First-Passage Exponent in Two-Dimensional Soap Froth

We report an experimental measurement of the temporal dependence of the area $A_{\mathrm{us}}$ in a two-dimensional soap froth which has not been swept by the passage of soap films up to time $t$, as the froth coarsens from an initial time $t_0$ within the scaling regime. We find $A_{\mathrm{us}}$ scales with the mean cell area $〈A〉$ as $A_{\mathrm{us}}\propto 〈A{〉}^{-{\theta }^{\prime }}$, with a first-passage exponent ${\theta }^{\prime }=1.16\mathrm{}\pm 0.02$; and for the average perimeter $〈P〉$: $〈P〉\propto 〈A{〉}^{{\psi }^{\prime }}$ and $A_{\mathrm{us}}\propto 〈P{〉}^{{\phi }^{\prime }}$ with values of the scaling exponents ${\psi }^{\prime }=0.49\mathrm{}\pm 0.01$ and ${\phi }^{\prime }=2.38\mathrm{}\pm 0.02$. We also find a scaling function in $A_{\mathrm{us}}\left(t\right)/A_{\mathrm{us}}\left(t_0\right)$ versus $〈A\left(t\right)〉/〈A\left(t_0\right)〉$.