“Vector Chromatography”: Modeling Micropatterned Separation Devices

Abstract

A repetitive sequence of quiescent fluid layers of differing viscosities through which small spherical Brownian particles move is analyzed so as to illustrate in a simple context how the theory of macrotransport processes, a generalization of Taylor dispersion theory, may be employed to rigorously analyze spatially periodic micropatterned chromatographic separation devices for circumstances in which the solute species to be separated are animated by the action of species-specific external forces oriented asymmetrically relative to the body-fixed pattern. In the generic "vector" separation scheme, illustrated by our elementary example, the different species undergoing separation move, on average, in different directions relative to pattern-fixed axes, whence their chromatographic sorting is effected according to their different mean angular trajectories through the device. This scheme differs fundamentally from traditional "scalar" chromatographic separation schemes, wherein all species move on average parallel to the animating force (including circumstances in which they are passively entrained in a unidirectional solvent flow) and hence for which the sorting is effected by the relative speeds of the several species through the chromatographic column.Vector chromatography is quantified by two global "macrotransport coefficients," namely the solute mobility dyadic M * (representing the tensor proportionality coefficient between the mean solute velocity vector U * and the external force vector F acting upon the solute molecules) and the dispersivity dyadic D * (resulting from the deviation of the instantaneous position of the particle from its mean position based upon its mean velocity vector). In the present example these coefficients are studied parametrically as functions of: (i) the orientation of the external force relative to the symmetry axis of the fluid layers; (ii) the local viscosity distribution within a layer; (iii) the vector particle Peclet number (constructed from the vector force, the length of the viscosity period, and the Boltzmann factor kT ); and (iv) the thermodynamic interphase solute partition distribution coefficient between the two fluid layers comprising a unit cell.

Dispersive transport of biomolecules in periodic energy landscapes with application to nanofilter sieving arrays

“…In the special case with e 5 1 and Ko1, which corresponds to a system of periodic immiscible fluid layers studied in [26], our results are equivalent to those obtained in the later study. Finally, for e 5 1 and K 5 1, we have D Ã 5 1, verifying that in a flat channel (free solution), the effective diffusivity obtains its free-solution value.…”

“…Despite the fact that some of the assumptions made [6] -namely idealized channel geometry, uniform electric fields in both the deep and shallow regions, and fast equilibrium in the transverse channel directions -are sometimes not satisfied under the relevant experimental conditions, these results offer a useful tool for evaluating and improving the performance of nanofluidic devices without the need for complex and costly numerical simulations. A similar model albeit describing a different physical scenario (force-driven transport of Brownian particles across immiscible fluid layers) has been previously considered in [26]. The latter model is different from the present work because it considers driving forces of equal magnitudes in the two fluid layers, in contrast to the problem considered here, where the magnitude of the force in the shallow and deep regions of the nanofilter is different.…”

Exact computation of the mean velocity, molecular diffusivity, and dispersivity of a particle moving on a periodic lattice

“…In the case of so-called rectified Brownian motion [11,12,21] (or vector chromatography [22]), a directional separation is achieved by applying the force at an angle with respect to the symmetry axes of the array.…”

Partition-induced vector chromatography in microfluidic devices

“…The orientation angle of U ⁄ is the relevant parameter in vector chromatography, termed hereafter the chromatographic trajectory angle, more simply the trajectory angle [24], or the migration angle.…”

“…In particular, a periodic dielectrophoretic potential has been shown to result in a force that selectively opposes one of the components of the driving force acting on different particles, thus causing them to move in different average directions [28][29][30]. These methods fall in the category of vector chromatography (VC) tecniques [24,25], where the fractionation relies on differences in the average direction in which different species move.…”