Optimizing the performance of the entropic splitter for particle separation

Abstract

Recently, it has been shown that entropy can be used to sort Brownian particles according to their size. In particular, a combination of a static and a time-dependent force applied on differently sized particles which are confined in an asymmetric periodic structure can be used to separate them efficiently, by forcing them to move in opposite directions. In this paper, we investigate the optimization of the performance of the "entropic splitter". Specifically, the splitting mechanism and how it depends on the geometry of the channel, and the frequency and strength of the periodic forcing is analyzed. Using numerical simulations, we demonstrate that a very efficient and fast separation with a practically 100% purity can be achieved by a proper optimization of the control variables. The results of this work could be useful for a more efficient separation of dispersed phases such as DNA fragments or colloids dependent on their size.

The concept of entropic rectifier facing experiments

“…5, the rectification efficiency α , is plotted as a function of || V || for three different PAA molecular weights M and compared to acetic acid. For the two highest molecular weights, the α -values are clearly non-zero and comparable to the values obtained by simulations on other systems1927. To appreciate this point, one has to keep in mind that for an entropic rectifier of ionic current, the contributions of anions and cations to the conductance add, so that || α || < 1 even if the entropic ratchet works perfectly.…”

“…Hence, would give a simple estimate of the cycle-frequency above which rectification vanishes27. Recent simulations of polyelectrolyte chains translocating through asymmetric nanochannels confort this idea29.…”

“…6 that remains quite puzzling. In the literature, equation of motion through entropic barriers was not solved analytically, but with brownian dynamic simulations20242527. These simulations amount to integrate Langevin equation in some particular cases, which inevitably do not match to our experimental system.…”

Non-monotonous polymer translocation time across corrugated channels: Comparison between Fick-Jacobs approximation and numerical simulations

“…The staring point of our model is the Fick-Jacobs approximation [24][25][26] that has already been characterized [27][28][29][30][31][32][33] and exploited for diverse systems ranging from particle splitters [34,35], cooperative rectification [36][37][38] diffusion through porous media [39,40], electro-osmotic systems [41][42][43] and entropic stochastic resonance [44,45] just to mention a few cases among others. The Fick-Jacobs approximation allows us to project the convection-diffusion equation of a noninteracting particle, confined in a two-dimensional (2D) or three-dimensional (3D) corrugated channel, onto a one-dimensional (1D) equation in which the particle dynamics is controlled by an effective potential.…”

Giant enhancement of hydrodynamically enforced entropic trapping in thin channels

“…Recently, novel devices for particle separation were proposed [9,10,[15][16][17]. The capability of such devices for separation of particles is rooted in the effect of entropic rectification, i.e., the rectification of motion caused by broken spatial symmetry caused by asymmetric variations of the accessible local volume [18][19][20]. The transport in channels with periodically varying cross-section exhibits peculiar transport phenomena [21][22][23][24][25][26] which can be treated by means of the so-termed Fick-Jacobs formalism and its generalizations [1,[27][28][29][30][31][32][33][34][35][36].…”