Rotational flux influenced cusp entrainment in a viscous pool

Evolution of entrained gaseous cusp in a viscous liquid pool caused by a fully immersed horizontal revolving circular drum is elucidated thoroughly. Finite volume-based open source Gerris is employed to carry out the numerical simulations. Length theta(s)* and width (H*) of the cusp are characterized thoroughly by varying the strength of rotational flux (measured by the capillary number, Ca) and depth of immersion (submersion height to roller diameter ratio, h / D) of the spinning roller. Locus and travel rate of cusp tip are also elaborated from origination to attainment of steady state with the progress of time for different combinations of C a and h / D. We have also reported the bubble ejection mechanism from the advancing end of the cusp after achieving macroscopic steady length. Bubbling frequency and volume accumulation of detached bubbles show strong dependency on C a or h / D. Entrainment patterns are also observed by investigating the effect of gravitational pull (measured by employing the Archimedes number, Ar) and viscous drag (specified by using the Morton number, Mo). Correlations are developed to estimate the cusp width (H*) at different angular locations and steady length of gaseous cusp theta(s)*, which show satisfactory agreement within +/- 6%. Finally, an analytical model is proposed to determine the cusp width by using the relevant influencing forces acting on the cusp. A satisfactory agreement is obtained between the analytical solutions and computational results. Published under an exclusive license by AIP Publishing.

Automated summary

This article thoroughly elucidates the evolution of an entrained gaseous cusp in a viscous liquid pool caused by a fully immersed horizontal revolving circular drum. The numerical simulations using the finite volume-based open source Gerris provide comprehensive characterization of the cusp's length and width by varying the rotational flux strength and depth of immersion. The locus and travel rate of the cusp tip are also explored as functions of time, rotational flux strength, and depth of immersion. The bubble ejection mechanism from the cusp's advancing end is reported, showing a strong dependency on rotational flux strength and depth of immersion. The effects of gravitational pull and viscous drag on the entrainment patterns are investigated, and correlations are developed to estimate the cusp width and steady length. The proposed analytical model shows satisfactory agreement with the computational results.