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Drop coalescence in technical liquid/liquid applications: a review on experimental techniques and modeling approaches

  • Johannes Kamp

    Johannes Kamp studied mechanical engineering at Ruhr-Universität Bochum (Germany) and graduated with a degree in biochemical engineering at RWTH Aachen (Germany). In 2009, he began his doctorate at the Chair of Chemical and Process Engineering at Technische Universität Berlin (Germany). His research focuses on the fundamentals of droplet coalescence in liquid/liquid dispersions and liquid/liquid separation using phase inversion.

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    , Jörn Villwock

    Jörn Villwock studied and graduated with a degree in environmental engineering at HTW Berlin (Germany) and chemical engineering at Technische Universität Berlin (Germany). Since 2012, he has been a PhD student at the Chair of Chemical and Process Engineering at Technische Universität Berlin (Germany). His research focuses on coalescence in liquid/liquid systems under the influence of electrostatic forces.

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    and Matthias Kraume

    Matthias Kraume studied chemical engineering at Universität Dortmund (Germany). In 1985, he received his PhD for his work on direct contact heat transfer. After finishing his PhD, he worked at BASF, Ludwigshafen, in the research and engineering departments. Since 1994, he has been a full professor at Technische Universität Berlin (Germany) and head of Chair of Chemical Engineering. His research fields include transport phenomena in multiphase systems, membrane processes, and reactor design.

Published/Copyright: July 7, 2016
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Abstract

The coalescence phenomenon of drops in liquid/liquid systems is reviewed with particular focus on its technical relevance and application. Due to the complexity of coalescence, a comprehensive survey of the coalescence process and the numerous influencing factors is given. Subsequently, available experimental techniques with different levels of detail are summarized and compared. These techniques can be divided in simple settling tests for qualitative coalescence behavior investigations and gravity settler design, single-drop coalescence studies at flat interfaces as well as between droplets, and detailed film drainage analysis. To model the coalescence rate in liquid/liquid systems on a technical scale, the generic population balance framework is introduced. Additionally, different coalescence modeling approaches are reviewed with ascending level of detail from empirical correlations to comprehensive film drainage models and detailed computational fluid and particle dynamics.

About the authors

Johannes Kamp

Johannes Kamp studied mechanical engineering at Ruhr-Universität Bochum (Germany) and graduated with a degree in biochemical engineering at RWTH Aachen (Germany). In 2009, he began his doctorate at the Chair of Chemical and Process Engineering at Technische Universität Berlin (Germany). His research focuses on the fundamentals of droplet coalescence in liquid/liquid dispersions and liquid/liquid separation using phase inversion.

Jörn Villwock

Jörn Villwock studied and graduated with a degree in environmental engineering at HTW Berlin (Germany) and chemical engineering at Technische Universität Berlin (Germany). Since 2012, he has been a PhD student at the Chair of Chemical and Process Engineering at Technische Universität Berlin (Germany). His research focuses on coalescence in liquid/liquid systems under the influence of electrostatic forces.

Matthias Kraume

Matthias Kraume studied chemical engineering at Universität Dortmund (Germany). In 1985, he received his PhD for his work on direct contact heat transfer. After finishing his PhD, he worked at BASF, Ludwigshafen, in the research and engineering departments. Since 1994, he has been a full professor at Technische Universität Berlin (Germany) and head of Chair of Chemical Engineering. His research fields include transport phenomena in multiphase systems, membrane processes, and reactor design.

Nomenclature

Latin letters
Ah

Hamaker constant

[N m]

B˙b

birth rate by breakage

[m3/s]

B˙c

birth rate by coalescence

[m3/s]

Bo

Bond number Bo=ΔϱgR2/γ

[-]

CD

drag coefficient/friction factor

[-]

CD,S

single-drop friction factor

[-]

CD,φ

drop swarm friction factor

[-]

Ca

Capillary number Ca=μv/γ

[-]

d32

Sauter mean diameter

[m]

dp

particle/droplet diameter

[m]

dp, max

maximal particle/droplet diameter

[m]

deq

equivalent drop diameter

[m]

d*

specific drop diameter

[m]

D˙b

death rate by breakage

[m3/s]

D˙c

death rate by coalescence

[m3/s]

Eσ

surface energy

[J]

Ekin

kinetic energy

[J]

Eo

Eötvös number EoϱgR2

[-]

f

number density function

[m-3]

F

coalescence rate

[m3/s]

F

force

[N]

Fγ

dimensionless van der Waals attraction Fγ=Ah/(γR2)

[-]

g

gravity acceleration

[m/s2]

g

breakage rate

[s-1]

h

film thickness

[m]

h0

film thickness at the start of drainage

[m]

hcrit

critical film thickness at which film rupture occurs

[m]

hmin

minimal film thickness

[m]

Ma

Marangoni number Ma=-/dx·Δx/(μv)

[-]

Mo

Morton number Mo=4Δϱ/(ϱ2γ3)

[-]

nd

number of daughter droplets

[-]

N

number of (coalescence) events

[-]

N0

total number of (coalescence) events

[-]

Oh

Ohnesorge number Oh=μ/ϱγR

[-]

R, r

radius

[m]

Rbridge

coalescence bridge radius

[m]

Rd

draining film radius

[m]

Req

equivalent droplet radius

[m]

Re

Reynolds number Re=(vdρ)/μ

[-]

Reφ

Reynolds number for droplet swarm Re=(vdρc)/μφ

[-]

s

drop separation distance

[m]

scontact

drop separation distance at “contact”

[m]

sinteraction

drop separation distance at which interaction occurs

[m]

t0

starting time

tdrainage

film drainage time

[s]

tcoalescence

coalescence time, tcoalescence=tdrainage+trupture

[s]

tcontact

drop “contact” time

[s]

trupture

film rupture time

[s]

v

velocity

[m/s]

vcrit

critical velocity

[m/s]

vrel

relative velocity

[m/s]

V˙

volume flow rate

[m3/s]

We

Weber number We=ϱv2R/γ

[-]

x

variable/exponent

[various]

Greek letters
β

daughter drop size distribution

[-]

γ

interfacial tension

[N/m]

γ˙

shear rate

[s-1]

Δ

difference

[-]

ϵ

energy dissipation rate

[m2/s3]

λ

coalescence efficiency/probability

[-]

μ

dynamic viscosity

[Pa s]

μc

continuous phase dynamic viscosity

[Pa s]

μd

disperse phase dynamic viscosity

[Pa s]

μφ

mean dispersion dynamic viscosity μφ=f(φ, μc, μd)

[Pa s]

μ*

dynamic viscosity ratio μ*=μdc

[-]

Π

disjoining pressure

[N/m2]

ϱ

density

[kg/m3]

ϱc

continuous phase density

[kg/m3]

ϱd

disperse phase density

[kg/m3]

τ

time

[s]

τ1/2

median rest (or coalescence) time

[s]

τbridge

bridge formation time

[s]

φ

phase fraction

[-]

ξ

collision frequency

[m3/s]

Acknowledgments

The financial support provided by the German Research Foundation (DFG) within the project KR 1639/19-2 is gratefully acknowledged.

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Received: 2015-12-2
Accepted: 2016-5-10
Published Online: 2016-7-7
Published in Print: 2017-2-1

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