Effect of chaotic interfacial stretching on bimolecular chemical reaction in helical-coil reactors

We investigate the yield of bimolecular chemical reaction between two initially separated reactants in a tubular reactor of different coiling geometries. Laminar and steady flow with high mass Peclet number, Pe, are assumed. Asymptotic approximations for slow reactions are obtained by studying the reaction at a thin interfacial boundary layer. For a straight tube it is found that the area-averaged product mass fraction at a given axial position z goes z^{$\text{3}\text{2}$} Λ(z) Pe^{−$\text{1}\text{2}$}, where Λ(z) is the length of the interface separating the two reactants. Coiling and flow kinematics have a strong effect on Λ(z). Regular mixing produced by secondary transverse flow in a helical coil stretches the interface linearly with z, yielding a z^{$\text{5}\text{2}$} dependence for hte product mass fraction. Further enhancement derived from chaotic mixing and stretching is possible in a coil with a coiling axis that is periodically changed in the flow direction. If the switching length exceeds a critical value, the folding and stretching of the chaotic action leads to an exponentially growing length that can be related to a positive Lyapunov exponent. Numerical solutions show that this enhancement by chaotic mixing also exists for fast reactions, and that the stretching effect can be overwhelmed by tight and uneven interfacial separation in a long, high-yield reactor when the reaction boundary layers begin to overlap or interact with the wall.