Experimental and Numerical Studies on fluid flow in evaporating droplets
Mohd Aslam
Department of Chemical EngineeringIndian Institute of Technology
Guwahati2015
By
144107016
IntroductionApplicationLiterature reviewObjectiveMechanismMathematical modelReferences
Outline
Introduction In physics, a "coffee ring" is a
pattern left by a puddle of particle-laden liquid after it evaporates. The phenomenon is named for the characteristic ring-like deposit along the perimeter of a spill of coffee.
When a coffee droplet is spilled on a solid surface, it leave a dense ring-like stain along the perimeter as shown in Fig 2. This is called coffee ring effect.
Fig.2:coffee ring effect
Fig.1:droplets evaporation
Type of evaporation mode
Pinned-contact line evaporation
Depinned-contact line evaporation
Fig.3:pinned contact line Fig.4:depinned-contace line Fig.5:Both contact angle
and contact area decrease
Both contact angle and contact area decrease
Introduction
1-Pinned-contact line evaporatoin
Fig.4: Ring-like deposition
Fig.3: Constant contact area mode evaporation
unchanged contact area between liquid and solid surface. The contact angle decreases while the contact radius remains the same.
Edges the rate of evaporation is much higher than the Centre. Consequently, a flow is generated toward the edges.
The roughness of the surface favors the pinning phenomena .
If solute particles are present, then after evaporation we get ring-like deposition
Introduction
Fig.1: Small contact angle
Fig2: at different Time like t1,t2,and t3
(a) Small receding angle prevents depinning at the ring
show that a smaller wetting angle (φ’rec) for the pure liquid air-particles substrate leads to a situation. where the ring forms without depinning.
Introduction
Fig.1:Constant contact angle mode evaporation
Fig.6: Centre spot deposition
2. Depinned-contact line evaporation The contact angle remains unaltered during
evaporation while the contact radius decreases.
Rate of evaporation of solvent at the edges is more than the rate of replacement. The resulting Marangoni flow carry particle from the edge towards the apex .
It is generally seen if the surface on which droplet placed is smooth.
If solute particles are present, then after evaporation we get centre-spot deposition.
Introduction
Fig.1:Large contact angle
(b)Large receding angle induces depinning at the ring
(b) show that depinning at point (I)occurs during drying of the colloidal drop on a smooth solid substrate when φrec is reached atpoint (I).
Fig2: at different Time like t1,t2,and t3
Introduction
Time
Evap
orati
on p
aram
eter Wetted radius(r)
Wetting angle(Φ)Volume of drop
=Φ>Φ𝑟𝑒𝑐=
Receding at Wetting line start to recedeSubstrate pinned wetting line
Fig.1: Depinning mechanism for the evaporation of a pure liquid drop. Recedingstarts when the wetting angle reaches a given receding value φrec and then proceeds at constant wetting angle.
Introduction
ApplicationApplications:-
Disease diagnosis: Sompol et al.(2011) found that the dried drop blood of persons suffering from a anemia disease show similar kind of deposition profile.
Drops of blood from individuals (a) in good health, (b) with anemia, (c) in good health, and (d) with hyperlipidemia
• a polymer solution is fed to an inkjet head and small sized droplets are ejected onto a substrate.• flat shape is required for
electrical devices such as picture element of display .
Ink-jet printing
J. Biomed. Opt. 18(12), 127003 (Dec 16, 2013)
Zhang et al. have utilized coffee-ring drying pattern to pre-concentrate the protein solutions prior to Raman analysis in so called Drop Coating Deposition Raman (DCDR) technique.
DCDR used in biomedical.
ApplicationDCDR Technique
DNA micro arrays• Use in Gene analysis.
• Li et al. (2001) found that stretching behavior is strongly affected by evaporation rate.
• At a low evaporation rates folded or coiled DNA molecules are found such as Fig.1.
