Inertial impedance of coalescence during collision of liquid drops

Sambath, Krishnaraj; Garg, Vishrut; Thete, Sumeet S.; Subramani, Hariprasad J.; Basaran, Osman A.

doi:10.1017/jfm.2019.498

Title: Inertial impedance of coalescence during collision of liquid drops

Journal Article · Thu Aug 01 00:00:00 EDT 2019 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2019.498· OSTI ID:1800844

Sambath, Krishnaraj;

; Thete, Sumeet S.; Subramani, Hariprasad J.;

The fluid dynamics of the collision and coalescence of liquid drops has intrigued scientists and engineers for more than a century owing to its ubiquitousness in nature, e.g. raindrop coalescence, and industrial applications, e.g. breaking of emulsions in the oil and gas industry. The complexity of the underlying dynamics, which includes occurrence of hydrodynamic singularities, has required study of the problem at different scales – macroscopic, mesoscopic and molecular – using stochastic and deterministic methods. In this work, a multi-scale, deterministic method is adopted to simulate the approach, collision, and eventual coalescence of two drops where the drops as well as the ambient fluid are incompressible, Newtonian fluids. The free boundary problem governing the dynamics consists of the Navier–Stokes system and associated initial and boundary conditions that have been augmented to account for the effects of disjoining pressure as the separation between the drops becomes of the order of a few hundred nanometres. This free boundary problem is solved by a Galerkin finite element-based algorithm. The interplay of inertial, viscous, capillary and van der Waals forces on the coalescence dynamics is investigated. It is shown that, in certain situations, because of inertia two drops that are driven together can first bounce before ultimately coalescing. This bounce delays coalescence and can result in the computed value of the film drainage time departing significantly from that predicted from existing scaling theories.

Cite

Export

Save

Research Organization:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

DOE Contract Number:: FG02-96ER14641

OSTI ID:: 1800844

Journal Information:: Journal of Fluid Mechanics, Vol. 876; ISSN 0022-1120

Publisher:: Cambridge University Press

Country of Publication:: United States

Language:: English

References (73)

