this is for holding javascript data
Pol Grasland-Mongrain edited Let_s_describe_the_phenomenon__.tex
over 8 years ago
Commit id: 0043a6ccdcfa75093673831aeccff4d653686bcd
deletions | additions
diff --git a/Let_s_describe_the_phenomenon__.tex b/Let_s_describe_the_phenomenon__.tex
index cd313c4..ac5323e 100644
--- a/Let_s_describe_the_phenomenon__.tex
+++ b/Let_s_describe_the_phenomenon__.tex
...
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.