• At high evaporation rate, the shape become dumbell like Fig.2
Application
Fig.1: folded or coiled DNA
Y Wang et al. Nature 491, 51-55 (2012) doi:10.1038/nature11564
Fig.2:dumbbell shape DNA
Literature review Larson et al.(2014) Transport and Deposition Patterns in Drying Sessile Droplets . In this theory he explained that common types of deposition patterns are summarized, including those produced by pinned contact lines, sticking-and-slipping contact lines, and Marangoni effects Hua et al.(2005) Analysis of the effect of Marangoni Stresses on the Micro flow in an
Evaporating Sessile Droplet. find that surfactant contamination, at a surface concentration as small as 300 molecules/ím2, can almost entirely suppress the Marangoni flow in the evaporating droplet.
Bhardwaj et al.(2010) Pattern formation during the evaporation of a colloidal nanoliter droplets . Measured evaporation times, deposit Shape and sizes, and flow fields are in very good agreement with the numerical results.
Ristenpart et al.(2007) Influence of Substrate Conductivity on Circulation Reversal in Evaporating Drops. demonstrated experimentally that thermal Marangoni flow in evaporating droplets depends sensitively on the ratio of thermal conductivities of the liquid and substrate,
Zhang et al.(2013) Temperature distribution along the surface of evaporating droplets. analyses indicate that a non monotonic spatial distribution of the surface temperature should occur
Mechanism
Larson et al.(2006) suggests the evaporation induces a Marangoni flow inside a drople.
Marangoni Stress
Fig.1:Marangoni stress
The marangoni effect is the mass transfer along an interface between two fluids due to surface tension gradient.
Mechanism
Deegan et al.(1997) pattern is due to capillary flow induced by the differential evaporation rates across the drop: liquid evaporating from the edge is replenished by liquid from the interior
In the case of temperature dependence, this phenomenon may be called thermo-capillary convection.Fig.1
Fig.1 Thermo capillary convection
Objective To study of Experimental and Numerical fluid flow
inside evaporating droplets at study state heating of substrate.
Mathematical modelThe system is an axis-
symmetric sessile droplet of incompressible fluid (water) of constant viscosity and having the shape of a spherical cap resting on a flat surface.
AssumptionFig. 9: Sessile drop resting on a flat surface
Ashish et al . Analysis of fluid flow and particle transport in evaporating droplets exposed to infrared heating
I. At steady state, the solution will remain constant with time.
II. No evaporation is taking place.III. The droplet is pinned to the substrate i.e. the contact
radius and contact angle do not change with time. R and Ѳ are constant
1. Continuity equation :
)1(0)()(
y
v
x
u
)2()()(
2
2
2
2
y
u
x
u
x
P
y
uv
x
uu
)3()()()(
02
2
2
2
ygTTy
v
x
v
y
P
y
vv
x
vu
In the y-momentum equation, the buoyancy force term due to temperature is considered by Boussinesq approximation.
Buoyancy force term
)4()()(
2
2
2
2
y
T
x
Tk
y
Tv
x
TuC p
2. Momentum equations :
3. Energy equation:
Mathematical modelFollowing are the governing equations considered for steady state
Mathematical model Boundary condition:The boundary conditions considered in the
are given belowI. The temperature of the solid as well as free surface of the droplet are
specified in the form of linear profile obtained from the experimental values of temperatures at the apex as well as left and right edge.
II. The no –slip boundary condition is applied on the bottom solid surface. III At the liquid–gas interface, a tangential Marangoni stress due to surface temperature variation is considered as follows:
=
A constant value of temperature coefficient of surface tension = 0.0001657 N m1 C1
(as reported by Hu and Larson )
Mathematical modelDiscretizetion of the equations of continuity,
momentum and energy and solve by ANSYS Fluent software
Kai Zhang et.al ;Temperature distribution along the surface of evaporating droplets .phys.rev.2014
Larson et .al ;Transport and Deposition in drying droplets sessile droplets.fluid.Mech.2014
Singh A et al; Thokchom.A.K et.al Fluid Flow and Particle Dynamics Inside an Evaporating Droplet Containing Live Bacteria Displaying Chemotaxis.Langmuir .2014
Bhardwaj et.al;Pattern formation during the evaporation of colloid nanoliter drop. New Journal of Physics
Savva et.al; Asymptotic analysis of evaporating droplets. phys.fluids 2014
References
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