Marangoni number

Physical key figure
Surname	Marangoni number
Formula symbol	${\displaystyle {\mathit {Ma}},{\mathit {Mg}}}$
dimension	dimensionless
definition	${\displaystyle {\mathit {Ma}}=-{\frac {\partial \sigma }{\partial T}}{\frac {L\Delta T}{\eta a}}}$
${\displaystyle \sigma }$ Interfacial tension ${\displaystyle L}$ characteristic length ${\displaystyle \Delta T}$ Temperature difference ${\displaystyle \eta }$ dynamic viscosity ${\displaystyle a}$ Temperature diff
Named after	Carlo Marangoni
scope of application	Marangoni convection

The Marangoni number or (named in honor of the Italian physicist Carlo Marangoni ) is a dimensionless number from the field of fluid mechanics . It is a measure of the strength of the capillary convection at interfaces ( Marangoni convection ). ${\displaystyle {\mathit {Ma}}}$ ${\displaystyle {\mathit {Mg}}}$

Marangoni convection is a flow at interfaces that is caused by local differences in interfacial tension . Since the interfacial tension of most substances decreases with increasing temperature , there is a flow from warm to cold areas of the interface. In this case of thermocapillary convection, which is caused by temperature differences , the Maragoni number can be defined as: ${\displaystyle \sigma }$ ${\displaystyle T}$ ${\displaystyle \Delta T}$

${\displaystyle {\mathit {Ma}}=-{\frac {\partial \sigma }{\partial T}}{\frac {L\Delta T}{\eta a}}}$

Here designated

• ${\displaystyle L}$the characteristic length
• ${\displaystyle \eta }$the dynamic viscosity , d. H. the viscosity of the fluid, which counteracts convection
• ${\displaystyle a}$the thermal diffusivity ( English thermal diffusivity ).

Similarly, the local differences in interfacial tension can also arise from differences in the concentration of dissolved substances (e.g. detergents) or the charge density and can be expressed by a corresponding definition of the Marangoni number.

Individual evidence

1. ^ J. Straub, A. Weinzierl, M. Zell: Thermocapillary boundary surface convection on gas bubbles in a temperature gradient field . In: heat and mass transfer . tape 25 , no. 5 , 1990, pp. 281–288 , doi : 10.1007 / BF01780740 ( online [PDF]).
2. ↑ Thierry Duffar (Ed.): Crystal Growth Processes Based on Capillarity . John Wiley & Sons, 2010, ISBN 1-4443-2021-1 , pp. 414 ( limited preview in Google Book search).