Pol Grasland-Mongrain edited Let_s_describe_the_phenomenon__.tex  over 8 years ago

Commit id: 0043a6ccdcfa75093673831aeccff4d653686bcd

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u_z = \frac{(3\lambda + 2\mu)}{(\lambda + 2\mu)} \frac{\alpha E \zeta}{\rho C S \zeta}  \label{eq:deplThermo}  \end{equation}  . As in a biological soft tissues, $\mu \ll \lambda$, the displacement can be approximated as: \begin{equation}  u_z = \frac{3 \alpha E}{\rho C S}  \label{eq:deplThermoApprox}  \end{equation}  Taking as an order of magnitude $\alpha$ = 70.10$^{-6}$ K$^{-1}$ (water linear thermal dilatation coefficient), $E$ = 200 mJ, $\rho$ = 1000 kg.m$^{-3}$ (water density), $C$ = 4180 kg.m$^{-3}$ (water calorific capacity) and $S$ = 20 mm$^2$, we obtain a displacement $u_z$= 0.5 $\mu$m. This value is slightly smaller than the experimental displacement (about 3 $\mu$m). This local displacement can lead to shear waves because of the limited size of the source. In a 3D model, displacements along X and Y axis would also occurs, as the local expansion acts as dipolar forces parallel to the surface, but calculus is beyond the scope of this article.  If the With stronger or more focused  laser beam is focused, pulse,  the local increase of temperature could also vaporize a part of the surface of the medium. However in our case, the temperature did not increase enough (about 15 K) vaporize or event melt the medium.