Flow induced coalescence of drops in a viscous fluid Leal, L. G. Physics of Fluids, Vol. 16, Issue 6 https://doi.org/10.1063/1.1701892	journal	June 2004
The effect of slight deformation on droplet coalescence in linear flows Rother, Michael A.; Davis, Robert H. Physics of Fluids, Vol. 13, Issue 5 https://doi.org/10.1063/1.1358871	journal	May 2001
Regimes of coalescence and separation in droplet collision Qian, J.; Law, C. K. Journal of Fluid Mechanics, Vol. 331 https://doi.org/10.1017/S0022112096003722	journal	January 1997
Plethora of transitions during breakup of liquid filaments Castrejón-Pita, José Rafael; Castrejón-Pita, Alfonso Arturo; Thete, Sumeet Suresh Proceedings of the National Academy of Sciences, Vol. 112, Issue 15 https://doi.org/10.1073/pnas.1418541112	journal	March 2015
Buoyancy-driven viscous interaction of a rising drop with a smaller trailing drop Davis, Robert H. Physics of Fluids, Vol. 11, Issue 5 https://doi.org/10.1063/1.869973	journal	May 1999
Wetting: statics and dynamics de Gennes, P. G. Reviews of Modern Physics, Vol. 57, Issue 3, p. 827-863 https://doi.org/10.1103/RevModPhys.57.827	journal	July 1985
A finite element method for free surface flows of incompressible fluids in three dimensions. Part II. Dynamic wetting lines Baer, Thomas A.; Cairncross, Richard A.; Schunk, P. Randall International Journal for Numerical Methods in Fluids, Vol. 33, Issue 3 https://doi.org/10.1002/1097-0363(20000615)33:3<405::AID-FLD14>3.0.CO;2-4	journal	January 2000
Electric Field Driven Separations: Phenomena and Applications Ptasinski, K. J.; Kerkhof, P. J. A. M. Separation Science and Technology, Vol. 27, Issue 8-9 https://doi.org/10.1080/01496399208019021	journal	July 1992
Nanoparticles for Drug Delivery: Review of the Formulation and Process Difficulties Illustrated by the Emulsion-Diffusion Process Moinard-Checot, D.; Chevalier, Y.; Briançon, S. Journal of Nanoscience and Nanotechnology, Vol. 6, Issue 9 https://doi.org/10.1166/jnn.2006.479	journal	September 2006
Determination of coalescence frequencies in liquid—liquid dispersions: effect of drop size dependence Tobin, T.; Muralidhar, R.; Wright, H. Chemical Engineering Science, Vol. 45, Issue 12 https://doi.org/10.1016/0009-2509(90)87154-K	journal	January 1990
Shear flow over a translationally symmetric cylindrical bubble pinned on a slot in a plane wall Feng, James Q.; Basaran, Osman A. Journal of Fluid Mechanics, Vol. 275 https://doi.org/10.1017/S0022112094002399	journal	September 1994
Dynamics and breakup of a contracting liquid filament Notz, Patrick K.; Basaran, Osman A. Journal of Fluid Mechanics, Vol. 512 https://doi.org/10.1017/S0022112004009759	journal	July 2004
Thin-sheet flow between coalescing bubbles Munro, James P.; Anthony, Christopher R.; Basaran, Osman A. Journal of Fluid Mechanics, Vol. 773 https://doi.org/10.1017/jfm.2015.253	journal	May 2015
A coalescence redispersion model for drop-size distributions in an agitated vessel Bajpai, R. K.; Ramkrishna, D.; Prokop, A. Chemical Engineering Science, Vol. 31, Issue 10 https://doi.org/10.1016/0009-2509(76)87041-8	journal	January 1976
Local dynamics during pinch-off of liquid threads of power law fluids: Scaling analysis and self-similarity Suryo, Ronald; Basaran, Osman A. Journal of Non-Newtonian Fluid Mechanics, Vol. 138, Issue 2-3 https://doi.org/10.1016/j.jnnfm.2006.04.008	journal	October 2006
Drop oscillations in liquid-liquid systems Basaran, Osman A.; Scott, Timothy C.; Byers, Charles H. AIChE Journal, Vol. 35, Issue 8 https://doi.org/10.1002/aic.690350805	journal	August 1989
Thermal delay of drop coalescence Geri, Michela; Keshavarz, Bavand; McKinley, Gareth H. Journal of Fluid Mechanics, Vol. 833 https://doi.org/10.1017/jfm.2017.686	journal	November 2017
Effect of nonlinear polarization on shapes and stability of pendant and sessile drops in an electric (magnetic) field Basaran, Osman A.; Wohlhuter, Fred K. Journal of Fluid Mechanics, Vol. 244, Issue -1 https://doi.org/10.1017/S0022112092002945	journal	November 1992
Drop Ejection from an Oscillating Rod Wilkes, Edward D.; Basaran, Osman A. Journal of Colloid and Interface Science, Vol. 242, Issue 1 https://doi.org/10.1006/jcis.2001.7729	journal	October 2001
