Fluidic capacitance

The relationship between pressure, deformation and geometry plays a critical role in microchip design, as it essentially dictates the actuation pressure of valves and the fluidic capacitance introduced by deformable channels. Table 39.2 summarizes several classical results for simple geometries. 

Table 39.2 lists the pressure-volume relationships for various geometries the fluidic capacitance is found simply by differentiating with respect to pressure. For small deformations, volume varies linearly with applied pressure, such that the capacitance is not a function of the pressure it merely defines the proportionality between increases in pressure and increases in stored mass. For such cases, the fluid circuit analysis is linear, because flow rate and pressure drops are related via linear expressions. For large deformations (i.e., the membrane limit), the fluidic capacitance is a function of the pressure this implies that the fluidic circuit behavior will be nonlinear. Obviously, once the fluidic resistance, capacitance and inductance have been identified via geometry (and material properties), complicated networks can be analyzed using commercially available circuit analysis software such as SPICE [42]. 

Fluidic capacitance, that is, volume of fluid stored in a deformable element per unit pressure, deflection of a film or half-space in the direction normal to the interface (or axis of the film), may appear as a function of position along the film axis (i.e., 3(Jc)). 

Easley et al." " also provided proof-of-principle data for discrete components referred to as fluidic capacitors. While the concept of fluidic capacitance is by no means a new concept, little workhas been done to exploit this behavior in microfluidic networks. To the knowledge of the authors, only recently has there been a report that discusses the fluidic compliance of an entire microchip made up of a flexible polymer, PDMS. In this work, which was concurrent with the work by Easley... 

The fluidic capacitance is the pressure-dependent volume change under isothermal (or adiabatic) conditions and can be expressed as... 

Volume in fluidics is equivalent to electrical charge, and mechanical elasticity of the walls of the channels (known as compliance deflned as change of volume due to change in pressure) is equivalent to electrical capacitance. More details on analogy related to channel with compliant wall will be discussed in a later section. Also the inertia of fluids has an eleetrical analog, namely, electrical inductance. 

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