Skip to main content
×
×
Home

Thermal delay of drop coalescence

  • Michela Geri (a1), Bavand Keshavarz (a1), Gareth H. McKinley (a1) and John W. M. Bush (a2)
Abstract

We present the results of a combined experimental and theoretical study of drop coalescence in the presence of an initial temperature difference $\unicode[STIX]{x0394}T_{0}$ between a drop and a bath of the same liquid. We characterize experimentally the dependence of the residence time before coalescence on $\unicode[STIX]{x0394}T_{0}$ for silicone oils with different viscosities. Delayed coalescence arises above a critical temperature difference $\unicode[STIX]{x0394}T_{c}$ that depends on the fluid viscosity: for $\unicode[STIX]{x0394}T_{0}>\unicode[STIX]{x0394}T_{c}$ , the delay time increases as $\unicode[STIX]{x0394}T_{0}^{2/3}$ for all liquids examined. This observed dependence is rationalized theoretically through consideration of the thermocapillary flows generated within the drop, the bath and the intervening air layer.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Thermal delay of drop coalescence
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Thermal delay of drop coalescence
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Thermal delay of drop coalescence
      Available formats
      ×
Copyright
Corresponding author
Email address for correspondence: bush@math.mit.edu
References
Hide All
Aryafar H. & Kavehpour H. P. 2006 Drop coalescence through planar surfaces. Phys. Fluids 18 (7), 072105.
Batchelor G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Blanchette F. & Bigioni T. P. 2006 Partial coalescence of drops at liquid interfaces. Nat. Phys. 2, 254257.
Blanchette F. & Bigioni T. P. 2009 Dynamics of drop coalescence at fluid interfaces. J. Fluid Mech. 620, 333352.
Blanchette F., Messio L. & Bush J. W. M. 2009 The influence of surface tension gradients on drop coalescence. Phys. Fluids 21 (7), 072107.
Bush J. W. M. 2015 Pilot-wave hydrodynamics. Annu. Rev. Fluid Mech. 47, 269292.
Charles G. E. & Mason S. G. 1960a The coalescence of liquid drops with flat liquid/liquid interfaces. J. Colloid Sci. 15, 236267.
Charles G. E. & Mason S. G. 1960b The mechanism of partial coalescence of liquid drops at liquid/liquid interfaces. J. Colloid Sci. 15, 105122.
Dell’Aversana P., Banavar J. R. & Koplik J. 1996 Suppression of coalescence by shear and temperature gradients. Phys. Fluids 8 (1), 1528.
Dell’Aversana P. & Neitzel G. P. 1998 When liquids stay dry. Phys. Today 3841.
Dell’Aversana P., Tontodonato V. & Carotenuto L. 1997 Suppression of coalescence and of wetting: the shape of the interstitial film. Phys. Fluids 9 (9), 24752485.
Jeffreys G. V. & Davis G. A. 1971 Coalescence of liquid droplets and liquid dispersion. In Recent Advances in Liquid–Liquid Extraction, chap. 14, pp. 495584. Pergamon.
Kavehpour H. P. 2015 Coalescence of drops. Annu. Rev. Fluid Mech. 47 (1), 245268.
Kavehpour H. P., Ovryn B. & McKinley G. H. 2002 Evaporatively-driven Marangoni instabilities of volatile liquid films spreading on thermally conductive substrates. Colloids Surf. A 206 (1–3), 409423.
Lappa M. 2005 Coalescence and non-coalescence phenomena in multi-material problems and dispersed multiphase flows: part 2, a critical review of CFD approaches. Fluid Dyn. Mater. Process. 1 (3), 213234.
Mahadevan L. & Pomeau Y. 1999 Rolling droplets. Phys. Fluids 11 (9), 2449.
Meunier P. & Villermaux E. 2003 How vortices mix. J. Fluid Mech. 476, 213222.
Mohamed-Kassim Z. & Longmire E. K. 2004 Drop coalescence through a liquid/liquid interface. Phys. Fluids 16 (7), 21702181.
Monti R. & Savino R. 1997 Correlation beween experimenal results and numerical solutions of the Navier–Stokes problem for noncoalescing liquid drops with Marangoni effects. Phys. Fluids 9 (2), 260262.
Monti R., Savino R. & Cicala A. 1996 Surface tension driven-flow in non-coalescing liquid drops. Acta Astron. 38 (12), 937946.
Neitzel G. P. & Dell’Aversana P. 2002 Noncoalescence and nonwetting behavior of liquids. Annu. Rev. Fluid Mech. 34, 267289.
Ottino J. M., Ranz W. E. & Macosko C. W. 1979 A lamellar model for analysis of liquid–liquid mixing. Chem. Engng Sci. 34 (6), 877890.
Ranz W. E. 1979 Applications of a stretch model to mixing, diffusion, and reaction in laminar and turbulent flows. AIChE J. 25 (1), 4147.
Rayleigh L. 1899 XXXVI. Investigations in capillarity. Philos. Mag. Ser. 5 48 (293), 321337.
Reynolds O. 1881 On the floating of drops on the surface of water depending only on the purity of the surface. Manchester Lit. Phil. Soc. Mem. Proc. 21, 12.
Savino R., Paterna D. & Lappa M. 2003 Marangoni flotation of liquid droplets. J. Fluid Mech. 479 (March), 307326.
Stefan M. J. 1874 Versuch Uber die scheinbare adhesion. Sitzungsberichte der Akademie der Wissenschaften in Wien. Mathematik-Naturwissen 69, 713721.
Thoroddsen S. T. & Takehara K. 2000 The coalescence cascade of a drop. Phys. Fluids 12 (6), 12651267.
Walker J. 1978 Drops of liquid can be made to float on a liquid. What enables them to do so? Sci. Am. 151158.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Type Description Title
VIDEO
Movies

