Dear Dan and All:
I checked the idea of Colin Berry in the website you quoted. In short, from a physics point of view, his model is untenable, especially concerning the depth of coloration. Let me explain why.
Berry wrote: “The scorching will initially be confined to those parts of the fabric that are in immediate contact with the hot metal; no air gap is permissible, since radiated heat will not scorch white linen. What is more, the scorch will be confined to the outermost fibres of the thread, because the scorch will tend remain trapped within the first-encountered fibres, rather than being able to “jump across” to adjacent fibres. Why is that? It is because the resistant cellulose cores that are unaffected are able to conduct away heat rapidly, bringing the temperature of the hot template down to below that which will induce scorching Is it realistic to suppose that cellulose fibres could conduct away heat without themselves becoming degraded? Yes. I believe it is.”
It is quite easy showing the above assumption is wrong, and it is one of the few cases where it is faster doing the experiment than to explain the theory. According with a paper quoted by Berry, the onset of pyrolysis in hemicelluloses is at about 220°C. We have heated a 5-cents euro coin at about 230 °C in contact with a linen cloth. Just 5 seconds after the coin reached the max temperature the whole cross section of threads in contact with the coin was colored. After15 seconds all the thickness of the cloth was colored and the round shaped image of the coin appeared on the opposite side. After checking in our Lab, we repeated this easy and small-size experiments in the RAI3 TV studios (GeoScienza) to demonstrate that heating linen cannot give a superficial coloration. See http://www.tvrit.it/enea/20120103-RAI_3-COSE_DELLALTRO_GEO_1555-175825001a.ASF starting from the minute 16:30.
After the experimental demonstration, let’s approach the basic elementary physics that explain why the idea of Berry is untenable, and heat cannot produce a superficial coloration.
The hot metal transfers energy(heat) to the primary cell wall (pcw) of the linen fibrils by contact. From a microscopic view, transferring energy by contact means the hot (i.e. fastly moving)atoms of metal hit hemicelluloses molecules transferring momentum, thus increasing both amplitude and velocity of the motion of hemicellulose molecules around the equilibrium position (centroid). As a consequence, hemicellulose increases its temperature.
In the regions of contact between pcw and cellulosic medulla, we still have a transfer of heat by contact, like in the previous metal-pcw case. The temperature of the medulla will increase. In the region where there is no contact (e.g.,a small air gap between pcw and medulla) we have heat transfer by irradiation.In fact, every material emits radiation having a spectrum peaked at a wavelength which depends on its temperature: the higher the temperature, the shorter the wavelength. This is the well known phenomenon of the black body emission, governed by Planck’s law, Wien’s law and so on (first year exam for students of Physics, Mathematics, Chemistry, Engineer).
As an example, at 20 °C the walls of a room emit radiation with a broad spectrum, peaked in the far infrared at about 10-micrometers wavelength. In the case of hemicelluloses at 200 °C the pcw emits infrared radiation peaked at 6,1 micrometers. In the case we are considering, the 6-micrometer wavelength will interact with the cellulose of the core of the linen fibril (medulla), exciting vibrational levels of cellulose that decay in heat thus increasing the temperature of the medulla.
In addition, a well known optics law tells us the penetration depth of the interaction between radiation and medulla cannot be smaller than the wavelength, that is, not smaller than 6 micrometers in this case. This fact alone explain why infrared radiation cannot produce a superficial coloration of fibers.
By the way, it is not possible that “the resistant cellulose cores that are unaffected are able to conduct away heat rapidly” (see above Berry’s statement) because of elementary fluid dynamic equations (a classical engineering problem), of a not convenient area/volume ratio of cylinders (elementary geometry) and because Berry assumes a exothermic pyrolysis of cellulose, that is,by definition, a runaway process, extended in time.
In summary, when heating a linen cloth by a hot metal in contact, well known physics models foresee the pyrolysis of the whole fibers and threads, and this is exactly what we observe in the experiments.
Useless to say, it is all the approach of Colin Berry to find a middle age technology able to create the Shroud image that is hopeless: just consider the half tone effect. It could not have been made by medieval forgers because they would need a modern microscope to observe and then control their micrometric-scale coloration.
All the best