Effect of laminar chaos on reaction and dispersion in eccentric annular flow

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Abstract
Generalized Taylor dispersion theory is used to study the chaotic laminar transport of a reactive solute between eccentric rotating cylinders in the presence of an inhomogeneous chemical reaction. The circumstance considered is that of laminar axial ‘Poiseuille’ flow in the annular region between the two non-concentric cylinders, accompanied by a secondary, generally chaotic, flow induced via alternate rotation of the cylinders. A Brownian tracer introduced into the flow is assumed to undergo an instantaneous, irreversible reaction on the surface of the outer cylinder. The resulting effective transversely and time-averaged reaction rate, axial solute velocity, and axial convective dispersivity are computed. When chaos is present, the effective reaction rate is increased to a value several times larger than occurs in the absence of chaotic transport. It is found that an optimum alternation frequency exists, and that this frequency decreases with increasing transverse Péclet number (Peq). It is also observed that the maximum achievable reaction rate increases with (Peq). The effect of laminar chaotic mixing on the mean axial solute/solvent velocity ratio is to drive its value towards the perfectly mixed value of 1.0, despite the removal of solute from the slower-moving axial streamlines near the outer (reactive) cylinder wall. Lastly, in the presence of transverse chaotic transport, the convective Taylor contribution to the axial solute dispersivity acquires a value up to several orders of magnitude smaller than that achievable by means of non-chaotic convection.