Numerical simulation of surface acoustic wave actuated enantiomer separation by the finite element immersed boundary method

Abstract

Abstract. Enantiomers are chiral objects such as chemical molecules that can be distinguished by their handedness. They typically occur as racemic compounds of left-and right-handed species which may have completely different properties. Therefore, in applications such as drug design in pharmacology, enantiomer separation is an important issue. Here, we present a new technology for enantiomer separation by surface acoustic wave generated vorticity patterns consisting of pairwise counter-rotating vortices in a carrier fluid. The enantiomers are injected onto the surface of the fluid between two counter-rotating vortices such that right-handed (left-handed) enantiomers get attracted by left-rotating (right-rotating) vortices. In particular, we are concerned with the numerical simulation of this separation process by an application of the finite element immersed boundary method which relies on the solution of a coupled system consisting of the incompressible NavierStokes equations and the equations of motion of the immersed enantiomers described with respect to an Eulerian and a Lagrangian coordinate system. For a model system of deformable, initially L-shaped enantiomers the results of the numerical simulations reveal a perfect separation.

Transport at Interfaces in Lipid Membranes and Enantiomer Separation

“…On the other hand, as shown in Figure 29 shows that a right-handed (left-handed) enantiomer initially placed a little bit to the right of the middle between the two counter-rotating vortices gets attracted by the counter-clockwise (clockwise) rotating vortex in the upper-right (lower-right) quadrant. This behavior is in accordance with experimental measurements and similar to numerical simulation results that have been obtained for deformable L-shaped enantiomers by an application of the FEIBM [5]. We note that [5] also contains numerical results for multiple enantiomers of different handedness which confirm the separation mechanism described above.…”

“…After soft baking, the photoresist is exposed using a mask aligner and then baked a second time (4). After the substrate has cooled to room temperature, the unexposed photoresist is developed using MR-DEV300 leaving the desired particles attached to the sacrificial layer of omnicoat (5). In order to render the particles hydrophobic on one side, a layer of Trichloro(octadecyl)silane (OTS) is applied by spin coating (6).…”

“…Given an equidistant partition of the time interval [0, T ], for discretization in time we have used the implicit Euler scheme for (28) and the explicit Euler method for (29) resulting in a semi-implicit Backward Euler/Forward Euler FE-IB which has to satisfy a CFL-type stability condition (see also [27] for a related application of the FEIBM and [35] for an alternative unconditionally stable fully implicit scheme). For further details we refer to [5].…”

Mechanical chiral resolution

“…For such relatively large particles, the effects of thermal fluctuations are negligibly small. Both studies 32,33 consistently predicted that these enantiomers are separated in the 4-vortex flow according to their handedness when injected into the flow approximately in the middle between two counter-rotating vortices, because Two earlier studies 35,36 had investigated flexible chiral particles, which are built of "atoms" connected by elastic springs, when moving in three-dimensional uniform shear flows. For helical particles, Talkner et al 36 showed from numerical simulations that hydrodynamic interactions between the component "atoms" (via the Rotne-Prager mobility tensors) lead to mechanically induced drift in a direction lateral to the shear plane, which depends on the chirality of the object and the sign of the shear rate.…”

“…Concerning hydrodynamic interactions, two follow-up studies 32,33 analysed the same 4-vortex flow pattern and its potential for chiral separation employing two different computational methods, which both allow for a full hydrodynamic treatment of the problem. The first study 32 uses a so-called fictitious domain Lagrange multiplier method, which has been developed specifically to capture the deterministic motion of rigid particles in carrier fluids.…”