# Marangoni number

The Marangoni number (Ma) is a dimensionless number named after Italian scientist Carlo Marangoni. The Marangoni number may be regarded as proportional to (thermal-) surface tension forces divided by viscous forces. It is – for example – applicable to bubble and foam research or calculations of cryogenic spacecraft propellant behaviour.

${\displaystyle \mathrm {Ma} =-{\frac {d\gamma }{dT}}{\frac {L\Delta T}{\mu \alpha }}}$
• γ: surface tension, (SI units: N/m);
• L: characteristic length, (SI units: m);
• ${\displaystyle \alpha }$: thermal diffusivity, (SI units: m2/s);
• ${\displaystyle \mu }$: dynamic viscosity, (SI units: kg/(s·m));
• T: temperature difference, (SI units: K).