A new form of mixing in turbulent sedimentation

Abstract

We study the sedimentation of finite-size inertial particles in a Rayleigh-Taylor-like setup using state-of-the-art direct numerical simulations. The falling particles are observed to produce two distinct regions: a leading mixing layer with a linear concentration profile followed by a bulk region of uniform density. Unlike classical RT turbulence, the mixing layer extension accelerates with an anomalous, non-integer exponent, while the bulk region moves at a constant velocity. A one-dimensional model based on a local hindered settling law accurately captures the observed dynamics and its dependence on the particle-to-fluid density ratio. The present work identifies a new regime of convective mixing which develops at the front of particle suspensions in sedimentation processes.

Figures (5)

• Figure 1: Volumetric rendering of the instantaneous vertical fluid velocity field $v_z({\bm x},t)$ and particle positions at $t\approx0.17\tau_t$. Upward/downward velocities are shown in blue/orange, more intense for higher magnitudes of $v_z$. Regions where $v_z\approx0$ are rendered as transparent.
• Figure 2: Particle concentration profiles for the $\gamma=2$ case at different times. Dashed lines represent the profile model (\ref{['eq4']}) together with the positions of its characteristic points $z_0$, $z_1$ and $z_2$ for the latest time. In the inset, the latest three curves are rescaled according to the instantaneous locations of $z_0$ and $z_1$.
• Figure 3: Time evolution of the width $h(t)$ (filled symbols) and geometric center $z_c(t)$ (empty symbols) of the mixing region for the simulations at different $\gamma$. For the geometric center, a black continuous line of slope $r$ is included for guidance.
• Figure 4: Time evolution of the width $h(t)$ of the mixing region. Results from different $\gamma$ are rescaled according to the model (\ref{['eq9']}), which is represented by the black continuous line.
• Figure 5: Vertical profile of the particle flux $\Pi(z,t)$ for the case $\gamma=4$ at different times. Lines represent the predictions of the theoretical model in the mixing layer given by (\ref{['eq11']}), markers represent the flux according to the simulation data.