Advancing Contact Angle: Wettability, Couttee Flow, and Contact Angles

This report delves into the intricacies of advancing contact angles, a crucial concept in materials science and engineering, particularly concerning wettability. It begins with an introduction to advancing contact angles, contrasting them with static angles and highlighting their significance in understanding solid-liquid interactions. The report then explores the underlying physics, focusing on surface tension, contact angles, and hysteresis, explaining how these factors influence wettability prediction. A comprehensive literature review follows, examining historical perspectives and recent developments in the field, including the use of advancing contact angles in various industrial applications. The report also provides a comparative analysis of advancing, receding, and equilibrium contact angles, clarifying their differences and implications. Finally, it explains how Couttee flow enhances the establishment of advancing contact angles, providing a detailed understanding of the dynamics involved. This report, contributed by a student, is available on Desklib, a platform offering AI-powered study tools for students.

Running head: ADVANCING CONTACT ANGLE 1
Advancing Contact Angle
Name
Institution

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Introduction
According to Tadmor (2004) advancing contact angle between two immiscible liquids
occurs over solid when both fluids are experiencing flow in the same direction. This
phenomenon is a contrast of what is evident in static contact angle where consideration is not
given in terms of changing the area of contact between a solid and a liquid. The advancing
contact angle can, therefore, be generally termed as the dynamic contact angle with a constant
change in the area of contact between a solid and a liquid. Preference is thus made for the
advancing contact angle to the static contact angle in terms of the investigation of the solid and
liquid surfaces. Surface energies best describe the existence of a surface between a solid and a
liquid This forms the basis of wettability measurement. Wettability is the tendency of one liquid,
e.g., water, to spread over a solid (e.g., calcite) in the presence of other liquid ( e.g., oil), due to
significant adhesion energy. According to Koishi, Yasuoka, Fujikawa, & Zeng (2011), both
advancing and receding contact angles are referred to as dynamic contact angles. Contact angle
at equilibrium is more accurate and straightforward, measuring advancing contact angle is very
complicated and achieving accurate results is almost impossible. Several results are very
effective in considerably arriving at more accurate results. This write-up discusses the physics
that is involved while using advancing contact angle to predict wettability of a solid, reviews
advancing contact angle literature, compares the advancing angle with receding and equilibrium
contact angles and explains how Couttee flow enhances the establishment of advancing contact
angles.
Physics involved in using advancing contact angle to predict solid wettability.
The concept of surface tension and its relationship with the contact angle

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Assuming a liquid droplet on a flat surface as shown in the figure below
The contact angle is termed as the angle developed between a solid and a liquid. In
providing a conclusive analysis of the contact angle between solids and liquids, consideration is
therefore made to a three face contact line (an interface of solid, liquid and vapor coexistence so
that more accurate results are obtained in providing the measurements of contact angle for this
given research work.
Consider the diagram shown below. In case the liquid spreads on the solid surface then a
small contact angle will be observed.
When the liquid beads instead of spreading on the surface, a large contact angle is
observed. Wetting surfaces with higher contact angles are usually considered unfavorable. For
such cases, the liquid will have high levels of minimization of the level of contact between the
liquid and the surface thereby making the liquid to form a droplet on the solid surface. An
example is seen in water which can be termed as generally non-wettable hydrophobic (Omori,
Kobayashi, Yamaguchi, & Kajishima, 2019, p. 4)
Complete wetting is known to happen whenever the contact angle is 0o because the
droplets are changing into a flat slick. The angle at which wetting surfaces becomes favorable

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becomes very limited at an angle of approximately 150ͦ. This results from an effect termed as the
“lotus effect.”
Considering an ideal case, all the molecules in pure liquids are equally pulled in all the
directions in every surrounding fluid molecules yielding no net force (Koplik, Banavar, &
Willemsen, 1989, p. 781). The molecules at the surface, however, lacks surrounding molecules
thus forming an internal pressure which result from inward pulling The surface liquids, therefore,
have to contract thus maintaining the lowest surface free voluntarily.
According to Thomas Young, the equations for ideal cases are shown below.
Which explain liquid drops on the surface, mechanical equilibrium drop resulting from 3
interfacial tensions
ylv cos θ y= ysl− ylv❑
Where ysl, ysv, and ylv are solid-liquid, solid-vapor and liquid-vapor in the interfacial
tensions determined by θy as the contact angle. Considerations to the ideal case are essential
while performing a critical analysis of the advancing contact angle between solid and liquid
surfaces.

