Concentration Matters: Enhancing Particle Settling in Narrow Tilted Channels

Abstract

Particles are known to sediment faster in containers with tilted walls than in vertical ones, a phenomenon known as the Boycott effect. In this work, we investigate how the tilt angle influences sedimentation in narrow channels across different particle volume fractions. Using particle-resolved computational fluid dynamics simulations, we reveal that there exists a concentration-dependent optimal tilt angle that maximizes sedimentation rates. Furthermore, at large tilt angles, the flow profiles across the channel deviate from the classical parabolic shape. We show that these non-parabolic profiles can be accurately captured by a one-dimensional Brinkman model, providing a predictive framework for understanding and tuning sedimentation in tilted geometries. Our findings demonstrate the potential to control and optimize particle settling by adjusting the channel tilt according to particle concentration, opening new possibilities for design in industrial and laboratory processes.

Figures (5)

• Figure 1: (a) Schematic view of the domain geometry, a channel of span $L_y$ tilted an angle $\theta$ respect gravity $\boldsymbol{g}$. The solute particles sediment primarily near the lower wall while a counterflow is generated near the upper wall. The dashed line represents the interface between the clear fluid on the top and the particle suspension on the bottom of the channel. (b) Snapshot of a SPH simulation at volume fraction $\phi=0.2$ and tilt angle $\theta=30^{\circ}$. The particles are represented as solid spheres while the dots represent SPH particles.
• Figure 2: Particle sedimentation velocities versus time for volume fraction $\phi=0.3$ and tilts $\theta \in [0^{\circ}, 75^{\circ}]$ (curves from dark to light). In the main figure the velocities and the time are scaled with the tilt-dependent steady state velocity $\langle u_z \rangle$ and with $1/\sin \theta$ respectively. Inset: same data without scaling. The curve for $\theta = 0^{\circ}$ is only shown in the inset. Results for other volume fractions are shown in the Supplemental Fig. 1.
• Figure 3: Steady state sedimentation velocity normalized with the single-particle sedimenting velocity, $u_0$, versus tilt angle for different volume fractions. The inset shows the steady state sedimentation velocity in vertical channels versus the volume fraction and the fit $-\langle u_z \rangle \sim (1-\phi)^n$ with $n \approx 2.6$.
• Figure 4: Velocity profiles across the channel for volume fraction $\phi=0.3$ and tilt angles (from left to right) $\theta=10,\, 20 \text{ and } 60^{\circ}$. The velocity is normalized with the isolated particle velocity $u_0=1$. The dashed vertical line represents the interface position, $h$, obtained from the fits to the one-dimensional model, Eqs. \ref{['eq:model_stokes']}-\ref{['eq:model_up']}. Results for other volume fractions are shown in the Supplemental Fig. 2.
• Figure 5: Optimal angle to enhance sedimentation, $\theta_{\text{opt}}$, versus volume concentration obtained from the SPH simulations (dots) and the one-dimensional model (lines). Theoretical predictions for $\gamma = 1.5 \cdot 10^{-5},\, 3 \cdot 10^{-5},\, 4.5 \cdot 10^{-5} \text{ and } 6 \cdot 10^{-5}$ from dark to light colors.