The influence of surfactants on thermocapillary flow instabilities in low Prandtl melting pools

Abstract

Flows in low Prandtl number liquid pools are relevant for various technical applications, and have so far only been investigated for the case of pure fluids, i.e. with a constant, negative surface tension temperature coefficient $\partialγ/\partial T$. Real-world fluids containing surfactants have a temperature dependent $\partialγ/\partial T > 0$, which may change sign to $\partialγ/\partial T < 0$ at a critical temperature $T_c$. Where thermocapillary forces are the main driving force, this can have a tremendous effect on the resulting flow patterns and the associated heat transfer. Here we investigate the stability of such flows for five Marangoni numbers in the range of $2.1\times 10^6 \leq Ma \leq 3.4\times 10^7$ using dynamic large eddy simulations (LES), which we validate against a high resolution direct numerical simulation (DNS). We find that the five cases span all flow regimes, i.e. stable laminar flow at $Ma \leq 2.1\times 10^6$, transitional flow with rotational instabilities at $Ma = 2.8\times 10^6$ and $Ma = 4.6\times 10^6$ and turbulent flow at $Ma = 1.8\times 10^7$ and $Ma = 3.4\times 10^7$.