Krista Day
ChE/MATSE 510
HW #1
Literature Review
“The measurement of the surface energy of solids by sessile drop accelerometry”
Alfredo Calvimontes, Predevelopment, Division Dish Care, BSH Hausgeräte GmbH (a subsidiary of
Robert Bosch GmbH), Robert5 Bosch-Straße 16, 89407 Dillingen an der Donau, Germany
Key Questions and Assumptions
The surface energies of solid-liquid-gas systems have long been of interest within the fields of
chemical engineering and materials science. This paper investigates the sessile drop accelerometry
(SDACC) method of measuring the surface energy of materials, and its mathematical model that supports
Young’s equation. A drop shape analyzer, a high-speed camera, and a laboratory drop tower – combined
with evaluation algorithms were used to measure the surface energies of smooth polymers, such as
polypropylene (PP) and polytetrafluoroethylene. The surface energies were measured as a function of the
changes in shape of a water droplet in the absence of gravity to determine the functionality of the SDACC
method. SDACC is based on the thermodynamic equilibrium of the interfaces of the materials.
Methods
First in the process, this paper describes the dimensionless parameter κ, and contrasts this
parameter with respect to Young’s equation. “κ” characterizes a drop in the absence of gravity that is
resting on a flat, smooth surface. However, in the condition of weightlessness, κ is independent of the
drop size, and is not equivalent to cosine as in Young’s initial equation; it instead represents the ratio of
the decrease in liquid-gas area and the solid-liquid area, an effect of wetting. It measures the balance of
the surface tension and the surface energy of the solid-liquid area. These are estimations that were
tested in the physical experiment that the paper outlines. There are two components of the mechanical
work of the drop that must be considered which modify its shape and allow its surface energy: the work
W P necessary to move up its center of mass and the work W S necessary to radially move the contour line
solid-liquid-gas during a short de-wetting process. The equation and modification for mechanical work is
shown below in (1):
→
(1)
Next, an experiment was conducted which involved a vertical tower with the height of 3 meters
that controlled the integrated capsule’s movement using upper/lower ignition devices (which controlled
the free fall), a displacement tower, an acceleration device, a braking mechanism, and a liquid dosing
device to illustrate the connection between the shapes of the drops in the absence of gravity and the
surface energies. The enclosed capsule contained the solid-liquid-gas system. The liquid dosing device
dropped small water droplets of 5μL to 100μL onto various positions of sample surface inside the capsule,
then the capsule’s high-speed camera obtains videos of the drop during its motion; sessile droplets were
first measured while under the effects of gravity, then in the absence of gravity. In each process, the
accelerometer and vibrometer then measure the accelerations in the X and Y axes to evaluate the
vibrations of the drop, which would then illustrate the oscillations in size and shape of the sessile drops.
Key Results/Take-Aways
This paper cites another published article to state that during the period of freefall drop, the
sudden variation in the gravity force is what induces the oscillations in the sessile drop. The title of the
cited published article is “Sessile Drop Wettability in Normal and Reduced Gravity”, contributed to by A.
Diana, M. Castillo, D. Brutin, and T. Steinberg, and published in 2012. The surface energies for each
experiment (gravity and freefall respectively) were solved using (1) from above and (2) below:
(2)
where ⍴ is the is the density of the liquid, V is the drop volume, af is acceleration, Ω is surface area, γ
terms are the surface energies of the states, and z is the center mass of the particles.
Shown below in (3) are the results of solving equations (1) and (2) to calculate surface energies of PP
and polytetrafluoroethylene:
(3)
These results confirmed that gravity release leads to receding wetting of surfaces. The results were also
compared with the results obtained by the method of Owens for Polypropylene (PP), as well as
Polyethylene (PE). The values obtained by the SDACC and by the Owens method correlated in the way
that the values obtained by SDACC are intermediate between the values obtained by the Owens method
shown in (4). Therefore, the SDACC method investigated by this paper was confirmed to be an accurate
method of determining surface energies of polymer materials.
(4)