Drop deformation, breakup, and coalescence with compatibilizer Hu, Y. T.; Pine, D. J.; Leal, L. Gary Physics of Fluids, Vol. 12, Issue 3 https://doi.org/10.1063/1.870254	journal	March 2000
Shapes of rotating free drops: Spacelab experimental results Wang, T. G.; Trinh, E. H.; Croonquist, A. P. Physical Review Letters, Vol. 56, Issue 5 https://doi.org/10.1103/PhysRevLett.56.452	journal	February 1986
Drop-size effects on coalescence of two equal-sized drops in a head-on collision Hsu, Adam S.; Roy, Anshuman; Leal, L. Gary Journal of Rheology, Vol. 52, Issue 6 https://doi.org/10.1122/1.2980013	journal	November 2008
Self-similar rupture of thin films of power-law fluids on a substrate Garg, Vishrut; Kamat, Pritish M.; Anthony, Christopher R. Journal of Fluid Mechanics, Vol. 826 https://doi.org/10.1017/jfm.2017.446	journal	August 2017
A scaling relation for the capillary-pressure driven drainage of thin films Frostad, J. M.; Walter, J.; Leal, L. G. Physics of Fluids, Vol. 25, Issue 5 https://doi.org/10.1063/1.4807069	journal	May 2013
XXXVI. Investigations in Capillarity:—The size of drops.—The liberation of gas from supersaturated solutions.—Colliding jets.—The tension of contaminated water-surfaces The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 48, Issue 293 https://doi.org/10.1080/14786449908621342	journal	October 1899
Close approach and deformation of two viscous drops due to gravity and van der waals forces Yiantsios, Stergios G.; Davis, Robert H. Journal of Colloid and Interface Science, Vol. 144, Issue 2 https://doi.org/10.1016/0021-9797(91)90407-Y	journal	July 1991
Hindered and Enhanced Coalescence of Drops in Stokes Flows Nemer, M. B.; Chen, X.; Papadopoulos, D. H. Physical Review Letters, Vol. 92, Issue 11 https://doi.org/10.1103/PhysRevLett.92.114501	journal	March 2004
How Liquids Spread on Solids Teletzke, Gary F.; Ted Davis, H.; Scriven, L. E. Chemical Engineering Communications, Vol. 55, Issue 1-6 https://doi.org/10.1080/00986448708911919	journal	May 1987
Multiscale computations of thin films in multiphase flows Thomas, S.; Esmaeeli, A.; Tryggvason, G. International Journal of Multiphase Flow, Vol. 36, Issue 1 https://doi.org/10.1016/j.ijmultiphaseflow.2009.08.002	journal	January 2010
Coalescence of liquid drops Eggers, Jens; Lister, John R.; Stone, Howard A. Journal of Fluid Mechanics, Vol. 401 https://doi.org/10.1017/S002211209900662X	journal	December 1999
The limits of Navier-Stokes theory and kinetic extensions for describing small-scale gaseous hydrodynamics Hadjiconstantinou, Nicolas G. Physics of Fluids, Vol. 18, Issue 11 https://doi.org/10.1063/1.2393436	journal	November 2006
Nonlinear oscillations of viscous liquid drops Basaran, Osman A. Journal of Fluid Mechanics, Vol. 241 https://doi.org/10.1017/S002211209200199X	journal	August 1992
Universal scaling laws for the disintegration of electrified drops Collins, R. T.; Sambath, K.; Harris, M. T. Proceedings of the National Academy of Sciences, Vol. 110, Issue 13 https://doi.org/10.1073/pnas.1213708110	journal	March 2013
Axisymmetric boundary integral simulations of film drainage between two viscous drops Janssen, P. J. A.; Anderson, P. D.; Peters, G. W. M. Journal of Fluid Mechanics, Vol. 567 https://doi.org/10.1017/S0022112006002084	journal	October 2006
Scaling laws and dynamics of bubble coalescence Anthony, Christopher R.; Kamat, Pritish M.; Thete, Sumeet S. Physical Review Fluids, Vol. 2, Issue 8 https://doi.org/10.1103/PhysRevFluids.2.083601	journal	August 2017
Modeling Film Drainage and Coalescence of Drops in a Viscous Fluid Janssen, Pieter J. A.; Anderson, Patrick D. Macromolecular Materials and Engineering, Vol. 296, Issue 3-4 https://doi.org/10.1002/mame.201000375	journal	March 2011
A novel boundary-integral algorithm for viscous interaction of deformable drops Zinchenko, Alexander Z.; Rother, Michael A.; Davis, Robert H. Physics of Fluids, Vol. 9, Issue 6 https://doi.org/10.1063/1.869275	journal	June 1997
Water-in-Crude Oil Emulsion Stabilization: Review and Unanswered Questions Kilpatrick, Peter K. Energy & Fuels, Vol. 26, Issue 7 https://doi.org/10.1021/ef3003262	journal	June 2012
Head‐on collision of drops—A numerical investigation Nobari, M. R.; Jan, Y. ‐J.; Tryggvason, G. Physics of Fluids, Vol. 8, Issue 1 https://doi.org/10.1063/1.868812	journal	January 1996
