A Numerical Study of Relaxation Phenomena in Microfluidic Reactive–Diffusive Systems

A method of lines technique that employs second–order accurate finite differences for the spatial derivatives is presented and used to determine the solution of one–dimensional reactive–diffusive systems in one–dimensional moving domains. The time discretization is based on linearized trapezoidal procedure that results in linear algebraic equations for the nodal values of the dependent variables and their first–order time derivatives. It is shown that the initial conditions play a paramount role in determining the evolution of the reaction region. For ignition sources located near the moving boundary, the region zone is located near this boundary and exhibits only a reaction front, whereas two reaction fronts are observed for ignition sources located away from the boundaries. The thickness and locations of the reaction zones are found to increase as both the amplitude and the frequency of the boundary motion are increased.