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Tissue Engineering · Problem type
Shear stress in a perfusion chamber
Use this for “Medium flows at 1 mL/min through a 20 mm by 0.5 mm chamber. What shear do the cells feel?”
Table
Flow rate (Q)
(mL/min)
Wall shear stress (τ)
(Pa)
This is an example. Type your own values to start a new problem.
τ (Pa)
=
6
×
μ (mPa·s)
×
Q (mL/min)
÷
(
w (mm)
×
(
h (μm)
)
2
)
Formulas
τ
=
6 ×
μ
×
Q
60 ×
w
×
h
2
0.02
=
6 × 1 × 1
60 × 20 ×
0.5
2
Formulas are worked in mm. The step-by-step shows the conversions.
Assumptions
•
The flow between the plates is laminar, its speed a parabola across the gap h.
•
The chamber is much wider than its gap, so the side walls barely slow the flow.
•
The cells lie flat on the floor plate, so they feel the shear at the wall.
•
With μ in mPa·s, Q in mL/min and w and h in mm, the 60 turns the units into pascals.
Step-by-step
WE KNOW
μ = 1 mPa·s, Q = 1 mL/min, w = 20 mm, h = 500 μm
FIND
wall shear stress (τ)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to mm).
h = 500 μm = 0.5 mm (1 mm = 1000 μm)
Step 2 · Find wall shear stress (τ)
Use τ = (6 × μ × Q) ÷ (60 × w × h²)
The wall shear of flow between plates: more flow shears harder, a taller gap far less.
τ
=
6 × 1 × 1
60 × 20 ×
0.5
2
6 × 1 × 1 = 6
60
×
20
×
0.5
2
=
60
×
20
×
0.25
=
300
τ
=
6
300
τ
=
0.02
Pa
Check
Put the numbers back in. Both sides should match.
0.02
=
6 × 1 × 1
60 × 20 ×
0.5
2
✓
Topic check
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