Measurement of Contact Angle in Sessile Drops: A Review of Methods

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Introduction
Sessile drops are a common encounter in everyday life among them drops of rainwater on
raincoats, espresso spills and even water on a cooking plate. For numerous years now, a lot of
research has been carried out over the sessile drop to explore the contact phenomenon and the
surface including dynamic spreading, contact angle, characteristics of the surface as well as
evaporation. Among the surfaces, characteristics that have been studied include roughness of the
surface and wettability1. Various strategies were deployed in the quantification and visualization
of the sessile drop as the study progressed including the Captive bubble methods/ Axisymmetric
Drop Shape Analysis, Goniometry method, and even the Wilhelmy plate method.
There is a relatively large variation in the characteristics of sessile drop when it comes into
contact with different surfaces of solids since some of the liquids have the capability of wetting
the surface tony to some extent and thus creating an intermediate drop shape at a specific contact
angle. On the other hand, other liquids are able to spread over the surface of the solid to form a
film. The characteristic of a sessile drop in which it tries to keep contact with the solid surface
refers to wetting2. A contact angle is the angle formed when between a tangent that is in line
with the liquid and the solid surface at the point of intersection of the three interfaces as shown in
figure 1. The three interphases include the solid-vapor, solid-liquid as well as the liquid-vapor
interfaces and their intersection is called the contact line. Contact angle defines the microscopic
representations of the phenomenon that is microscopic in natures among them surfaces

roughness, surface coating as well as surface energies all of which have an important role to play
in the wettability of materials for any provided liquid.
For a long time, the challenge with evaporation has been established and this recently once again
attracted the interest of scholars. This problem is quite defined in micro fluids in which
evaporation take part of the size of a small droplet. A deposited drop on the surface of a solid
substrate creates together with gas and solid phases the triple contact line2. A comprehension of
the heat transfers and evaporation process in a drop of a liquid and close to the contact line is
quite a very fundamental concept in numerous industrial applications among the ink-jet printing,
micro-electronics, nano and micro-fabrication among other applications.
There are abundant studies both in the theoretical and experimental dimensions on evaporating
droplet with the small size of the capillary in literature. The contact angle is a determinant of
diffusive evaporation. Investigations on the effect of the substrate nature are still vital. The
model f Larson and Hu have successfully and sufficiently defined the evaporation of sessile
drops from pure liquids with the aid of diffusive evaporation mass flux add in the case of natural
evaporation at an ambient temperature1. A review of Erbil has been used to illustrate the recent
attainments on the topic. Moreover, there is still need to conduct more refined research on the
problems of mass transfer and could heat transfer as such findings are fundamental in the
comprehension of enhancement of heat transfer and the dynamics of the contact line.
As common as the evaporation of a sessile droplet on a surface, it is a common situation that is
experienced in different situations and thus has received sufficient attention and interest in
literature. A shape in the form of a wedge is formed close to the contact line when a sessile drop
forms on a flat source. This wedge-like shape forms a capillary flow that is controlled by

evaporation. This capillary flow works by sucking the drop to the contact line and as a result of
the wedge shape of the evaporating droplet, there is an increase in the rate of evaporation
towards the wedge. The evaporations result in mass-loss from the phase of the liquid and this
change in the profile of the drop; either through a lowering the base radius or decreasing the
contact angle or even a blend of the two.
A hypothetical and trail examination was spearheaded by Picknett and Bexon about the
evaporation of small drops in which there was neglect in the effects of gravity and instead a
spherical cap approximation was for the shape of the drop was adopted. The results illustrated
the closeness of the three different modes of drop evaporation: constant contact angle, constant
contact radius or a mixed mode2. Numerous years after the turning point of this work, the
various modes of evaporation were explained and attributed to the wetting behavior by different
scholars. There is a decrease in the contact angle with time as the evaporation starts on
hydrophilic surfaces while the contact radius remains unchanged. This project aimed at
analyzing the spreading behavior of numerous liquids on an aluminum surface with various
roughnesses and to evaluate the pattern of evaporation of the sessile drop that is formed on the
surface of a solid.
1.1 Brief description of the previous research on the measurement of the contact angle
Measurements of contact angle have been achieved through the development of various drop
shape techniques as well as the artificial liquid tension derived from the sessile drop shape. The
technique and approach used in measuring the shape if a sessile drop depends on the similarity of
the theoretical profile that is calculated from the numerical integration of Laplace equation. As
soon as the principal radii of the curvature of the sessile drop and the surface tension are

calculated through the use of drop shape technique, integration of the Laplace equation can be
done in order to measure the contact angle1.
One of the earliest works in Axisymmetric Drop Shape Analysis was done by Adams and
Bashforth who came up with the drop profiles of various surface tensions and established the
numerical solution of the equilibrium shape of the interfaces of the axisymmetric fluids. The
findings from these calculations were represented in the forms of tables. It was thus possible to
determine the contact angle and the surface tension using the actual profile by the use of linear
interpolation of the values that are provided and obtained from their tables. The same approach
was conducted by Hartley and Harland who were able to present the numerous solutions in a
form a modified table that was used in finding the tension of the interface of the various shapes
of axisymmetric drop2. A computer program which was a contribution by FORTRAN was used
in the integration of the appropriate form of Laplace equation.
Through the FORTRAN computer, it is possible to automatically evaluate the drop profile in
which the results are thereafter presented in the forms of tables. Data acquisition acted as the
main source of error in this method. The FORTRAN computer program was accompanied by
numerous limitations and disadvantages. One of such is that the drop interface in determined
through taking measurements of the few preselected critical points from the entire drop surface
and because there location of this point is associated with such high criticality and they are in
correspondence with special characteristics including inflection surface point, a determination
must be done with utmost precision. Still, the method is confined to a specific size and thus for a
sessile drop that has a low contact angle say 20⁰, it turns out to be very challenging to measure
the contact angle using this method2.