this is for holding javascript data
Pol Grasland-Mongrain edited Introduction.tex
over 8 years ago
Commit id: 469d79cbb71b516f183a103672fefb08bcf81af2
deletions | additions
diff --git a/Introduction.tex b/Introduction.tex
index c3d94aa..29d90d3 100644
--- a/Introduction.tex
+++ b/Introduction.tex
...
\end{equation}
As in a biological soft tissues, $\mu \ll \lambda$, the displacement $u_z$ can be approximated as $\frac{3 \alpha E}{\rho C S}$. 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 typical ultrasound elastography resolution (5--10 $\mu$m \cite{22545033}). 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.
In the ablative regime, At high laser energy, the local increase of temperature
is so high that can vaporize a part of the surface of the
medium is vaporized. medium. This phenomenon creates a stress $\sigma_{zz}$ in the medium, as the sum of the P-wave modulus and a term given by the second law of motion \cite{scruby1990laser}:
\begin{equation}
\sigma_{zz} = (\lambda + 2 \mu) \frac{\partial u_z}{\partial z} - \frac{1}{\rho}\frac{I^2}{(L+C(T_V-T_0))^2}
\label{eq:stressAbla}