This tutorial video is from Cornell University Mechanical Engineering 6240 – Physics of Micro- and Nanoscale Fluid Mechanics – 29 Aug 2012. A discussion of the matrix formalism for solving P=QR in hydraulic circuit networks in microfluidic devices is presented.
Flow rate in a channel is proportional to the applied pressure drop . This can be summarized in
with the hydrodynamic resistance. This expression is formally the analog of the electrokinetic law between voltage difference and current, .
The expression for the hydraulic resistance is:
- channel of circular cross-section (total length , radius ):
- rectangular cross-section (width and height , expression valid when )
In a network of channels, equivalent resistances can be computed (as in electrokinetics):
- two channels in series have a resistance ,
- two channels in parallel have a resistance
These laws provide useful tools for the design of complex networks. Actually Kirchhoff’s laws for electric circuits apply, being modified in:
- the sum of flow rates on a node of the circuit is zero
- the sum of pressure differences on a loop is zero
The volume of fluid in a channel can change just because of a change in pressure: this is either due to fluid compressibility or channel elasticity. This behavior can be summarized with
with the hydrodynamic capacitance. It is the microfluidic analog of the electrokinetic law .