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46514-G9
Transport of Colloids in Micromodels: Average Motion and Dispersion Effects
German Drazer, Johns Hopkins University
Directional locking
in the deterministic transport of suspended particles
The transport of suspended particles through porous media is
central to a wide range of separation techniques that rely on the principle
that the trajectories followed by the suspended species depend on their
interaction with the porous material. In many cases, it is the geometrical
structure of the stationary phase that is the main factor influencing the
transport of suspended species in the mobile phase. These geometric (or
confinement) effects are most important when the pore dimensions are of the
same order as those of the transported species. A clear example of a separation
approach based on geometric effects is size-exclusion chromatography.
Therefore, controlling the structure of the stationary phase is an important
aspect in the development of an effective separation media. The advent of microfabrication techniques, and more specifically that of
soft lithography, has led to the design of microfluidic devices with features
in the micron and sub-micron scales. This allowed for the successful
miniaturization of various separation techniques, including those based on steric and hydrodynamic effects. In the present project we
investigate the transport of a sphere suspended in a quiescent fluid and moving
through a periodic array of solid obstacles under the action of a constant
external force by means of Stokesian Dynamics
simulations. In the first year of the project we have been able to show that in
the presence of non-hydrodynamic, short-range interactions between the solid
obstacles and the suspended sphere, the moving particle becomes locked into
periodic trajectories with an average orientation that coincides with one of
the lattice directions and is, in general, different from the direction of the
driving force. The locking angle depends on the details of the non-hydrodynamic
interactions, and could lead to vector separation of different species for
certain orientations of the external force. In fact, we have been able to
explicitly show the presence of separation for the case of a mixture of
suspended particles with different roughness moving through a square lattice of
cylindrical obstacles.
Experimental evidence
of deterministic separation in periodic systems
In this part of the project, we have been able to
experimentally confirm the presence of directional locking in deterministic
systems at low Reynolds numbers. The observed trajectories are periodic and as
a consequence the migration angles always correspond to a lattice direction. We have also demonstrated that
different particles might move in different lattice directions for specific
values of the forcing angle, resulting in size-based separation. We have also showed that the first
critical angle shows a strong dependence on the particle size. The observed
behavior is completely analogous to that observed in microfluidic systems that
induce size-based separation by deterministic lateral displacement. Our work
indicates that non-hydrodynamic interactions are crucial in determining the
observed directional locking behavior.
In fact, a two-particle model that includes the irreversible effects of
non-hydrodynamic interactions not only reproduces the observed directional
locking but also the entire dependence of the migration angle on the forcing
direction. The same two-particle
model without non-hydrodynamic interactions will predict that the particles
always move in the same direction as the external force independent of particle
size. The presence of
non-hydrodynamic interactions between the moving particle and the obstacle
disrupts the symmetry of the trajectory, inducing a net lateral
displacement. Even though the
resulting lateral displacement is typically small, the periodic nature of the
system allows such lateral displacement to accumulate, thus amplifying the
effect into a macroscopic change in the migration angle. Therefore, by controlling weak, short
range, non-hydrodynamic forces, such as electrostatic forces, microfluidic
devices employing periodic arrays should be able to enhance the separation of
species. We plan to explore
further the manipulation of these short-range, non-hydrodynamic forces in
microfluidic devices employing similar periodic arrays.
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