The mechanism of surfactant effects on drop coalescence Dai, Bing; Leal, L. Gary Physics of Fluids, Vol. 20, Issue 4 https://doi.org/10.1063/1.2911700	journal	April 2008
The Formation of Emulsions in Definable Fields of Flow Taylor, G. I. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 146, Issue 858 https://doi.org/10.1098/rspa.1934.0169	journal	October 1934
Comment on “Two touching spherical drops in uniaxial extensional flow: Analytic solution to the creeping flow problem” Nemer, M. B.; Chen, X.; Papadopoulos, D. H. Journal of Colloid and Interface Science, Vol. 308, Issue 1 https://doi.org/10.1016/j.jcis.2006.10.028	journal	April 2007
The coalescence of two equal-sized drops in a two-dimensional linear flow Yang, Hong; Park, C. Charles; Hu, Y. Thomas Physics of Fluids, Vol. 13, Issue 5 https://doi.org/10.1063/1.1358873	journal	May 2001
Nonlinear oscillations of inviscid free drops Patzek, T. W.; Benner, R. E.; Basaran, O. A. Journal of Computational Physics, Vol. 97, Issue 2 https://doi.org/10.1016/0021-9991(91)90010-I	journal	December 1991
Discretization of free surface flows and other moving boundary problems Christodoulou, K. N.; Scriven, L. E. Journal of Computational Physics, Vol. 99, Issue 1 https://doi.org/10.1016/0021-9991(92)90273-2	journal	March 1992
The inexorable resistance of inertia determines the initial regime of drop coalescence Paulsen, J. D.; Burton, J. C.; Nagel, S. R. Proceedings of the National Academy of Sciences, Vol. 109, Issue 18 https://doi.org/10.1073/pnas.1120775109	journal	April 2012
Electrohydrodynamic tip streaming and emission of charged drops from liquid cones Collins, Robert T.; Jones, Jeremy J.; Harris, Michael T. Nature Physics, Vol. 4, Issue 2 https://doi.org/10.1038/nphys807	journal	December 2007
Non-coalescence of oppositely charged drops Ristenpart, W. D.; Bird, J. C.; Belmonte, A. Nature, Vol. 461, Issue 7262 https://doi.org/10.1038/nature08294	journal	September 2009
Electrostatic enhancement of coalescence of water droplets in oil: a review of the technology Eow, J. Chemical Engineering Journal, Vol. 85, Issue 2-3 https://doi.org/10.1016/S1385-8947(01)00250-9	journal	January 2002
Formation of beads-on-a-string structures during break-up of viscoelastic filaments Bhat, Pradeep P.; Appathurai, Santosh; Harris, Michael T. Nature Physics, Vol. 6, Issue 8 https://doi.org/10.1038/nphys1682	journal	June 2010
Theoretical prediction of electric field-enhanced coalescence of spherical drops Zhang, Xiaoguang; Basaran, Osman A.; Wham, Robart M. AIChE Journal, Vol. 41, Issue 7 https://doi.org/10.1002/aic.690410704	journal	July 1995
Molecular dynamics simulation of the coalescence of nanometer-sized water droplets in n -heptane Zhao, Liyan; Choi, Phillip The Journal of Chemical Physics, Vol. 120, Issue 4 https://doi.org/10.1063/1.1635804	journal	January 2004
Coalescence of two equal-sized deformable drops in an axisymmetric flow Yoon, Yosang; Baldessari, Fabio; Ceniceros, Hector D. Physics of Fluids, Vol. 19, Issue 10 https://doi.org/10.1063/1.2772900	journal	October 2007
Discretization of three-dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles Fraggedakis, D.; Papaioannou, J.; Dimakopoulos, Y. Journal of Computational Physics, Vol. 344 https://doi.org/10.1016/j.jcp.2017.04.060	journal	September 2017
Experimental analysis of the coalescence process via head-on collisions in a time-dependent flow Borrell, Marcos; Yoon, Y.; Leal, L. Gary Physics of Fluids, Vol. 16, Issue 11 https://doi.org/10.1063/1.1795291	journal	November 2004
Effect of Insoluble Surfactants on Drainage and Rupture of a Film between Drops Interacting under a Constant Force Chesters, Allan K.; Bazhlekov, Ivan B. Journal of Colloid and Interface Science, Vol. 230, Issue 2 https://doi.org/10.1006/jcis.2000.7074	journal	October 2000
Capillary breakup of a liquid bridge: identifying regimes and transitions Li, Yuan; Sprittles, James E. Journal of Fluid Mechanics, Vol. 797 https://doi.org/10.1017/jfm.2016.276	journal	May 2016
The oscillations of a fluid droplet immersed in another fluid Miller, C. A.; Scriven, L. E. Journal of Fluid Mechanics, Vol. 32, Issue 3 https://doi.org/10.1017/S0022112068000832	journal	May 1968
