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Unformatted text preview: Ch 3 Diffusion Questions 1. What is Fick’s law of diffusion? 2. Why is carbon monoxide used in clinical tests of lung diffusion? 3. What is a compartmental model? 4. What does a diffusional transient response look like? So far the picture shown below summarizes the major features of diffusion in the lungs. We can envision a giant alveolus covered with capillaries containing red cells which carries oxygen. ¡ = ¢ £ D (P 1-P 2 ) is the expression used by West in Ch 3 to describe diffusion and is referred to as Fick’s law. This is not the form found in most advanced engineering math books (or even if you look it up on Google!) which is: J = - D ¤¥ ¤¦ called Fick’s first law of diffusion. There is also Fick’s sec ond law of diffusion which will be dealt with later. The only directly recognizable variable is D (diffusion constant). The ∂ P refers to a spatial partial derivative so is equivalent to – (P 1-P 2 ) and in this equation is equal to the more familiar dP. Note the sign change because the positive sense of the derivative is (P 2-P 1 ). J (flux per unit area )= § ¡ /A and ∂x = dx=T. So the Ch 3 equation is a discrete approximation to Fick’s first law. For most of what we will be concerned with this approximation is sufficient. However, there are practical situations where this difference becomes important. The need for partial derivatives arise when multiple variables such as x and time t must be accounted for within the same equation. This case arises when dealing with the transient response of biosensors (see below). There is always a space between the sensed quantity and the actual electrical output and diffusion between the two to deal with. It turns out that changes in the diffusional thickness has a big effect on the step transient response (see below). As the sensor thickness was increased sensor current increases but a large diffusional delay emerges. Before tackling this problem and looking at Fick’s second law , we will expand on what can be done with the discrete approximation. This involves introducing compartmental models which will be used for other applications as well. applications as well....
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This note was uploaded on 02/15/2012 for the course BME 403 taught by Professor Yamashiro during the Spring '07 term at USC.
- Spring '07