Separation of Chiral Particles in Micro- or Nanofluidic Channels

We propose a method to separate enantiomers in microfluidic or nanofluidic channels. It requires flow profiles that break chiral symmetry and have regions with high local shear. Such profiles can be generated in channels confined by walls with different hydrodynamic boundary conditions (e.g., slip lengths). Because of a nonlinear hydrodynamic effect, particles with different chirality migrate at different speeds and can be separated. The mechanism is demonstrated by computer simulations. We investigate the influence of thermal fluctuations (i.e., the Péclet number) and show that the effect disappears in the linear response regime. The details of the microscopic flow are important and determine which volume forces are necessary to achieve separation.

Figure 1

Illustration of the simulation model. A helical particle moves in a square channel with asymmetric Poiseuille-like flow profile (a). Maps show the profiles across the channel: (b) DPD flow profile; (c) corresponding theoretical profile calculated by numerical solution of the Stokes equation. The amplitudes depend on the applied pressure.

Figure 2

Separation of chiral particles in the asymmetric channel at volume force $f_y=0.1ϵ/\sigma$. (a) Histogram of distances traveled in the time $t=15.000\tau$ for left-handed helices (dark shaded) and right-handed helices (light shaded). (b) Same as (a) for the Langevin simulations without hydrodynamics. (c) Spatial distribution across the channel for left-handed helix (left) and right-handed helix (right) for the simulations with hydrodynamics. (d) Same as (c) for the Langevin simulations without hydrodynamics.

Figure 3

Separation of chiral particles in the asymmetric channel as a function of volume force $f_y$. (a) Relative velocity difference for left-handed and right-handed particles. Inset: Distance between means of the distributions $p_L$ and $p_R$ for left-handed and right-handed particles in the cross section of the channel [the ($x,z$) plane] divided by the mean standard deviation ${\sigma }_p=({\sigma }_{p_L}+{\sigma }_{p_R})/2$ of the two distributions. (b) Width (standard deviation) ${\sigma }_{x,z}$ of the distribution $P(u_x,u_z)$ of helix orientations $\overrightarrow{u}$ projected on the ($x,z$) plane. The limiting value for equidistribution on a sphere is ${\sigma }_{x,y}\sim 0.82$. Insets: Corresponding distributions at $f_y=0.1ϵ/\sigma$ for left-handed helices ($L$), right-handed helices ($R$), and helices without hydrodynamic interactions.

Figure 4

Spatial separation of chiral particles in a symmetric square channel with constant shear in $x$ direction as a function of Péclet number. The insets show explicit distributions at the encircled values.