Page 24 - Mike's published articles

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MURPHY
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20. Murphy MJ. Q-switched 532 nm laser energy causes significant vascular damage in the capillary plexus—How does this affect laser tattoo removal? Br J Dermatol. Accepted Author Manuscript. DOI: 10.1111/bjd.16130.
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APPENDIX
THE KINETIC ENERGY/VELOCITY OF THE ESCAPING AGGREGATES—A FIRST APPROXIMATION:
The following calculations are a first approximation and are based on a number of approximations and measurements. The compressive strain, e, within the glass slide following ink fragment impact may be calculated from the ratio of the depth of penetration, Dl, of the fragment to the thickness of the slide, l (2 mm). Knowing this and the Young’s Modulus, E, of glass (65 GPa) the compressive stress, s, may be found.
Multiplying s by the area of the impact zone, A, gives the impact force, F. The product of this force with the depth of penetration, Dl, yields the kinetic energy, KE, of the impact fragment.
Let us assume that the observed black ink particles are carbon ink aggregates, with the density of the carbon as 2,250 kg/ m3. From the dark material in Figure 5 we can see that the aggregates leaving the skin have diameters in the range 1– 10 mm (below the resolution of the human eye and, therefore, invisible). Assuming that the aggregates strike the glass and shatter into much smaller pieces, the sizes of the aggregates striking the glass might be in the range 10–100 mm. Assuming spherical aggregates, as a first approximation, this yields aggregates masses of between approximately 1.2⇥1012 to1.2⇥109kg.
It was not possible to accurately measure the penetration depth of the aggregates into the glass, but a visual inspection revealed craters with a maximum depth of 0.2 mm. Note that the smeared portions of ink were found to be significantly deeper than this (up to approximately 1 mm).
Knowing the masses we can calculate a range of corresponding impact velocities as a function of the penetration depth according to the equation:
sÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ ✓2 E A Dl2◆
và
where v is the velocity of the aggregates on impact (metres/second), E is Young’s modulus for glass (Pascals), A is the area of the impact zone (m2), Dl is the depth of the impact zone (m), m is the mass of the fragment (kg) and l is the thickness of the glass slide (m).
Note that these calculations are a very simple, first approximation based on relatively low-tech measurements of the samples.
ml