On interdependence of instabilities and average drop sizes in bag breakup
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914116627595264 |
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| author | Kulkarni, Varun Shirdade, Nikhil Rodrigues, Neil Radhakrishna, Vishnu Sojka, Paul E. |
| author_facet | Kulkarni, Varun Shirdade, Nikhil Rodrigues, Neil Radhakrishna, Vishnu Sojka, Paul E. |
| contents | A drop exposed to cross flow of air experiences sudden accelerations which deform it rapidly ultimately proceeding to disintegrate it into smaller fragments. In this work, we examine the breakup of a drop as a bag film with a bounding rim resulting from acceleration induced Rayleigh-Taylor instabilities and characterized through the Weber number, \textit{We}, representative of the competition between the disruptive aerodynamic force imparting acceleration and the restorative surface tension force. Our analysis reveals a previously overlooked parabolic dependence ($\sim We^2$) of the combination of dimensionless instability wavelengths $({\barλ}_{bag}^2/ {\barλ}_{rim}^4 {\barλ}_{film})$ developing on different segments of the deforming drop. Further, we extend these findings to deduce the dependence of the average dimensionless drop sizes for the rim, $\langle{\bar{D}}_{rim}\rangle$ and bag film, $\langle{\bar{D}}_{film}\rangle$ individually, on $We$ and see them to decrease linearly for the rim ($\sim We^{-1}$) and quadratically for the bag film ($\sim We^{-2}$). The reported work is expected to have far-reaching implications as it provides unique insights on destabilization and disintegration mechanisms based on theoretical scaling arguments involving the commonly encountered canonical geometries of a toroidal rim and a curved liquid film. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_16241 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On interdependence of instabilities and average drop sizes in bag breakup Kulkarni, Varun Shirdade, Nikhil Rodrigues, Neil Radhakrishna, Vishnu Sojka, Paul E. Fluid Dynamics A drop exposed to cross flow of air experiences sudden accelerations which deform it rapidly ultimately proceeding to disintegrate it into smaller fragments. In this work, we examine the breakup of a drop as a bag film with a bounding rim resulting from acceleration induced Rayleigh-Taylor instabilities and characterized through the Weber number, \textit{We}, representative of the competition between the disruptive aerodynamic force imparting acceleration and the restorative surface tension force. Our analysis reveals a previously overlooked parabolic dependence ($\sim We^2$) of the combination of dimensionless instability wavelengths $({\barλ}_{bag}^2/ {\barλ}_{rim}^4 {\barλ}_{film})$ developing on different segments of the deforming drop. Further, we extend these findings to deduce the dependence of the average dimensionless drop sizes for the rim, $\langle{\bar{D}}_{rim}\rangle$ and bag film, $\langle{\bar{D}}_{film}\rangle$ individually, on $We$ and see them to decrease linearly for the rim ($\sim We^{-1}$) and quadratically for the bag film ($\sim We^{-2}$). The reported work is expected to have far-reaching implications as it provides unique insights on destabilization and disintegration mechanisms based on theoretical scaling arguments involving the commonly encountered canonical geometries of a toroidal rim and a curved liquid film. |
| title | On interdependence of instabilities and average drop sizes in bag breakup |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2307.16241 |