Simulating the hydration of cementitious phases with an oscillating rate of reaction

To investigate how an oscillating reaction rate might influence the hydration of cementitious solids, a simple iterative mathematical model that includes recurrent passivation of the surface has been constructed. The algorithm generates a wide variety of hydration curves with a limited number of input parameters: i.e.. V0 (volume of unreacted solid after initial reaction), a, (degree of reaction upon initial wetting), x0 (fraction of particle surface passivated after initial wetting); running index: n (cycle number, with an arbitrary unit of time per cycle); constants: m (number of cycles with constant x, the relative rate of the hydration and passivation reactions), k (maximum linear rate of reaction front), and lambda (range 0-1, determines the general passivation behaviour, modelled by the algorithm x(new) = 4 lambda xold[1 - xold]). The hydration process is described by the sequence: (1) Delta V = k(1 - x)V^2/3, (2) Vnew = Vold - Delta V, (3) alpha = 1 - (V/V0) + alpha0.