SME
Biotransport · Problem type
Flux across a layer (Fick’s first law)
Use this for “Glucose crosses a 10 μm layer with a 0.1 mM difference. What is the flux?”
Diagram
12 glucose in the capillary blood, 4 in the tissue: they diffuse across the layer into the tissue, from high to low concentration. ΔC = 0.1 mM.
This is an example. Type your own values to start a new problem.
J (mol/(cm²·s))
=
D (cm²/s)
×
ΔC (mM)
Δx (μm)
Formulas
J
=
D
×
ΔC
100 × Δx
1 ×
10
-9
=
1 ×
10
-5
×
0.1
100 × 10
Assumptions
•
Steady diffusion straight across a flat layer, with the concentration falling evenly through it.
•
J counts moles crossing each square centimeter each second, from the higher side to the lower.
•
D is the solute’s diffusivity in the layer itself, which is often lower than in water.
Step-by-step
WE KNOW
D = 1 × 10⁻⁵ cm²/s, ΔC = 0.1 mM, Δx = 10 μm
FIND
flux (J)
Step 1 · Find flux (J)
Use J = D × ΔC ÷ (100 × Δx)
Flux
is
the
diffusivity
times
the
gradient
ΔC
Δx
;
mM
is
10
-6
mol/cm³
and
μm
is
10
-4
cm,
hence
the
100.
J
=
10
-5
×
0.1
100 × 10
J
=
10
-5
×
0.1
1,000
J
=
10
-6
1,000
J
=
10
-9
J
=
1 ×
10
-9
mol/(cm²·s)
Check
Put the numbers back in. Both sides should match.
1 ×
10
-9
=
10
-5
×
0.1
100 × 10
✓
Topic check
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