A new equivalent circuit is presented, which describes the transport of a chemical solution with a certain concentration in a fluidic channel. Channels are basic parts of a microfluidic systems and the concentration of the chemical solution can control the opening and closing of valves based on smart hydrogels. This type of microfluidic systems facilitates the autonomous control of fluid flow, e.g. in chemo-fluidic oscillators. Through this channel, the solution is transported at a velocity determined by the flow rate through the channel and its cross section. While the volumetric flow is not delayed in an ideal channel, the channel acts as delay line for the particles and thus for a certain concentration transport through the channel.
In this setting, the transport of the dissolved chemical by water traveling along the delay channel can be described by the one-dimensional transport equation. In order to derive the equivalent circuit, the transport equation is numerically approximated based on the well-known Method of Lines. This method consists in approximating the original PDE via a large system of ODEs. The ODEs are obtained by discretizing the PDE in space, in such a way that each component of the resulting system of ODEs approximates the solution of the PDE at some grid point along the spatial interval. Once the system of ODEs has been constructed, a flow and a difference quantity can be defined and the ODEs interpreted as finite network elements. Since the equations are isomorphic to electrical ODEs of electrical network elements, the fluidic channel can be expressed by an equivalent circuit. Thus the transient behavior of the transport mechanism can be calculated using a circuit simulator as part of a design automation. Simulation results are presented.
