. The particle contribution to both the storage and loss modulus can be negative. Since the suspending fluid is assumed Newtonian (and so has no storage modulus), the overall storage modulus can be negative. The intrinsic nonlinearities also show differences between passive and active suspensions. At small frequency, the active swimming can change the sign of the material functions. However, the viscous material functions are independent of the swimming motion at a very large frequency. The changes in sign of the material functions and the unique dependence on frequency may act as a rheological fingerprint of suspensions of swimming organisms.

Stochastic kinetic theory for collective behavior of hydrodynamically interacting active particles

“…The uniform isotropic configuration of pullers is always linearly stable, while for pushers it can suffer an instability when rotational diffusion is weak enough relative to the hydrodynamic coupling of orientations [15][16][17][18][19][20][21][22][23]. Much attention has been focused on patterning phenomena proceeding nonlinearly from the instability, including the associated longranged correlations [20,24], giant fluctuations [25,26], turbulence [27] and other factors that influence the instability and nonlinear oscillatory dynamics [28,29]. Indeed, the continuum mean-field equations describe only trivial dynamics in the linearly stable regime, which includes the general dynamics of pullers.…”

Microfluidic rheology of active particle suspensions: Kinetic theory

“…This was first noted in a theoretical study by Hatwalne et al, 17 who argued that extensile particles or so-called pushers for which r 0 < 0 should have a negative intrinsic viscosity ½g < 0, whereas contractile particles or pullers for which r 0 > 0 should have ½g > 0. A number of more sophisticated models have been proposed since, [18][19][20][21][22][23][24][25][26] which usually extend theories for the rheology of passive rod suspensions [27][28][29] to account for this active dipole and have led to similar predictions. Of particular relevance to the present study is the model of Saintillan, 20 which calculated the effective viscosity and normal stress differences in a dilute active suspension in uniform shear flow as functions of shear rate.…”

Exact Analytical Solution for Large‐Amplitude Oscillatory Shear Flow

“…ffi Chapter 8 of [81]; [82] Giacomin et al their own exact solutions to the oscillatory shear flow problem for at least some constitutive equations other than the one we use here. Specifically, we would expect educators to use our work in both their research and teaching, and for their graduate students to train themselves from our analysis (Section 4) and detailed appendices (Appendix: Fundamental Matrix; Appendix: I 1 , I 2 , and Their Limits; Appendix: Fourier Analysis of Compact Forms).…”