Dear Muhammad,

In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of gravitational forces compared to surface tension forces and is used together with Morton number to characterize the shape of bubbles or drops moving in a surrounding fluid. The Morton number can also be expressed by using a combination of the Weber number, Froude number and Reynolds number, Mo = W^3/(FxR^4).

Here is a document that will be very useful.

https://infoscience.epfl.ch/record/198760/files/2014_971_Pfister_Hager_history_and_significance_Morton_number_in_hydraulic_engineering.pdf

With my best regards

Prof. Bachir ACHOUR

Professor Bachir ACHOUR

Thanks for your resourceful reply. Kind regards.

In the case of bubble dynamics, we study the effect of Eo number on the shape instabilities of the rising bubble. However, Eo number contains the radius of the bubble which is actually changing continuously with time. Thus, there is a need to define Morton number which depends only on the fluid properties and not on the bubble radius. Morton number is a suitable ratio of Eo and Ga numbers so as to eliminate the bubble radius.