Rayleigh-Taylor Instability Analysis at Biobased Composite Interfaces

The Rayleigh-Taylor (RT) instability occurs when a light fluid (such as a gas) of density $\rho_{\mathrm{L}}$ forms an unstable interface with a heavy fluid of density $\rho_{\mathrm{H}}$ due to gravitational forces g in the heavy-over-light unstable configuration. The RT instability produces bubbles and spikes which grow with amplitude H $\sim$ [gkAt]$^{1/2}$ in the linear region (Hk\textless \textless 1) which evolves in a complex manner in the non-linear region (Hk\textgreater \textgreater 1). Here, the wavenumber k $=$ 2$\pi $/$\lambda $, $\lambda $ $=$ wavelength between instabilities, t $=$ time, and the Atwood number A $=$ ($\rho_{\mathrm{H}}$-$\rho_{\mathrm{L}})$/ ($\rho _{\mathrm{H}}+\rho_{\mathrm{L}})$. The RT instability is common in Inertial Confinement in Fusion reactors, Super Novas and for the first time reported here, in the interface of natural fibers with a liquid molding resin (soyoil) where the gas emitted from the natural fibers at T \textgreater 100 $^{\circ}$C explicitly forms and traps the bubbles and spike instabilities in the curing resin. The non-equilibrium spikes that form with A $=$ 0.999 (Hk\textgreater 1) are self-similar and behave as H $=$ H$_{\circ} + \beta \lambda $, where the initial instability height H$_{\circ} = $ 11.6 micron and $\beta = $ 0.6 for small spikes (\textless 50 $mu$m) and $\beta = $1.8 for larger spikes (\textgreater 50 $\mu$m). The RT spikes are used to tailor the permeability (\textit{breathability}) of the eco-leather like materials made with natural fibers and plant oils, where gas diffusion occurs by percolation along the natural fiber-spike interfaces. The eco-leather has substantially lower toxicity compared to natural leather, polyurethane and PVC (Funded by EPA).