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The contact angle Hysteresis.
Contact angle hysteresis is a difference between the advancing and the receding critical
angles. It arises from a topographical and chemical heterogeneity of the contact surface. The
contact angle hysteresis cannot be obtained through the direct measurements of the advancing
and the receding contact angle. An analysis is therefore conducted through putting consideration
of liquid droplets on a given solid surface. Hitting the solid surface causes some of the droplets
to slide due to the downward pull from gravity. In spite of this fact, it can still be noted that
some of the liquid droplets will still stay on the vertical surface. The hysteresis of te contact
angle is responsible for this given phenomenon.
Further analysis can also be conducted on a dynamic three-phase contact angle. For an
expanding contact angle, the angle is described as advancing while a contracting angle is referred
to as a receding angle. Measurements of dynamic angles are based on various speed rates. The
two angles are always different, and this difference is what was initially termed as the hysteresis
(H)
H=θa−θr
Homogenous surfaces tend to have existing domains which offer barriers to contact line’s
motion. According to Yuan & Lee (2013), hydrophobic domains always have some pinned
water motion fonts in their advances. This results in positive adjustments in the observed contact
angles. This causes an increase in the observed contact angle. Similar domains hold back the
angle when the motion is a contacting motion. In this case, this leads to a decline in the observed
angle. Experimentally, interpreting such data based on Young’s equation can be misleading. This
is attributed to the fact that Young’s equation does not consider topography (Al-Yaseri, Lebedev,
Barifcani, & Iglauer, 2016, p. 417).

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Literature Reviews
Through the review of different literature works, a historical perspective is employed in
the provision of a complete analysis of the advancing contact angle between solid and liquid
surfaces. A review is also made on the recent developments on the topic of discussion. The latest
developments include the control of CAH in different industrial processes. The opportunities and
the challenges in correlation to the topic of discussions are also placed into consideration. This
is also very important in the design of highly advanced engineering materials and other materials
that are soft and have a wide range of usability in the industrial space.
Advancing angle ( θa) and receding angle (θr ) for a liquid drop between the stationary top plate
and displaced bottom plate.
Kim, Kavehpour, & Rothstein (2015) studied the characteristics of pure samples and 55
crude oil samples. The study showed that crude oil has varied equilibrium contact angle. The
contact angles were found to be dependent on the natural surface active compound that is
dissolved in oils. Crude oil was found to contain surfactant and asphaltenes which are gradually
deposited on the surface making time the oil-wet system to increase with time. The findings of
this study showed that advancing contact angles are indicators of various wettability conditions.
Consider the findings of 4 studies conducted by Kim, Kavehpour, & Rothstein (2015) on oil
whose graphs are shown below.

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Chen, Tang, Zhao, Law, & Amirfazli (2016) found out that advancing contact angle
explicitly delineates variations of wet conditions. Because of the various factors such as a
possibility of the compounds dissolved in water contributing to differences in wettability, the test
surface used in predicting solid wettability should be tailored to match reservoir of interest to
ensure that proper interpretations are made. Advancing contact angle is more significant than the
receding angle by as much as 750. This difference is a representation of delay in the equilibrium
values whenever the forces act on the liquid changes (Sbragaglia, Sugiyama, & Biferale, 2008,
p. 471).
Lu, Wang, &Duan (2016) investigated advanced contact angle and hysteresis using
sessile oil drops on mica. In this study drop of oil was placed on a place surface forming a
capillary tube. Larger contact angles were realized for the diluted crude oil (140o) compared to
the undiluted crude oil (75o). According to Koplik, Banavar, & Willemsen (1988) measurements
of contact angles are made on polished crystals of either mica or silica. This aimed at avoiding
complications which result from roughness and heterogeneity of the surface. Lu, Wang, & Duan
(2016) discovered that surface roughness and surface heterogeneity as a result of minerals
dissolved in solvents are responsible for a wide range of contact angles.

