F¼mg ð 1 : 2 Þwhere,
m is mass of the liquid, and g is gravity constant.
Since,
m¼ρV ð 1 : 3 Þwhere,
V is volume of container, andρis mass density of the liquid.
Therefore, replacing (1.3)in(1.2) will give us
F ¼VðÞ¼ρg hAðÞðρg 1 : 4 Þsuch that volume¼height of the liquid (h) area of the surface (A¼length
width)
Similarly, replacing (1.4)in(1.1) will give us the relation of height to the
pressure
P ¼hAρg=A¼hρg ð 1 : 5 ÞContinuing with the case that we were discussing, in Fig.1.1bpressure exerted
by a layer on the other separated by certain height within the liquid will be
P 2 Pl¼ΔP¼ðhhlÞρg¼Δh:ρg ð 1 : 6 ÞEquation (1.6) constitutes the basic ofhydrostatic pressure-based pumpingin
microfluidic systems.‘ΔP’is known as pressure head.
2.3.2 Buoyancy and the Problem of Microfluidic Mixing
Buoyancy is the apparent loss of weight of a body when submerged in liquid and
this is mainly known as Archimedes Principle. This loss is attributed to the
resistance offered by the liquid to the body. Buoyancy from Fig.1.2can be
mathematically expressed as
Fnet¼FBðÞbuoyant force FgðÞðweight 1 : 7 Þ
¼ðÞρfVfρoVo g ð 1 : 8 Þ8 C.K. Dixit