SME
Biotransport · Problem type
Mass-transfer coefficient
Use this for “A 1 m² membrane with k = 10⁻⁴ cm/s sees a 5 mM difference. How fast does solute cross?”
Diagram
12 solute in the blood, 4 in the dialysate: they diffuse across the membrane into the dialysate, from high to low concentration. ΔC = 5 mM.
This is an example. Type your own values to start a new problem.
N (μmol/s)
=
k (cm/s)
×
A (cm²)
×
ΔC (mM)
Formulas
N
=
k
×
A
×
ΔC
5
=
1 ×
10
-4
×
10,000
×
5
Assumptions
•
One coefficient k lumps the membrane and the still fluid films beside it together.
•
Each side is well mixed, so ΔC is the difference between the two bulk concentrations.
•
Solute crosses from the side with more to the side with less, at a rate that grows with ΔC.
•
1 mM is 1 μmol in each cm³, so cm/s × cm² × mM gives μmol/s.
Step-by-step
WE KNOW
k = 1 × 10⁻⁴ cm/s, A = 10,000 cm², ΔC = 5 mM
FIND
solute crossing (N)
Step 1 · Find solute crossing (N)
Use N = k × A × ΔC
Multiply the coefficient by the area and the concentration difference.
N
=
10
-4
×
10,000
×
5
N
=
5
μmol/s
Check
Put the numbers back in. Both sides should match.
5
=
10
-4
×
10,000
×
5
✓
Topic check
See what you know: 5 questions on this topic
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