In this course a survey was presented of flows where surface tension is relevant and/or dominant. Topics of current research interest, including drops, bubbles, thin films, jets, sheets, interfaces, wetting, de-wetting, coating, imbibition, etc., were examined and, wherever possible, their relation to nature and industrial applications are discussed. The course began with standard problems involving fluid statics and then proceeded to a wide class of dynamical situations.
As part of the course, students were required to complete a term paper surveying the literature on a capillarity-related phenomenon or application of their choice. Listed below is a selection of some of these papers. Links to the pdf files of the term papers are provided.
Name: Frederik Brasz
Title: Soap Films: Statics and Dynamics
Soap films and bubbles have long fascinated humans with their beauty. In particular, the study of soap films is believed to have started around the time of Leonardo da Vinci. Since then, research has proceeded in two distinct directions. On one hand are the mathematicians, who have been concerned with finding the shapes of these surfaces by minimizing their area, given some boundary. On the other hand, physical scientists have been trying to understand the properties of soap films and bubbles, from the macroscopic behavior down to the molecular description. A discussion of soap films is carried out under this framework.
Name: Oren Breslouer
Title: Rayleigh Plateau Instability: Falling Jet
The Rayleigh-Plateau instability is best known as the reason behind the breakup of a liquid jet into a stream of droplets. Joseph Plateau and Lord Rayleigh may have been the first to characterize this instability experimentally and analytically, but never would they have envisioned the relevance of this phenomenon to such a wide range of applications. This paper presents a brief summary of the Rayleigh-Plateau instability in relation to applications amongst others, such as thin film coating, black holes and inkjet printing.
Name: Kevin Chen
Title: Analysis of Oil Film Interferometry Implementation in Non-ideal Conditions
An analytical study is performed to explain the effects of certain imperfect conditions on the implementation of oil film interferometry. After a review of classical thin film theory as it pertains to oil film interferometry, an analysis is given for a flat 1-D wall surface roughness, hysteresis when the applied wind shear changes, and the linear error propagation from temperature variations. It is found that the experimental technique is robust to 1-D surface roughness, because the oil film thickness obeys the same underlying equations as the classical theory. Two examples are given. Furthermore, a scaling argument shows that an instantaneous change in applied shear stress would create a new steady state in the oil film within a mere fraction of a second; therefore hysteresis is negligible. Finally, error analysis shows that for typical silicone oils, every degree Celsius of temperature error creates a 2.2% error in the calculated shear stress. Therefore, accurate temperature sensing is an absolute requirement for this technique.
Name: Tat Loon Chng
Title: Capillary Switches
By manipulating a capillary surface such that it can exist in two or more stable states, one can essentially create a capillary switch. Here, a simple approach consisting of two capillary droplets pinned to a circular orifice channel is reviewed. Conditions for bistable equilibria (two stable states) are discussed, along with three different design implementations and how this device may find favour in existing applications.
Name: Tristen Hohman
Title: Exploring the Motions of Long Bubbles in Tubes: “Understanding the Bretherton Bubble Problem”
A bubble of fluid with negligible viscosity moves with constant velocity in a tube filled with a fluid of arbitrary viscosity at a low Reynolds number (a.k.a the Bretherton problem). This problem can be characterized in two main cases, which are discussed at length in this paper. The first is the case in which the tube is horizontal such that the gravitational effect on the motion can be neglected. The second case explored is one in which the bubble is in a vertical, closed end, fluid-filled tube of larger diameter where the gravitational effects on the bubble motion are now important and appear with the inclusion of a buoyancy force on the bubble. It is found from static treatment of the bubble that there exists a critical value of the bond number below which the bubble will not rise in the tube.
Name: Paul Reverdy
Title: Ballpoint Pen
The ballpoint pen is one of the most simple and yet ubiquitous devices whose function depends on surface tension. Although they come in varied forms and designs, anyone who has used a pen would probably experience the occasional skipping or smudging of ink. In this paper, an attempt is made at understanding these phenomena by examining this problem from the standpoint of lubrication theory. More specifically, since the ballpoint pen is, at its heart, a device consisting of a ball in a socket, ideas relating to the stability of a thin film on a sphere are applied. A cure for writer’s block in the making perhaps?
Name: Jeff Santner
Title: Waves in Thin Liquid Films
Waves in thin films behave differently than waves in deeper water, because of the high viscous stresses, low impact of inertial forces, low velocity, and influence of surface tension at the small scales involved. In this paper, the governing equations of thin films will be derived from the Navier-Stokes equations. This step is then followed by investigating the behavior of different types of waves.
Name: Jessica Shang
Title: Underwater Propulsion Using Surface Tension
Underwater propulsion in the context of the locomotion of marine snails is studied in this paper. Most fascinatingly, this creature has the uncanny ability to propel itself on the underside of a free surface. This motion is analyzed through the interaction between the mucus secreted by the snail (which is essentially a thin film) and its ‘foot’ contractions which take place in a wave-like manner. Treatment of the mucus as either a Newtonian and non-Newtonian fluid is found to give rise to different magnitudes of propulsive forces.