Microfluidics for Biologists Fundamentals and Applications

U is linear velocity of the liquid plug in the channel/particle (velocity relative to
the rotation speed), andωis angular velocity,
Hence,

Fc¼2mUω¼ 2 ðρVÞUω ð 1 : 69 Þ

where,
ρis density and V is volume of the particle.
The force is also expressed as force density, as expressed below

fc¼Fc=V¼ 2 ρUω ð 1 : 70 Þ

In centrifugal microfluidics the velocity of the liquid plug or particle (U) in the
channel depends on angular velocity (ω), radial location of the fluid reservoir,

Fig. 1.9 Explanation of the Coriolis effect. (a) In an inertial frame of reference the observer is out
of the rotating disk. The stationary observer will see the rolled ball following a straight path. (b)
However, when observer stands on the same rotating disk on which the ball was rolled then to this
rotating observer ball will seem to follow a curved path outwards. This perspective of curving of
the path of ball is Coriolis effect. (c) This effect is used in rotating microfluidics for separating
particles in a fluid plug of length‘l’. In this plug, the particle will experience an outward
centrifugal force normal to the rotation axis and an outward force normal but opposite to the
direction of the rotation, as depicted in‘(c)’. Due to this effect particles will move to the wall of the
channel continuously pulled the disk boundary

1 Fundamentals of Fluidics 25