A new solution for the rotation-driven spreading of a thin fluid film

Lie groups are used to solve the equation governing the flow of a thin liquid film subject to centrifugal spreading and viscous resistance. A new implicit solution is found. It is shown how this relates to the previous known solutions for the spreading of an initially flat film, the steady state and a separable solution. New permissible forms for the film evolution are also studied, including solutions exhibiting finite time blow-up. Near the contact line, where the film height tends to zero, an approximate explicit solution is obtained which may be used to describe a film with any size contact angle.     

Ethylenically unsaturated polycarbosiloxanes for novel silicone hydrogels: synthesis,end‐group analysis,contact lens formulations,and structure–property correlations

A series of novel mono‐ethylenically unsaturated polycarbosiloxanes macromonomers as compatibilizer materials for soft silicon hydrogels were prepared from the anionic ring‐opening polymerization (AROP) of 2,2,5,5‐tetramethyl‐2,5‐disila‐1‐oxacyclopentane followed by methacrylation. The characterization was performed by end‐group analysis and included the determination of molecular weight, molecular weight distributions, end‐group functionality, and impurity profiles using gas chromatography‐mass spectrometry, gel permeation chromatography, nuclear magnetic resonance, and matrix‐assisted laser desorption/ionization time of flight mass spectrometry. The synthetic procedure was optimized to minimize the formation of any dimer that would have the potential to act as a low molecular weight cross linker. In addition, the novel di‐ethylenically unsaturated polycarbosiloxanes were synthesized by cationic polymerization. Use of these silicone derivatives was explored in the formulation of contact lenses, and the structure–property relationship was examined. When copoymerized with hydrophilic monomers, these were able to give transparent and wettable films with desired properties, particularly a low moduli for contact lenses. Contact lens with high modulus is often shown to impart a higher degree discomfort when worn upon the eye. It was clear from the structure–property relationship that the modulus and the tensile strength of the formulated material depend on the nature and length of the polycarbosiloxane used and may be tuned for the purpose as needed. Copyright © 2013 John Wiley & Sons, Ltd.     

An elementary proof of the theorem that absolute gauge integrability implies Lebesgue integrability

It is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.