The inexorable resistance of inertia determines the initial regime of drop coalescence

Drop coalescence is central to diverse processes involving dispersions of drops in industrial, engineering, and scientific realms. During coalescence, two drops first touch and then merge as the liquid neck connecting them grows from initially microscopic scales to a size comparable to the drop diameters. The curvature of the interface is infinite at the point where the drops first make contact, and the flows that ensue as the two drops coalesce are intimately coupled to this singularity in the dynamics. Conventionally, this process has been thought to have just two dynamical regimes: a viscous and an inertial regime with a cross-over region between them. We use experiments and simulations to reveal that a third regime, one that describes the initial dynamics of coalescence for all drop viscosities, has been missed. An argument based on force balance allows the construction of a new coalescence phase diagram.

[1]  Sidney R Nagel,et al.  Viscous to inertial crossover in liquid drop coalescence. , 2010, Physical review letters.

[2]  H. Stone,et al.  CAPILLARY BREAKUP OF A VISCOUS THREAD SURROUNDED BY ANOTHER VISCOUS FLUID , 1998 .

[3]  R. Hopper.  Coalescence of two equal cylinders: exact results for creeping viscous plane flow driven by capillarity , 1984 .

[4]  Håkan Wennerström,et al.  The Colloidal Domain: Where Physics, Chemistry, Biology and Technology Meet , 1994 .

[5]  Daniel Bonn,et al.  Hydrodynamics of droplet coalescence. , 2005, Physical review letters.

[6]  I. Cohen,et al.  The two fluid drop snap-off problem: experiment and theory , 1999, physics/9902071.

[7]  S. Nagel,et al.  Coalescence in low-viscosity liquids. , 2006, Physical review letters.

[8]  David A. Weitz,et al.  Electrocoalescence of drops synchronized by size-dependent flow in microfluidic channels , 2006 .

[9]  Alvin U. Chen,et al.  Computational and experimental analysis of pinch-off and scaling. , 2002, Physical review letters.

[10]  John R. Lister,et al.  Coalescence of liquid drops , 1999, Journal of Fluid Mechanics.

[11]  G. Seidel,et al.  Coalescence of viscous liquid drops. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  N. Ashgriz,et al.  Coalescence and separation in binary collisions of liquid drops , 1990, Journal of Fluid Mechanics.

[13]  P. Taborek,et al.  Role of dimensionality and axisymmetry in fluid pinch-off and coalescence. , 2007, Physical review letters.

[14]  S. Zaleski,et al.  Coalescence of liquid drops by surface tension. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Robert W. Hopper,et al.  Plane Stokes flow driven by capillarity on a free surface , 1990, Journal of Fluid Mechanics.

[16]  Chih-Ming Ho,et al.  Scaling law in liquid drop coalescence driven by surface tension , 2004 .

[17]  J. Eggers,et al.  Inviscid coalescence of drops , 2002, Journal of Fluid Mechanics.

[18]  J. Sartor.  Electricity and rain , 1969 .

[19]  J. Derby,et al.  Transport mechanisms and densification during sintering: I. Viscous flow versus vacancy diffusion , 2009 .

[20]  Kamel Fezzaa,et al.  Ultrafast x-ray phase-contrast imaging of the initial coalescence phase of two water droplets. , 2008, Physical review letters.

[21]  O. Basaran,et al.  Local dynamics during pinch-off of liquid threads of power law fluids: Scaling analysis and self-similarity , 2006 .

[22]  Vittorio Cristini,et al.  An adaptive mesh algorithm for evolving surfaces: simulation of drop breakup and coalescence , 2001 .

[23]  S. Case.  Coalescence of low-viscosity fluids in air. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  J. Derby,et al.  Viscous Sintering of Spherical Particles via Finite Element Analysis , 1995 .

[25]  E. Villermaux,et al.  Physics of liquid jets , 2008 .

[26]  K. Okumura,et al.  Dimensional crossover in the coalescence dynamics of viscous drops confined in between two plates , 2011, Proceedings of the National Academy of Sciences.

[27]  Mojtaba Ghadiri,et al.  Electrostatic enhancement of coalescence of water droplets in oil: a review of the technology , 2002 .

[28]  C. Gourdon,et al.  Drainage and Rupture of Partially Mobile Films during Coalescence in Liquid-Liquid Systems under a Constant Interaction Force , 1995 .

[29]  T. Etoh,et al.  The coalescence speed of a pendent and a sessile drop , 2005, Journal of Fluid Mechanics.

[30]  L. E. Scriven,et al.  Discretization of free surface flows and other moving boundary problems , 1992 .

[31]  Bing Dai,et al.  The mechanism of surfactant effects on drop coalescence , 2008 .

[32]  P. Fischer,et al.  Eliminating parasitic currents in the lattice Boltzmann equation method for nonideal gases. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  D. Ramkrishna,et al.  Coalescence in Creaming Emulsions. Existence of a Pure Coalescence Zone , 1996 .