Entropic Splitter for Particle Separation

We present a particle separation mechanism which induces the motion of particles of different sizes in opposite directions. The mechanism is based on the combined action of a driving force and an entropic rectification of the Brownian fluctuations caused by the asymmetric form of the channel along which particles proceed. The entropic splitting effect shown could be controlled upon variation of the geometrical parameters of the channel and could be implemented in narrow channels and microfluidic devices.

Figure 1

(top) Schematic illustration of the two-dimensional channel confining the motion of the Brownian particles. The structure is defined by Eq. (2). Brownian particles are driven by a constant force $\overrightarrow{f}$ and a square wave force $\overrightarrow{F}(t)$ along the longitudinal direction. The values of the chosen parameters defined in Eq. (2) are: $m_1=2$, $m_2=0.4$, $b/L=0.1$. The dashed lines represent the limit for the positions of the center of the particles within the channel. (bottom) Effective entropic potential for the two particle sizes depicted above.

Figure 2

Average current vs the amplitude of the periodic forcing $F_0$ in the adiabatic limit ($\Omega ={\Omega }_0=\pi /10$) for particles of different radii, for a channel with $m_1=2$, $m_2=0.4$, and $b/L=0.1$. The solid lines indicate the results of the simulations, whereas the dashed line plots the prediction according to the FJ equation for $r=0.9b$. For $f_0<0$ small particles go to the left, whereas big particles move to the right. The critical size that divides these two behaviors can be tuned by the value of $F_0$.

Figure 3

Schematic illustration of the functioning of the entropic splitter. A mixture of particles of different radii is placed initially in the center. Under the combined presence of the static and periodic forcing, large particles move towards the right, whereas small particles follow the bias, i.e., are moving towards the left.

Figure 4

Average current vs the value of the static force $f_0$ in the adiabatic limit ($\Omega =\pi /10$) for particles of different radii, for the channel plotted in Fig. 1 with $F_0=20$. In all cases the velocity increases linearly with $f_0$. As $f_0$ gets more negative, the particles invert their velocity and start to move to the left. The critical force that determines this velocity inversion depends on the radius $r$ and gets progressively larger (in absolute value) for larger radii.