Microfluidics
ENGR 1182.03
Pre Lab
Review: hydrostatic pressure
Pa
The pressure at the bottom of an open container
filled with liquid:
P  Pa   gh
h
P
Pa  atmospheric pressure
 = density of the liquid
g = acceleration due to gravity
h = height of liquid
Example: for water (r = 1000 kg/m3) at sea level (g = 9.80 m/s2) the
hydrostatic pressure at a depth of h =10 m is:
P  P  Pa   gh  1000 kg/m3  9.80 m/s 2  10 m 
kg
kg m
N
P  98,000
 98,000 2 2  98,000 2  0.967 atm
2
ms
m s
m
Pressure conversion factors:
1 atm = 1.01325 × 105 N/m2 = 14.696 psi
Surface tension
concave meniscus

When a glass tube is immersed in water, liquid rises
inside the tube due to surface tension and a
concave meniscus forms.

Surface tension can be thought of as a force, acting
along the air/water/glass contact line, that “pulls”
the liquid up the tube.

Surface tension is caused by intermolecular forces.
Capillary flow
 Surface tension can therefore cause fluid to
flow in a capillary channel. Important factors
are:
 tube orientation and the gravitational constant (g)
 diameter of tube
 density (r) and surface tension (g) of the liquid
 chemical nature of the tube walls
A capillary “valve”
 If a tube initially filled with water is allowed
to slowly drain, not all of the liquid drains
out.
 In addition to surface tension at the top of
the liquid, surface tension also acts to
counter the expansion of surface area at the
exit, and therefore prevents further flow.
 This is the basic principle behind a capillary
check valve; undesired flow can be resisted
by introducing a sudden expansion in a flow
channel.
Let’s take another look at a vertical capillary tube
immersed in liquid. Liquid spontaneously rises until it
reaches an equilibrium height.
P1
 The hydrostatic pressure at height hA
is:
P2
 P1 - P2 = rghA
 P2 = P1 – rghA
hA
P1
 Note that pressure P2 (just beneath
the surface) is not equal to P1! This is
a consequence of this interface being
curved.
P1
Now let’s take another look at a capillary tube that is
initially filled and allowed to slowly drain until it reaches
the equilibrium state shown here.
P2
 At equilibrium,
 P3 = P2 + rghB
 Substituting equation for P2:
 P3 = P1 – rghA + rghB
hB
 P3 – P1 = rg(hB – hA)
P3
P1
(P3– P1) is the pressure rating of this capillary valve. A pressure >
(P3– P1) is required to make liquid flow through this valve.
Capillary check valves
Capillary check valves
can be used to
prevent undesired
flow into or out of a
fluid reservoir in a
device with micronsized channels.
Learning Objectives of Lab
 Understand capillary flow and how a capillary valve works.
 Explore how the flow of fluid in a micro-channel depends on pressure
and geometry.
 Practice delivering and cleansing mock samples.