where,
Rois Rossby number, U is the relative velocity of the particle,fcis Coriolis
factor, and L is the length scale of the motion. Coriolis factor,fcis expressed as
fc¼ 2 ωSinΘ ð 1 : 79 Þwhere,Θis the angle of the body to the plane of the reference surface. In case of
particles in centrifugal microfluidics,Θwill be 90thus changing the Coriolis
factor to 2ω.
- Dean number: Flows in curved pipes
It is defined as the product of Reynolds number and the square root of the
curvature ratio.
De¼Re:ðÞd=2r^1 =^2 ¼ðÞρVd=μ:ðÞd=2r^1 =^2 ð 1 : 80 Þwhere,
De is Deans number, Re is Reynolds number, r is curvature radius of the channel/
tube, d is travelled length of the liquid, and V is axial velocity.
2.5 Key Dimensionless Numbers Explained
2.5.1 Reynolds Number: Inertial Focusing to Separate Plasma from
Whole Blood
The Reynolds number is one of the most crucial dimensionless numbers in fluid
mechanics. However, when we discuss it with reference to microfluidics, its
relevance is practically limited. The reason is that the fluids employed in
microfluidics-related applications have small values for their respective Reynolds
numbers that make the inertial effects irrelevant.
Still, importance of the Reynolds number can’t be undermined. One best exam-
ple to explain the importance of inertia in microfluidics is separation of plasma from
whole blood. A straight channel, as illustrated in Fig.1.10, is curved at one end. The
liquid flowing through this channel will feel a sudden curve on its path. At the
corner, liquid still tends to go straight due to which in the process of changing path,
it loses momentum at the corner. In this case,
Time taken for this liquid to turn around the corner is expressed as
tiw=U 0 ð 1 : 81 Þwhere, tiis turn time, w is width of the curve, U 0 is velocity of the fluid before
turning.
1 Fundamentals of Fluidics 27