Geri et al. supplementary movie 1
A droplet (diameter 1.2 mm) of 1 cSt silicone oil (Ohnesorge number Oh= 0.01) is released onto a bath of the same liquid under isothermal conditions ΔT0= 0. The drop coalesces only after about 200 ms and a coalescence cascade is observed with 5 daughter droplets. The sequence if filmed at 2000 fps and back-lit with a white LED.

 Video (9.3 MB)
9.3 MB
VIDEO
Movies

Geri et al. supplementary movie 2
A droplet (diameter 1.2 mm) of 5 cSt silicone oil (Oh = 0.05) is formed and pinned by the dispensing needle on a bath of the same liquid with an initial temperature difference ΔT0 = 5○C. The oil is seeded with TiO2particles with average diameter of 3 μm. Images are captured with a Canon EOS Rebel 75i at 30 fps, and the drop illuminated with a green laser sheet (10 mW, 532 nm).

 Video (7.6 MB)
7.6 MB
VIDEO
Movies

Geri et al. supplementary movie 5
A droplet (diameter 1.2 mm) of 1 cSt silicone oil (Oh = 0.01) is dispensed onto a bath of the same liquid under isothermal conditions. The sequence is filmed at 6100 fps, illuminated with a halogen lamp.

 Video (8.8 MB)
8.8 MB
VIDEO
Movies

Geri et al. supplementary movie 3
A droplet (diameter 1.2 mm) of 1 cSt silicone oil (Oh= 0.01) is released onto a bath of the same liquid with ΔT0 = 3○C. Drop coalescence is delayed by more than 5 s. The sequence if filmed at 2000 fps and back-lit with a white LED.

 Video (5.4 MB)
5.4 MB
VIDEO
Movies

Geri et al. supplementary movie 4
A droplet (diameter 1.2 mm) of 20 cSt silicone oil (Oh = 0.2) is dispensed onto a bath of the same liquid under isothermal conditions. The sequence is filmed at 6100 fps, illuminated with a halogen lamp. Coalescence proceeds without significant propagation of capillary waves.

 Video (9.2 MB)
9.2 MB
VIDEO
Movies

Geri et al. supplementary movie 6
Numerical simulations of the evolution of a generic fluid element being convected and deformed by the assumed internal flow, Hill's spherical vortex, for the case of a 5 cSt silicone oil (Oh = 0.05) and ΔT0 = 10○C. The lamella changes from blue to green to red with time, which is indicated at the top of the movie. This Lagrangian perspective shows how an initially compact fluid element can be deformed into a substantially thinner geometry, a lamella, by the flow field.

 Video (9.5 MB)
9.5 MB

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 323
Total number of PDF views: 967 *
Loading metrics...

Abstract views

Total abstract views: 2327 *
Loading metrics...

* Views captured on Cambridge Core between 8th November 2017 - 15th December 2017. This data will be updated every 24 hours.