Simulation of variable delays in material transport models

The time for material to pass through a plug flow vessel is modelled by a delay function. If the flow rate is time-variable, the varying delay is difficult to calculate analytically even for general test functions of the flow rate. In this paper, the properties of delay functions are studied theoretically. Two different methods for the simulation of the delay are derived. Several examples are studied, in which known analytical solutions as well as simulations of delay functions are presented.