Most cases where a chemical diffuses through the skin into the body are transient; that is the concentration of the chemical changes over time. In the cases we are showing in these webpages we are considering that the chemical is on the top surface of the membrane, and its concentration is constant over time. Therefore we are imagining an infinite supply (or vehicle), like a fully stirred solution. In some cases we imagine that this covering is only applied to a portion of membrane, like the patches cases shown below and described in more detail on the distributed sources page.

For transient cases there are several quantities of interest. These are (1) the final steady-state flux through the membrane into the body, (2) the lag time, which is a measure of how long the membrane takes to reach a steady-state, and (3) the total mass into the membrane and into the body.

In the case shown here the chemical is only applied on the top surface of the membrane in a circular patch, radius 0.5, centred at one corned. In this case there are no corneocyte-esque obstacles in the way, as we assuming that the patch size is much larger meaning we can assume averaged diffusivities through the continuum of the membrane.

In the picture to the left the mass into the membrane is shown in red, and the mass out in white. The lag time can be found by extrapolating the steady-state mass out back to the x-axis, in this case to a non-dimensional time of about 0.2. Movies are provided for the mass in and out (Quicktime) - final profile shown below, and the overall solution concentrations in both Quicktime and MPEG formats.

Other transient cases of interest include diffusion around the complex geometries formed by the corneocytes, such as shown on the periodic domains and the hexes pages. The effects of finite sources, i.e. thus which deplete over time, hence reducing the area covered or the top concentration are also important.

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