SME
Biotransport
Diffusion in tissue
Use this for “Oxygen diffuses through tissue at 2 × 10⁻⁵ cm²/s. About how long does it take to spread 100 μm, and 1 cm?”
Diagram
t
=
L
2
2D
t
=
(100 μm)
2
÷
(2
×
2 ×
10
-5
cm²/s)
t = 2.50 s
At L, C is 32% of C₀; half of C₀ has reached 67.4 μm.
Doubling L takes four times as long.
This is an example. Type your own values to start a new problem.
t (s)
=
(
L (μm)
)
2
2
×
D (cm²/s)
Formulas
t
=
(
L
10,000
)
2
÷
(2
×
D
)
2.5
=
(
100
10,000
)
2
÷
(2
×
(2
×
10
-5
))
Assumptions
•
The spread is one-dimensional, from a face held at a fixed concentration into tissue with none at first.
•
t = L² ÷ (2D) is a typical time to spread a distance L, not an exact arrival: at L the concentration is about a third of the source’s.
•
The time grows with the square of the distance: doubling L takes four times as long.
Step-by-step
WE KNOW
D = 2 × 10⁻⁵ cm²/s, L = 100 μm
FIND
time to spread (t)
Step 1 · Find time to spread (t)
Use t = (L ÷ 10,000)² ÷ (2 × D)
Change
L
to
cm
(10,000
μm
to
the
cm),
square
it,
and
divide
by
twice
the
diffusivity.
t
=
(
100
10,000
)
2
÷
(2
×
(2
×
10
-5
))
t
=
0.01
2
4 ×
10
-5
t
=
0.0001
4 ×
10
-5
t
=
2.5
s
Check
Put the numbers back in. Both sides should match.
2.5
=
(
100
10,000
)
2
÷
(2
×
(2
×
10
-5
))
✓
Topic check
See what you know: 5 questions on this topic
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