Scaling Laws in Microsystems

The dynamics of a microsystem depend on the relevant forces, that is, volume forces (gravity and inertia) and surface forces (viscous effect). The ratio of these two forces based on the scaling law is given by 

As I becomes smaller, the ratio approaches infinity. Hence, volume forces, which are prominent in real-life system, are unimportant in microfluidic system. The surface forces become dominant, and our intuition may not be valid at all situations in case of microsystem. Some examples are provided in the following sections to clarify this point. 

The capacitance C of a parallel-plate capacitor, with plate area equal to A, voltage difference between the two plates V, and separation distance d, is given by 

Force used to displace one of the plates leads to a gradient of the energy given as 

for constant electric field E and fixed environment, we have 

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