On interdependence of instabilities and average drop sizes in bag breakup

A drop exposed to cross flow of air experiences sudden accelerations, which deform it rapidly, ultimately proceeding to disintegrate 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, 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 (∼We2) of the combination of dimensionless instability wavelengths (λ¯bag2/λ¯rim4λ¯film) developing on different segments of the deforming drop. Furthermore, we extend these findings to deduce the dependence of the average dimensionless drop sizes for the rim, ⟨D¯rim⟩, and bag film, ⟨D¯film⟩, individually, on We and see them decreasing linearly for the rim (∼We−1) and quadratically for the bag film (∼We−2). The reported work is expected to have far-reaching implications as it provides unique insight 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.

[1]  V. Kulkarni An analytical and experimental study of secondary atomization of vibrational and bag breakup modes , 2023, 2306.10421.

[2]  Yanlin Song,et al.  Drop impact dynamics on solid surfaces , 2022, Applied Physics Letters.

[3]  N. Chandra,et al.  Advances in droplet aerobreakup , 2022, The European Physical Journal Special Topics.

[4]  S. Dash,et al.  Impact Dynamics of Air-in-Liquid Compound Droplets , 2022, Physics of Fluids.

[5]  N. Ashgriz,et al.  Prediction of the droplet size distribution in aerodynamic droplet breakup , 2022, Journal of Fluid Mechanics.

[6]  L. Bourouiba,et al.  Mass, momentum and energy partitioning in unsteady fragmentation , 2022, Journal of Fluid Mechanics.

[7]  T. Anand,et al.  Droplet deformation in secondary breakup: Transformation from a sphere to a disk-like structure , 2021, International Journal of Multiphase Flow.

[8]  Jun Chen,et al.  Experimental characterization of secondary atomization at high Ohnesorge numbers , 2021, International Journal of Multiphase Flow.

[9]  V. Kulkarni,et al.  Coalescence and spreading of drops on liquid pools. , 2020, Journal of colloid and interface science.

[10]  M. Vadivukkarasan,et al.  Breakup morphology of expelled respiratory liquid: From the perspective of hydrodynamic instabilities , 2020, Physics of fluids.

[11]  S. Dash,et al.  Bubble-Induced Rupture of Droplets on Hydrophobic and Lubricant Impregnated Surfaces. , 2020, Langmuir : the ACS journal of surfaces and colloids.

[12]  C. Law,et al.  Atomization of acoustically levitated droplet exposed to hot gases , 2020 .

[13]  C. Ohl,et al.  Merging of soap bubbles and why surfactant matters , 2019, Applied Physics Letters.

[14]  Emmanuel Roucounas Fragmentation , 2019, A Landscape of Contemporary Theories of International Law.

[15]  K. Sahu,et al.  Deformation and breakup of droplets in an oblique continuous air stream , 2019, International Journal of Multiphase Flow.

[16]  O. Druzhinin,et al.  The “Bag Breakup” Spume Droplet Generation Mechanism at High Winds. Part II: Contribution to Momentum and Enthalpy Transfer , 2018, Journal of Physical Oceanography.

[17]  L. Bourouiba,et al.  Ageing and burst of surface bubbles , 2018, Journal of Fluid Mechanics.

[18]  Jian Gao,et al.  Characterization of drop aerodynamic fragmentation in the bag and sheet-thinning regimes by crossed-beam, two-view, digital in-line holography , 2017 .

[19]  Tianyou Wang,et al.  Transitions of deformation to bag breakup and bag to bag-stamen breakup for droplets subjected to a continuous gas flow , 2017 .

[20]  L. Bourouiba,et al.  Drop impact on small surfaces: thickness and velocity profiles of the expanding sheet in the air , 2017, Journal of Fluid Mechanics.

[21]  J. M. Bush,et al.  Visualization of sneeze ejecta: steps of fluid fragmentation leading to respiratory droplets , 2016, Experiments in Fluids.

[22]  N. Vandenberghe,et al.  Explosive fragmentation of liquid shells , 2016, Journal of Fluid Mechanics.

