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

Commit id: 14e4d979af468abb25dd50d366c49460368f7347

deletions | additions      

       

u_z = \frac{(3 \lambda + 2 \mu)}{(\lambda + 2\mu)} \frac{\alpha E}{\rho C S}  \label{eq:deplUnidim}  \end{equation}  where $\lambda$, $\mu$ are respectively the first and second Lamé's coefficient and $\alpha$ is the thermal dilatation coefficient. In a biological soft tissues, $\mu \gg \lambda$, so that \ref{eq:deplUnidim} becomes:  \begin{equation}  u_z becomes $u_z  = \frac{3\alpha E}{\rho 3\alpha E/(\rho  C S}  \end{equation} S)$.  Taking as an order of magnitude $\alpha $\alpha$  = ???$, 69.10$^{-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 $u_z$= ??? $\mu$m. This value is still smaller than the typical displacement resolution with ultrasound, of a few micrometers. However, displacements along X and Y axis are higher, as $\delta V = u_x u_y u_z = \frac{3\alpha E}{\rho C}$ where displacement along $z$ is known, so that displacement along $x$ (or, equivalently, along $z$) is equal to ??? $\mu$m. In the ablative regime, the local increase of temperature is so high that the surface of the medium melts. This phenomenon creates a point-like force $f$ in the medium, given by \cite{scruby1990laser}:  \begin{equation}