Defense Date


Document Type


Degree Name

Doctor of Philosophy


Mechanical and Nuclear Engineering

First Advisor

Dr. Hooman V. Tafreshi



Multiphase Droplet Interactions with a Single Fiber

By: Noor M. Farhan

A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University.

Virginia Commonwealth University, 2019

Director: Hooman V. Tafreshi,

Professor, Department of Mechanical and Nuclear Engineering

Formulating the physics of droplet adhesion to a fiber is interesting intellectually and important industrially. A typical example of a droplet–fiber system in nature is the dew droplets on spider webs, where droplets first precipitate and grow on the fibers, but they eventually fall when they become too heavy. Obviously, quantifying the force of adhesion between a droplet and a fiber is crucial in designing fog harvesting devices or manufacturing filtration media for liquid–gas or liquid–liquid separation, among many other industrial applications. This study is aimed at developing a mathematical framework for the mechanical forces between a droplet and a fiber in terms of their physical and wetting properties. To this end, a series of experiments were conducted to detach ferrofluid droplets of varying volumes from fibers with different diameters and Young–Laplace contact angles (YLCAs) in a controlled magnetic field. The force of detachment was measured using a sensitive scale and used along with the results of numerical simulations to develop a semi-analytical expression for the force required to detach a droplet from a fiber. This universally-applicable expression allows one to predict the force detachment without the need to run an experiment or a computer simulation.

This work also reports on the use of magnetic force to measure the force of detachment for nonmagnetic droplets for the first time. This is accomplished by adding a small amount of a ferrofluid to the original nonmagnetic droplet to create a compound droplet with the ferrofluid nesting inside or cloaking the nonmagnetic droplet. The ferrofluid is then used to induce a body force to the resulting compound droplet and thereby detach it from the fiber. The recorded detachment force is used directly (the case of nesting ferrofluid) or after scaling (the case of cloaking ferrofluid) to obtain the force of detachment for the original nonmagnetic droplet. The accuracy of these measurements was examined through comparison with numerical simulations as well as available experimental data in the literature. In addition, a simple method is developed to directly measure the intrinsic contact angle of a fiber (i.e., Young–Laplace Contact angle of the fiber material) with any arbitrary liquid. It is shown that the intrinsic contact angle of a fiber can be obtained by simply measuring the angle between the tangent to the fiber surface and the tangent to the droplet at the contact line, if the droplet possesses a clamshell conformation and is viewed from the longitudinal direction. The novelty of the proposed method is that its predictions are not affected by the volume of the droplet used for the experiment, the wettability of the fiber, the surface tension of the liquid, or the magnitude of the body force acting on the droplet during the experiment.

Also, a liquid droplet interaction with granular coatings is simulated and the droplet apparent contact angle (ACA) and the transition from Cassie (fully dry) to Wenzel (fully wet) state as a function to the roughness wavelength have been studied. For a fixed droplet volume, two different granular coatings have been used, spherical and hemispherical bumps. It is demonstrated that the chemistry (YLCA) and geometrical parameters for the granular microtexture play an important effect on the droplet ACA and its transition from Cassie to Wenzel state.


Noor M. Farhan

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