Separation of chiral molecules: a way to homochirality.

A mechanism for separating chiral molecules is proposed. The separation of two enantiomers in an aquifer is considered. The molecules are dragged in the aquifer porous medium by a flow of water or of another liquid. The molecule velocity is u=v/R, where v is the liquid velocity, and R is the retardation factor. The aquifer consists of two one-dimensional layers disposed in series. The layers differ by the retardation factor or by the liquid velocity. The enantiomer velocity is a function of the enantiomer concentrations. This function is different in the two layers. For certain values of the model parameters and when the molecules entering the aquifer are enantiomerically enriched or when the medium is chiral, the concentration of one enantiomer increases around the interface between the two layers and in one layer, whereas the concentration of the other enantiomer decreases. Enantiomer synthesis and decay are not taken into account. The needed values of the parameters can be obtained when the enantiomers are moved by an alternating liquid flow, and the retardation factor oscillates in synchronism with the alternating liquid flow. The parameters of the model are then understood as quantities averaged over one oscillation period. The equations that give the values of the stationary concentrations of the enantiomers are found. The evolution of the enantiomer concentrations is determined by numerically solving a system of two nonlinear advection-dispersion equations. The proposed mechanism may have played a role in the emergence of biomolecular homochirality.