The phenomenon of a liquid droplet interacting with a surface is dependent on many factors. Some of them are properties of droplet, the surface upon which impact takes place, velocity at impact, geometry, as well as the medium through which the droplet travels before impacting the liquid surface. The complexity of detailed fluid mechanics related to liquid droplet and liquid surface interaction continues to be a topic of intensive research, but here in this blog we will try to summarize the process in order to generate curiosity as well as to see how CFD is playing a role in studying this phenomenon. For my blogs kindly visit: https://www.learncax.com/knowledge-base/blog/by-author/ganesh-visavale

1. The Falling Droplet
learncax.com /blog/2013/11/12/the-f alling-droplet-2/
Ganesh Visavale
We all have seen the rain drops falling on roof tops or road or car roofs, or water droplets falling from tap…
Fa l l i n g d r o p l e t
When we usually see these phenomenons occur around us they happen within no time. We don’t even notice them.
But if we look closely there are very complex physics involved in them. What if we could really slow down time and
observe closely these phenomenon occurring? Like this video from Discovery Channel which shows a slow motion
capture of a droplet falling into a liquid surface…
After watching this video it really feels like a complex phenomenon doesn’t it? Well indeed it is, and a droplet falling
into a liquid surface has been a much researched topic for long time. Experimental and theoretical studies have
been going on in this area and this little phenomenon finds large number of application in industry as well. So let us
see in this blog where does this ‘falling droplet’ find its place!!
Physics behind ‘t he f alling droplet ’:
The phenomenon of a liquid droplet interacting with a surface is dependent on many factors. Some of them are
properties of droplet, the surface upon which impact takes place, velocity at impact, geometry, as well as the
medium through which the droplet travels before impacting the liquid surface. The complexity of detailed fluid
mechanics related to liquid droplet and liquid surface interaction continues to be a topic of intensive research, but
here in this blog we will try to summariz e the process in order to generate curiosity as well as to see how CFD is
playing a role in studying this phenomenon.
Depending upon various factors different scenarios exists when a liquid droplet impacts on the liquid surface, i.e.
there can be droplet floating or a droplet bounce, also as shown in the video below.
Coalesce happens as shown in the figure below:
Droplet impact is crucial

2. Droplet impact is crucial
phenomenon in many natural
and industrial processes. For
example, impact of raindrops is
responsible for aeration of lake
which plays important role in
sustenance of underwater life.
Industrial examples where
droplet impact plays important
role are fuel injection inside IC
engine, spray cooling of turbine
blades, surface cooling, inkjet
printing etc. Considerable recent
attention has been given to drop
impact on super hydrophobic
surfaces.
Dr o p l e t co a l a ce n s e
Droplet impact in a liquid pool
When a liquid droplet impacts another liquid body, either liquid pool or drop or film, it can coalesce or bounce, i.e.
may remain in one piece or split into several droplets. When a drop impacts on liquid pool, as the drop approaches
near liquid surface air is expelled from subsequent air layer. The droplet will bounce or coalesce according to
whether this layer achieves critical thickness during impact. In general this critical thickness depends on both fluid
properties and system cleanliness. This critical thickness is typically of the order of few micrometers.
Droplet coalescence
If sub- micrometric thickness is reached, the air layer ruptures in response to cohesive Van Der Waals forces acting
between the liquids. Then the large curvature of interface causes the air film between drop and pool retracts quickly
and prompting drop coalescence.
Droplet bouncing
To let the drop bounce, air layer should sustain which exerts a lubrication force and so causes the drop to deform,
de- accelerate, and ultimately reverse direction. In other words for the drop to bounce back momentum should be
reversed in a finite time by restoring force as in spring. The translational kinetic energy is converted into
deformational potential energy associated with surface tension for liquids. This energy is then partly restored to
translational motion following impact. Remaining energy is fed into internal drop motion, including waves and
oscillations. Droplet bouncing is not stable, we can make it stable by refreshing the air layer under liquid droplet.
This air layer can be refreshed by vibrating the water surface.
Dr o p l e t b o u n ci n g
Experiment s on ‘The f alling droplet ’
Let us now review an experimental study done on falling droplet. For this we are briefly going to see highlights of the
experiment published in “An experimental study of a water droplet impinging on a liquid surface” by S. L. Manzello, J.
C. Yang. In this publication an experimental study is presented for water droplet impingement on a liquid surface. The

3. impaction process was recorded using a high- speed digital camera at 1,000 frames/s. The initial droplet diameter
was fixed at 3.1 mm ± 0.1 mm, and all experiments were performed in atmospheric air. The impact velocity was
varied from 0.36 m/s to 2.2 m/s thus varying the impact Weber number from 5.5 to 206. The impacted liquid surface
consisted of two fluids, namely water and methoxy- nonafluorobutane. Here we will see results of water only and for
detailed review you can refer to the full paper.
In this experiment the authors have named impacts based on observed results.Splashes – The impacts which
formation of jets
Coalescing – drops causing formation of vortex
The impact is characterised by impact Weber number. The impact Weber number in this study was defined as;
where is the droplet diameter, is the impact velocity, is the droplet liquid density, and is the droplet liquid surface
tension.
Figure below displays the time- elapsed images of water droplet impingement upon a 2- mm film of water with an
impact Weber number of 206. At a time of 6 ms after impact, the splash created by the water droplet in the 2- mm
water layer which resembles the classical crown shape. At 20 ms after impact, the collision dynamics have ended in
the water pool. The next sequence considered is water droplets with impact Weber number of 206 into a pool of 7mm depth, also shown. Water droplet impact into the water pool results in a splash with a jet (defined here as the
column of liquid rising from the liquid surface) breaking up at a time of 55 ms after impact.
Now we will see the time- elapsed images for an increase in the pool depth to 10 mm and 25 mm for We number
206. At 25 mm, impact with the water pool forms a jet that is seen to break up at 35 ms after impact. Similar to the 10mm depth, droplets generated from the liquid jet float upon the liquid surface after returning to the surface.

