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A simple reaction-diffusion-advection equation is proposed in a dichotomoustree network to discuss an optimal network. An optimal size ratio r isevaluated by the principle of maximization of total reaction rate. In the caseof reaction-limited conditions, the optimal ratio can be larger than(1/2)^{1/3} for a fixed value of branching number, which is consistent withobservations in mammalian lungs. We find furthermore that there is an optimalbranching number when the Peclet number is large. Under the doubly optimalconditions with respect to the size ratio and branching number, the optimalvalue of r is close to (1/2)^{1/3}.

Reaction-diffusion-advection equation in binary tree networks and optimal size ratio