Sweep-Stick Mechanism of Heavy Particle Clustering in Fluid Turbulence

It is proposed that the inertial range clustering of small heavy particles in fluid turbulence occurs as a result of the sweep-stick mechanism which causes inertial particles to cluster so as to mimic the clusters of points where the fluid acceleration is perpendicular to the direction of highest contraction between neighboring particles. Direct numerical simulations of inertial particles subjected to linear Stokes drag and suspended in homogeneous isotropic turbulence support the validity of the sweep and stick properties on which the sweep-stick mechanism is based, and also support the clustering consequences of this mechanism. It also explains the observed Stokes-number dependence of inertial particle clustering.

Figure 1

(a) Heavy small particles (black small dots) of $\mathrm{St}=2$ in a thin layer (thickness $5\eta$ and side length $500\eta$), and the set $\mathcal{A}$ of points where (3) is satisfied (red larger balls). The three-dimensional view is shown in (b) for the particles and in (c) for $\mathcal{A}$ in a box of size $50\eta \times 50\eta \times 25\eta$.

Figure 2

(a) Distributions of points in $\mathcal{A}$ at two different times $t$ (dark red points) and $t+\delta t$ (light blue) on a plane of size $(140\eta {)}^2$. (b) $\mathcal{A}$ at $t+\delta t$ (light blue) and the structure (dark red) of $\mathcal{A}$ at $t$ swept by the local fluid velocities for the duration $\delta t$.

Figure 3

Average relative velocity component between a particle and the fluid at the particle position ${\mathit{x}}_p$ conditioned by the fluid acceleration component at ${\mathit{x}}_p$. Normalized by the rms values $u^{\prime }$ and $a^{\prime }$ of fluid velocity and acceleration. ▪, $\mathrm{St}=0.1$; □, 0.5; $\circ$, 2. Formula (2) for $\mathrm{St}=0.1$ and 0.5 is indicated by the solid lines.

Figure 4

(a) Distribution (dark red, ${\lambda }_1>0.2{\tau }_{\eta }^{-2}$; light blue, ${\lambda }_1<0.2{\tau }_{\eta }^{-2}$; the threshold $0.2{\tau }_{\eta }^{-2}$ is chosen so that (4) is satisfied for $\mathrm{St}=2$ at ${\lambda }_1$ equal to that threshold.) of points in $\mathcal{A}$ in a square plane of size $(140\eta {)}^2$. (b)–(d) Particle distribution in a thin (thickness is $5\eta$) layer in the same location as (a). $\mathrm{St}=2$ (b), 0.1 (c), and 5 (d).