4. Now let us see the effect of change in number. Reduction in number to 123 means a reduction in impact velocity. For
water–water impact, the formation of droplets emanating from the top of the crown does not occur in this case like for
number 206.
(e)
Many more experimental studies and results have been published in this paper which is definitely worth a detailed
further reading.
Simulat ion of ‘The f alling droplet ’:
The phenomenon of droplet surface interaction has been extensively studied in the simulation world. CFD comes
into forefront when we talk about simulating droplet and liquid surface interaction. When we talk about droplet
modeling; the extensively used modeling technique for flow modeling is the multiphase model. Application of
multiphase models has made it possible to model not only single droplet simulation but also complex droplet
dominated flow within spray modelling and microfluidics domain.
Let us review how the phenomenon of droplet falling and impact can be simulated using CFD. When we consider a

5. liquid droplet falling through air and impacting another liquid or same liquid surface, the physics involve modelling of
multiple phases. For such simulations multiphase models within commercial CFD software like STAR- CCM+ or
ANSYS FLUENT can be used. When we are dealing with free surfaces and different phase velocities like in this
impact problem, the VOF multiphase model becomes the ideal choice.
The VOF model
The VOF multiphase model can model two or more immiscible fluids by solving a single set of momentum
equations and tracking the volume fraction of each of the fluids throughout the domain. Typical applications of this
model are prediction of jet breakup, the motion of large bubbles in a liquid, the motion of liquid after a dam break,
and the steady or transient tracking of any liquid- gas interface. In the VOF model within the computational domain
under consideration, a particular fluid phase is defined by the volume fraction in a control volume as the fraction of
the phase inside a cell. If is 0 the cell is empty of phase and if is 1 the cell is full of phase. If has any value between
0 and 1 the cell contains the interface between the qth phase and the other phase or phases. Depending upon local
values of volume fraction, a single set of Navier–Stokes equations is solved for the computational domain. Also
depending upon these volume fraction values, the flow variables and the fluid properties in any given cell are either
purely representative of one of the phases, or representative of a mixture of concerned phases. Based on the local
value of , the appropriate fluid properties and flow variables are assigned to each control volume within the domain.
In the VOF model, the motion of a moving interface is computed by solving an advection equation for the volume
fraction of the phase.
Simulat ion approach
When considering liquid impact, usually the liquid is assumed to be incompressible. The properties like viscosity
and surface tension can be taken as constant. The flow depending upon impacting media and velocity, can be
laminar and most of the times Newtonian. There can be possibility of formation of instability at the impact rim but if
that is neglected in the simulation we can use a modelling simplification of 2D axis symmetric grid. The simulation
has to be carried out using unsteady solver and the VOF model. The simulation time steps used have to be
proportional to the impact time scale.
Applicat ions of such droplet CFD simulat ions
Such type of droplet impact CFD simulations find wide applications in below areas of science.
Coating
Welding
Microfluidics
Film drainage in emulsions and foams
Drying of semi- conductor wafers
‘The f alling droplet ’ in Indust ry:
Practical applications of a droplet colliding with a surface include spray cooling of turbine blades, electronic devices,
and internal combustion engines. Droplet surface interaction is also important in agriculture, atmospheric sciences,
criminal forensics, and fire suppression by sprinkler systems.
Art in ‘The f alling droplet ’
And now before we end let us also see another aspect of this wonderful physics phenomenon. A falling droplet, as
complicated and difficult the physics involved is makes a beautiful and visually pleasing art as well!! Artists like
Corrie White have made beautiful photographic art forms out of this simple phenomenon. Some of her sample
photographs are below:

6. Fa l l i n g d r o p l e t b e a u ti fu l s n a p s
So to summariz e this ‘simple’ phenomenon that we see in daily life of a droplet falling is much more that just ‘simple’.
It involves complex physics which can be an interesting research topic. When we talk about CFD simulation this is
among the most interesting and detailed multiphase simulation problem and if you come from arts background this is
a beautiful art form as well!!
Ref erences and sources:
Physicscentral
http://www.cd- adapco.com/
Discovery channel
ESI group
An experimental study of a water droplet impinging on a liquid surface S. L. Manz ello, J. C. Yang
www.ansys.com
Ansys Fluent Users Guide
Water drop impact into deep pool: Influence of the liquid pool temperature; Stephanie Fest- Santini1,C,
Manfredo Guiliz z oni2, Mauriz io Santini1, Gianpietro Elvio Cossali
CFD modelling of impact and spreading of droplets on a smooth surface; M. Garbero, M. Vanni and G. Baldi
Numerical simulations of drop impact and spreading on horiz ontal andinclined surfaces Siddhartha F. Lunkad,
Vivek V. Buwa ∗ , K.D.P. Nigam
Youtube
www.cfd- online.com
Corrie White’s website
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