Coalescence of drops with mobile interfaces in a quiescent fluid Nemer, M. B.; Santoro, P.; Chen, X. Journal of Fluid Mechanics, Vol. 728 https://doi.org/10.1017/jfm.2013.288	journal	July 2013
Population balance modelling of phase inversion in liquid–liquid pipeline flows Hu, Bin; Matar, Omar K.; Hewitt, Geoffrey F. Chemical Engineering Science, Vol. 61, Issue 15 https://doi.org/10.1016/j.ces.2006.03.053	journal	August 2006
An Exact Method for Numerically Simulating the Stochastic Coalescence Process in a Cloud Gillespie, Daniel T. Journal of the Atmospheric Sciences, Vol. 32, Issue 10 https://doi.org/10.1175/1520-0469(1975)032<1977:AEMFNS>2.0.CO;2	journal	October 1975
Breakage and coalescence models for drops in turbulent dispersions Tsouris, C.; Tavlarides, L. L. AIChE Journal, Vol. 40, Issue 3 https://doi.org/10.1002/aic.690400303	journal	March 1994
Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids Yue, Pengtao; Feng, James J.; Liu, Chun Journal of Non-Newtonian Fluid Mechanics, Vol. 129, Issue 3 https://doi.org/10.1016/j.jnnfm.2005.07.002	journal	September 2005
Buoyancy-driven coalescence of slightly deformable drops Rother, Michael A.; Zinchenko, Alexander Z.; Davis, Robert H. Journal of Fluid Mechanics, Vol. 346 https://doi.org/10.1017/S002211209700623X	journal	September 1997
Shape oscillation and static deformation of drops and bubbles driven by modulated radiation stresses—Theory Marston, Philip L. The Journal of the Acoustical Society of America, Vol. 67, Issue 1 https://doi.org/10.1121/1.383798	journal	January 1980
Viscosity ratio effects on the coalescence of two equal-sized drops in a two-dimensional linear flow Yoon, Yosang; Borrell, Marcos; Park, C. Charles Journal of Fluid Mechanics, Vol. 525 https://doi.org/10.1017/S0022112004002824	journal	January 1999
Free oscillations of drops and bubbles: the initial-value problem Prosperetti, Andrea Journal of Fluid Mechanics, Vol. 100, Issue 02 https://doi.org/10.1017/S0022112080001188	journal	September 1980
Computational and Experimental Analysis of Pinch-Off and Scaling Chen, Alvin U.; Notz, Patrick K.; Basaran, Osman A. Physical Review Letters, Vol. 88, Issue 17 https://doi.org/10.1103/PhysRevLett.88.174501	journal	April 2002
A finite element method for free surface flows of incompressible fluids in three dimensions. Part I. Boundary fitted mesh motion Cairncross, Richard A.; Schunk, P. Randall; Baer, Thomas A. International Journal for Numerical Methods in Fluids, Vol. 33, Issue 3 https://doi.org/10.1002/1097-0363(20000615)33:3<375::AID-FLD13>3.0.CO;2-O	journal	January 2000
From Bouncing to Floating: Noncoalescence of Drops on a Fluid Bath Couder, Y.; Fort, E.; Gautier, C. -H. Physical Review Letters, Vol. 94, Issue 17 https://doi.org/10.1103/PhysRevLett.94.177801	journal	May 2005
Coalescence of surfactant covered drops in extensional flows: Effects of the interfacial diffusivity Vannozzi, Carolina Physics of Fluids, Vol. 24, Issue 8 https://doi.org/10.1063/1.4737659	journal	August 2012
Effect of interfacial slip on the thin film drainage time for two equal-sized, surfactant-free drops undergoing a head-on collision: A scaling analysis Ramachandran, A.; Leal, L. G. Physical Review Fluids, Vol. 1, Issue 6 https://doi.org/10.1103/PhysRevFluids.1.064204	journal	October 2016
Core-Centering of Compound Drops in Capillary Oscillations: Observations on USML-1 Experiments in Space Wang, T. G.; Anilkumar, A. V.; Lee, C. P. Journal of Colloid and Interface Science, Vol. 165, Issue 1 https://doi.org/10.1006/jcis.1994.1201	journal	June 1994

Similar Records

Numerical homogenization on approach for stokesian suspensions.

Technical Report · Fri Jan 20 00:00:00 EST 2012 · OSTI ID:1800844

Haines, B M; Berlyand, L V; Karpeev, D A

Localized Scale Coupling and New Educational Paradigms in Multiscale Mathematics and Science

Technical Report · Sun Jun 30 00:00:00 EDT 2013 · OSTI ID:1800844

LEAL, L. GARY

Self-assembly of a drop pattern from a two-dimensional grid of nanometric metallic filaments

Journal Article · Thu Oct 04 00:00:00 EDT 2018 · Physical Review E · OSTI ID:1800844

Cuellar, Ingrith; Ravazzoli, Pablo D.; Diez, Javier A.; +5 more

Related Subjects

Mechanics
Physics

Title: Inertial impedance of coalescence during collision of liquid drops

Citation Formats

References (73)

Similar Records

Related Subjects