Emergence of Purely Elasto-Plastic Turbulence in Shear Flows

Abstract

We observe the emergence of a distinct, elasticity-driven flow state in a yield-stress fluid in the absence of inertia. Numerical simulations show that this elasto-plastic turbulent state is characterized by a broad spectrum of fluctuations in velocity and stress. Results show a non-monotonic relationship between the volume fraction of the unyielded flow and plasticity. Surprisingly, we find that above a critical value of plasticity, the system can fluidize. Our results reveal the complex interplay between elasticity and plasticity in simple shear flows, indicating that plasticity can enhance rather than hinder momentum transport.

Figures (4)

• Figure 1: For $Bn\in\left\{0, 1, 2, 4, 8\right\}$, representative instantaneous profiles of (a): the trace of the conformation tensor $\mathrm{Tr}\,\mathsf{C}$ and (b): the streamwise velocity $u$, each normalized by the absolute maximum; note that $Bn = 0$ denotes the purely viscoelastic case. In each panel, the white regions represent unyielded fluid. Spatio-temporal averages (along $x$ and time, denoted by $\left\langle\cdot\right\rangle_{x,t}$) are plotted versus the wall-normal coordinate $y$ for $(c)$, $\mathrm{Tr}\,\mathsf{C}$ and $(d)$, $u$, again normalized by the absolute maximum. See Fig. 1 in SM for unnormalized behavior.
• Figure 2: From the top row to bottom, plots of the domain-averaged strain and kinetic energies, the volume fraction $\phi$, and the strain energy spectra for $(a)$, $Bn = 1$, $(b)$, $Bn = 2$, $(c)$, $Bn = 4$ and $(d)$, $Bn = 8$.
• Figure 3: (a) $I_k$, the magnitude of the velocity fluctuations normalized by the mean energy as a function of $Bn$, and the temporally-averaged kinetic energy (inset). $(b)$ The time-averaged volume fraction $\left\langle \phi\left(t\right)\right\rangle_t$ as a function of increasing plasticity, captured through non-dimensional Bingham number ($Bn$), show the emergence of a critical plasticity around critical Bingham number, $Bn_c \simeq 4$. The inset shows values of the root-mean-square of $\phi$ fluctuations ($\phi_{\mathrm{rms}}$) as a function of increasing $Bn$.
• Figure 4: The period return map $\left(T_n, T_{n+1}\right)$ in $\mathcal{T}$ for $Bn=2,4,6,8$, and with $Bn=1$ (inset). The map show the dynamical flow transition as a function of $Bn$.