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Comparison between Receding and Equilibrium Contact Angles
From the Young-Laplace equation, just a single contact angle can be acquired from a
pure liquid placed on a perfect rigid surface. Despite the possibility of having a thoroughly
cleansed surface, there are various contact angles which can be measured. The measured angles
fall within the highest or the lowest values of the of receding angle θr and advancing contact
angleθa.
Advancing contact angle is a function of increasing a contact area between liquid and
solid Receding angle on the other matches to a decrease in the contact area. The conditions of
wetting for the two aspects provides two configurations which can be significantly dissimilar.
While advancing contact angle represents the dynamics of the dehydrated substrate while
ignoring the antecedent film. Receding contact angle, on the other hand, reflects on the
repudiation on the wet substrate. Various techniques can be employed in the measurements of
both advanced and receding contact angles. The common ones include a pumped-out fluid.
Sessile drop pumped in a fluid and water drop on a tilted substrate as shown in the figure below.

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The contact line motion history is significant in the analysis of the equilibrium of the
contact line. This is very applicable in the analysis of surface surfaces. Advancing contact angle,
however, vary according to surface condition and is not specific at some given pressure and
temperature.
In practice, a phenomenon, contact hysteresis is very dynamic. This, therefore, produces
a range of perspectives with the advancing angle as the maximum angle contact angle and
receding as the minimum contact angle. The equilibrium angle is therefore within the scope of
values or evaluated from them.
Enhancement of the establishment of advancing contact angle via Couttee Flow
Moving contact line dynamics in a two Couette flow system is best explained via a
matching asymptotic study. Assuming a partially wetting wall, microscopic contact angle that is
finite and sufficiently large. Moving contact line dynamics is not explicitly described using
classical continuum hydrodynamics because the no-slip boundary conditions characterizing solid
walls results in uninterpretable viscous stress divergence of the given contact line. Two-phase
Couette is employed in studying the dynamics of moving contact. Because of its simple
geometry, Couette flows are easily implemented numerically despite the difficulties in
performing the experiments (Sbragaglia, Sugiyama, & Biferale, 2008, p. 471).

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Considering two-dimensional flow shown below, assuming that two solid walls have a
separation distance H and have a different velocity u. To take care of the contact line singularity,
Navier slip boundary conditions shown below is used.
Where ul and ur represent horizontal and vertical components of the microscopic slip
length, to obtain a motionless profile for a certain shear speed u which is a representation of the
relative velocities amongst the contact line and solid wall, assuming a sufficiently sizeable
viscous drag, the surface can be expected to be slightly tilted because the two angles are
relatively small in magnitude. The general lubrication equations proposed by Gao, Li, Feng,
Ding, & Lu, 2016) are thus used.
In this case, G1(x) and Gr(x) are the pressure gradients along the x-direction and the
surface tension. From the boundary conditions, Gr and Gal and velocity profiles can be obtained.
This makes it possible to express these variables in terms of h explicitly. This leads to a single
lubrication equation based on Couttee flow system shown below.
Where ha and x are non-dimensionalized relative to h.
Liquid-air system. Considering a liquid-air system where the influence of air is ignored
(m=0 and n=-1). The upper wall does not affect providing a constraint on the slope's interface
while the movement is insignificant because of the boundary conditions. The top section has no
singularity reducing lubrication equation to

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This equation enhances the establishment of advancing contact angle in the study of
wetting flows of a single fluid close to a moving contact angle where the balance between
viscous and capillarity dominates dynamics. The liquid-liquid system characterized by a matched
viscosity. Assuming that m is fixed at one while the contact angle is still varied, the impact of
velocity ratio remains quantitative and can be numerically obtained based on Gao, Li, Feng,
Ding, & Lu (2016)findings. This yield a governing equation shown below
This is an equation obtained by subjecting lubrication equation in Couttee flow system to
the boundary conditions. Through the incorporation of the preceding analysis, it can be noted
that the couttee flow is quite crucial concerning the establishment of the advancing contact angle
between the liquids and solid surfaces.

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Conclusion
This paper has provided a vivid discussion of the physics involved in advancing contact
angle prediction of wettability, literature review of wettability prediction using advancing contact
angle, comparison of advancing contact angle and equilibrium and receding angles. The paper
has also discussed the various ways by which Couttee Flow enhances the establishment of
advancing contact angle.