## Chemical Engineering:Dimensionless quantity : Marangoni number

2013.4.17

Lecture note of Dr. Hiroshi Yamamoto

The Marangoni number (Mg) 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. (WikiPedia)

σ: surface tension, (SI units: N/m)

L: characteristic length, (SI units: m)

α: thermal diffusivity, (SI units: m²/s)

η: dynamic viscosity, (SI units: kg/(s·m))

ΔT: temperature difference, (SI units: K)

ｋ is thermal conductivity (W/(m·K))

ρ is density (kg/m³)

Cp is specific heat capacity (J/(kg·K))

So, if we can estimate Surface Tension, viscosity, Thermal conductivity, Density, Heat Capacity of temperature dependency, then we can calculate Mg. I already built estimation scheme and put them on my Pirika HP.

If you draw molecule, set temperature then click EXE button, you will get result at text area.(You can Copy and Paste to Text Editor)

If you are not familiar to drawing moelcules, please refer to this page.

This program estimate Marangoni number with 3 methods.

QSPR method and Neural Network(NN) method estimate Mg with Functional Groups(FG) and reference temperature. Sometime, calculation will fail because of missing FG parameters.
The other method is calculate from thermo chemical properties with temperature dependency. It use 5 properties so sum of errors may cause to big error in Mg estimation. But can calculate all molecules that can draw with C, N, O atoms.

Calculated from Functional Groups

Marangoni(QSPR)=2727.8*E3*L(m)*ΔT（K）

Marangoni(NN)=1202.56*E3*L(m)*ΔT（K）

From Thermo Chemical Properies Estimation(TCPE)

Marangoni=-171.18 *E3*L(m)*ΔT（K）

I am building unlimited version of this program.

Please feed back me the result.

I got mail from HSPiP user. They said this function is working very well and want to use full funtion.

This function will be implement into HSPiP but it will take time. So Please mail me if HSPiP user wan to access full version applet. I will show tentative URL that can calulate with full function.

The marangoni number play very important role on solubility in Supercritical Carbon dioxide.