Role of Diffusion Induced Coalescence on Growth of Breath Figures

Growth of breath figure (the pattern formed due to condensation of water droplets on a cold surface) have been studied using experimentally and computer simulations. We studied the role of diffusion induced coalescence of droplet growth. We observed that for droplet growth without diffusion $\sim t^{1/3}$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.93in,height=0.21in]{120120181.eps}} \label{fig1} \end{figure} and $t$growth laws in an isolated and the self-similar growth regimes respectively. However, when the droplets were allowed to diffuse on the surface, in addition to \begin{figure}[htbp] \centerline{\includegraphics[width=0.27in,height=0.21in]{120120182.eps}} \label{fig2} \end{figure} $t^{1/3}$ and \begin{figure}[htbp] \centerline{\includegraphics[width=0.15in,height=0.20in]{120120183.eps}} \label{fig3} \end{figure} $t$ growth laws, after critical value of surface coverage, droplet growth also follows \begin{figure}[htbp] \centerline{\includegraphics[width=0.15in,height=0.20in]{120120184.eps}} \label{fig4} \end{figure} . The number of droplets decreases with time and follows the $N\sim t^{-\beta }$ \begin{figure}[htbp] \centerline{\includegraphics[width=0.50in,height=0.21in]{120120185.eps}} \label{fig5} \end{figure} for all growth stages with different $\beta $ values. The growth laws are in good agreement with the experimentally observed values.