SME
Transport Phenomena · Problem type
Time to diffuse a distance
Use this for “Sugar diffuses in still water with D = 5 × 10⁻¹⁰ m²/s. About how long to spread 2 mm?”
This is an example. Type your own values to start a new problem.
t (s)
≈
(
L (mm)
)
2
DAB (m²/s)
Formulas
t
=
L
2
DAB
1,000
=
0.001
2
1 ×
10
-9
Formulas are worked in m. The step-by-step shows the conversions.
Assumptions
•
An order-of-magnitude estimate: t ≈ L² ÷ D, good to a factor of 2 or so.
•
Diffusion alone: no stirring, flow or convection carries the solute.
•
The diffusivity DAB is constant over the distance.
Step-by-step
WE KNOW
L = 1 mm, DAB = 1 × 10⁻⁹ m²/s
FIND
diffusion time (t)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to m).
L = 1 mm = 0.001 m (1 m = 1000 mm)
Step 2 · Find diffusion time (t)
Use t = L² ÷ DAB
Diffusion spreads with the square of distance: twice as far takes four times as long.
t
=
0.001
2
10
-9
t
=
10
-6
10
-9
t
=
1,000
s
Check
Put the numbers back in. Both sides should match.
1,000
=
0.001
2
10
-9
✓
Topic check
See what you know: 5 questions on this topic
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