Enhanced buoyancy of active particles in convective flows

We numerically investigated the diffusion of a heavy active Brownian particle in a linear periodic array of steady planar counter-rotating convection rolls at high Péclet numbers. We show that, under certain conditions, the particle rises to the surface even if it is denser than the suspension fluid, and floats there for exceedingly long times. Such an apparently counterintuitive phenomenon of “enhanced buoyancy” is a combined effect of gravity, advection, and shear torque.

Figure 1

Spatial distributions, $p(x,y)$, of a JP in the laminar flow of Eq. (1) for $g=0.4$ and different $v_0$ [(a)–(d)]. The chart levels are color coded on natural logarithmic scales as indicated. Trajectory samples (2400 time-unit long, drawn in different colors) immediately before (e) and after (f) the EB onset, are reported for a comparison. Other simulation parameters are $D_0=D_{\theta }=0.01$, $U_0=1$, and $L=2\pi$.

Figure 2

Stationary longitudinal pdf's, $p\left(x\right)$, of a JP in the flow of Eq. (1): (a) $v_0=0$ and different $g$; (b) $g=0$ and (c) $g=0.1$ for different $v_0$ (see legends). Other simulation parameters are $D_0=D_{\theta }=0.01$; $U_0=1$ and $L=2\pi$.

Figure 3

Ratios of the longitudinal, $p\left(x\right)$, and transverse distributions, $p\left(y\right)$, at the boundaries of the convection rolls of Eq. (1) for (a) and (b): $g=0.4$ and different $D_{\theta }$; (c) and (d): $D_{\theta }=0.01$ and different $v_0$, see legends. Here $p_x\left(a\right)=p(x=a)$ and $p_y\left(a\right)=p(y=a)$ for $a=0$ and $\pi$. Other simulation parameters are $D_0=0.01$; $U_0=1$ and $L=2\pi$, with ${\mathrm{\Omega }}_L=1$.

Figure 4

Subtracted autocorrelation function $C\left(t\right)=\langle y\left(t\right)y\left(0\right)\rangle -{\langle y\rangle }^2$ for different $v_0$. The fitted exponential decay times, $\tau$ (in units of ${\mathrm{\Omega }}_L^{-1}$), and $\langle y\rangle$ (in units of $L/2$) vs. $v_0/U_0$ are plotted, respectively, in the top and bottom insets for different $D_0$. The values of $C\left(0\right)$ are reported in the SM [29]. If not given in the legends, then the simulation parameters are $g=0.4$, $D_0=D_{\theta }=0.01$; $U_0=1$ and $L=2\pi$, with $D_L={\mathrm{\Omega }}_L=1$.