# 4.2 Fick’s law: examples

Course subject(s) 4. First step into heat and mass transfer

## EXAMPLE 4.2A: CONCENTRATION AROUND A SPHERICAL PARTICLE (ELEMENTARY)

Let’s consider a spherical pill which only dissolves by diffusion. We wonder: how is the concentration distribution around the sphere? We know that: at the surface of the pill, the concentration is cR and if the radius goes to infinity, the concentration approaches zero.

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## EXAMPLE 4.2B: DIFFUSION THROUGH A FLAT PLASTIC FOIL (MEDIUM)

Today, many products are packed in plastic foils. Some products are sensitive to a long exposure to oxygen. In this example, we will show you how you can estimate the concentration of oxygen on the inside of a pharmaceutical product, under steady-state conditions. Consider the fact that we have a package with a plastic foil of 0.15 mm around the product and that the temperature of the air is 30⁰C.

On the outside, the concentration of oxygen (20%) can be calculated by applying the ideal gas law:

We now consider the diffusion through the plastic foil. Let’s write down Fick’s law of diffusion and calculate the concentration of oxygen on the inside of the foil.

From lab experiments, it is known that: The flux is

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## BONUS: EXAMPLE 4.2D: TRANSPORT OF OXYGEN IN HUMAN TISSUE (MEDIUM)

(Taken from the book Transport Phenomena, Van den Akker and Mudde, ISBN 978-90-6562-3584)

In a study on oxygen transport in human tissue, Nobel prize laureate August Krogh (Danmark, 1874-1949) considered a cylindrical vein surrounded by an annular ring of tissue.

The metabolism through which the tissue oxygen is converted into carbon dioxide was modelled by a zeroth order reaction (this means a constant conversion rate), with a reaction rate kr (in mol/(m3.s) ). Transport in the tissue takes places through diffusion with diffusion coefficient D.

Derive, using a basis of a mass balance, an expression for the transport rate per unit length at which oxygen is transferred from the vein into the tissue.

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