[23]  Kartik V. Bulusu,et al.  Fragment size distribution in viscous bag breakup of a drop , 2015 .

[24]  J. Keller,et al.  Instability of Liquid Surfaces and the Formation of Drops , 2015 .

[25]  G. Tomar,et al.  Secondary breakup of a drop at moderate Weber numbers , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[26]  P. Sojka,et al.  Fragmentation dynamics in the droplet bag breakup regime , 2014 .

[27]  P. Sojka,et al.  Bag breakup of low viscosity drops in the presence of a continuous air jet , 2014, 2204.06036.

[28]  Hongwei Wu,et al.  Modeling of Drop Breakup in the Bag Breakup Regime , 2014 .

[29]  Jun Chen,et al.  Quantitative, three-dimensional diagnostics of multiphase drop fragmentation via digital in-line holography. , 2013, Optics letters.

[30]  James J. Feng,et al.  Capillary breakup of a liquid torus , 2013, Journal of Fluid Mechanics.

[31]  M. Jalaal,et al.  Fragmentation of falling liquid droplets in bag breakup mode , 2012 .

[32]  D. Guildenbecher,et al.  Bag Breakup of Viscous Drops , 2012 .

[33]  D. Guildenbecher,et al.  Secondary Atomization of Newtonian Liquids in the Bag Breakup Regime: Comparison of Model Predictions to Experimental Data , 2012 .

[34]  E. Villermaux,et al.  Bursting bubble aerosols , 2011, Journal of Fluid Mechanics.

[35]  Hui Zhao,et al.  Experimental Study of Drop Size Distribution in the Bag Breakup Regime , 2011 .

[36]  Haifeng Liu,et al.  Breakup characteristics of liquid drops in bag regime by a continuous and uniform air jet flow , 2011 .

[37]  T. Theofanous Aerobreakup of Newtonian and Viscoelastic Liquids , 2011 .

[38]  Hui Zhao,et al.  Morphological classification of low viscosity drop bag breakup in a continuous air jet stream , 2010 .

[39]  E. Villermaux,et al.  Single-drop fragmentation determines size distribution of raindrops , 2009 .

[40]  J. Strutt Scientific Papers: Investigation of the Character of the Equilibrium of an Incompressible Heavy Fluid of Variable Density , 2009 .

[41]  A. Fernández-Nieves,et al.  Generation and stability of toroidal droplets in a viscous liquid. , 2009, Physical review letters.

[42]  D. Schmidt,et al.  Direct Numerical Study of a Liquid Droplet Impulsively Accelerated by Gaseous Flow , 2006 .

[43]  E. Villermaux,et al.  Bursting thin liquid films , 2005, Journal of Fluid Mechanics.

[44]  A. Yarin,et al.  Impact of drops on solid surfaces: self-similar capillary waves, and splashing as a new type of kinematic discontinuity , 1995, Journal of Fluid Mechanics.

[45]  G. Faeth,et al.  Drop deformation and breakup due to shock wave and steady disturbances , 1994 .

[46]  Stefan A. Krzeczkowski,et al.  MEASUREMENT OF LIQUID DROPLET DISINTEGRATION MECHANISMS , 1980 .

[47]  Fred E. C. Culick,et al.  Comments on a Ruptured Soap Film , 1960 .

[48]  Geoffrey Ingram Taylor,et al.  The dynamics of thin sheets of fluid. III. Disintegration of fluid sheets , 1959, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[49]  Richard Bellman,et al.  Effects of Surface Tension and Viscosity on Taylor Instability , 1954 .

[50]  G. Taylor The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[51]  J. Venzmer,et al.  Droplet-air collision dynamics: evolution of the film thickness. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  D. Guildenbecher,et al.  Secondary atomization , 2009 .

[53]  D. Assanis,et al.  A UNIFIED FUEL SPRAY BREAKUP MODEL FOR INTERNAL COMBUSTION ENGINE APPLICATIONS , 2008 .

[54]  J. M. Bush,et al.  Viscous sheet retraction , 2009, Journal of Fluid Mechanics.