Time-dependent coating flows in a strip, Part I: The linearized problem

This work is concerned with time-dependent coating flow in a strip . The Navier-Stokes equations are satisfied in the fluid region, the bottom substrate is moving with fixed velocity , and fluid is entering the strip through the upper boundary . The free boundary has the form for , where is the moving contact point. Our objective is to prove that if the initial data are close to those of a stationary solution (the existence of such a solution was established by the authors in an earlier paper) then the time-dependent problem has a unique solution with smooth free boundary, at least for a small time interval. In this Part I we study the linearized problem, about the stationary solution, and obtain sharp estimates for the solution and its derivatives. These estimates will be used in Part II to establish existence and uniqueness for the full nonlinear problem.

     

Dynamics of adsorption of an oppositely charged polymer-surfactant mixture at the air-water interface: poly(dimethyldiallylammonium chloride) and sodium dodecyl sulfate

The dynamic adsorption behavior of mixtures of the cationic polymer poly(dimethyldiallylammonium chloride) [poly(dmdaac)] and the anionic surfactant sodium dodecyl sulfate (SDS) has been studied at the expanding liquid surface of an overflowing cylinder. A combination of ellipsometry and external reflection Fourier transform infrared spectroscopy was used to measure the adsorbed amounts of poly(dmdaac) and SDS as a function of the bulk surfactant concentration for various polymer concentrations in the range 0-0.2 g dm-3. Laser Doppler velocimetry was used to determine the surface age, which was approximately 1 s for solutions where the polymer adsorbed. The interfacial behavior is rationalized in terms of competition between surface activity and mass transport to the expanding surface. At low surfactant concentrations, adsorption of both poly(dmdaac) and SDS is enhanced as a result of the formation in solution of polymer-surfactant complexes that are more surface active than either component alone. The rate of adsorption of these complexes is diffusion-controlled, and their interfacial composition remains constant at three dmdaac units per SDS molecule over a 5-fold change in the surfactant concentration. For the higher polymer concentrations studied, the complexes saturate the air-water interface: the adsorbed amount is independent of the polymer concentration and remains constant also over a factor of 5 in the surfactant concentration. Once the number of bound surfactant molecules per dmdaac monomer exceeds 0.3, the complexes begin to form large aggregates, which are not surface active due to their slower mass transport. The adsorbed amount decreases rapidly on approach to the equivalence point (one SDS molecule per dmdaac monomer), and when it is reached, only a very small amount of material remains at the interface. At still higher surfactant concentrations, the free SDS adsorbs but there is no adsorbed poly(dmdaac). The dynamic adsorption data are compared with equilibrium measurements of the same system by Staples et al. (Langmuir 2002, 18, 5147), which show very different surface compositions and no significant change in surface coverage at the equivalence point.     

Direct observation of phenylalanine orientations in statherin bound to hydroxyapatite surfaces

Extracellular biomineralization proteins such as salivary statherin control the growth of hydroxyapatite (HAP), the principal component of teeth and bones. Despite the important role that statherin plays in the regulation of hard tissue formation in humans, the surface recognition mechanisms involved are poorly understood. The protein-surface interaction likely involves very specific contacts between the surface atoms and the key protein side chains. This study demonstrates for the first time the power of combining near-edge X-ray absorption fine structure (NEXAFS) spectroscopy with element labeling to quantify the orientation of individual side chains. In this work, the 15 amino acid N-terminal binding domain of statherin has been adsorbed onto HAP surfaces, and the orientations of phenylalanine rings F7 and F14 have been determined using NEXAFS analysis and fluorine labels at individual phenylalanine sites. The NEXAFS-derived phenylalanine tilt angles have been verified with sum frequency generation spectroscopy.     

Spectroscopic analysis of immobilised redox enzymes under direct electrochemical control

This article reviews recent developments in spectroscopic analysis of electrode-immobilised enzymes under direct, unmediated electrochemical control. These methods unite the suite of spectroscopic methods available for characterisation of structural, electronic and coordination changes in proteins with the exquisite control over complex redox enzymes that can be achieved in protein film electrochemistry in which immobilised protein molecules exchange electrons directly with an electrode. This combination is particularly powerful in studies of highly active enzymes where redox states can be controlled even under fast electrocatalytic turnover. We examine examples in which UV-visible, IR, Raman and MCD spectroscopy have been combined with direct electrochemistry to probe redox-dependent chemistry, and consider future opportunities for 'direct' spectroelectrochemistry of immobilised enzymes.     

Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part IV. D(C)/D0=1+(αC)−β(αC)

Using the specific functional form D(C)/D₀=1+(αC)−β(αC)² an investigation has been made of (isothermal) transport through a slab membrane under ‘simple’ boundary conditions and governed by a diffusion coefficient, D(C), which, with increasing concentration, at first increases, passes through a maximum value and finally decreases. The flux, integral diffusion coefficient and concentration profile characteristic of steady-state permeation have been evaluated; special attention has been paid to the positions of such profiles in relation to the corresponding linear distribution associated with a constant diffusion coefficient.The corresponding transient-state transport has been studied within a framework of the time-lag ‘early-time’ and ‘ ’ procedures. Expressions for the ‘adsorption’ and ‘desorption’ time-lags are given. The concentration-dependence of these time-lags, of the (four) integral diffusion coefficients derived from them and of the arithmetic-mean time-lag ratios have been considered in some detail. The ‘early-time’ and ‘ ’ finite-difference procedures have likewise been employed to derive four further integral diffusion coefficients, so enabling a comparison to be made of the nine integral coefficients pertaining to established experimental techniques.Particular interest attaches to the situation for which n≡β(αC₀)=1 (where C₀ is the ingoing or upstream concentration of diffusant) resulting in D(C₀) being symmetrical about C₀/2. Some consideration has been given, in general, to features of transient-state transport when governed by a symmetrical D(C).