A laminar roughness boundary condition

A modified slip boundary condition is obtained to represent the effects of small roughness-like perturbations to an otherwise-plane fixed wall which is acting as a boundary to steady laminar flow of a viscous fluid. In its simplest form, for low local Reynolds number and small roughness slope, this boundary condition involves a constant apparent backflow at the mean surface or, equivalently, represents a shift of the apparent plane boundary toward the flow domain. Extensions of the theory are also made to include finite local Reynolds number and finite roughness slope.E. O. Tuck and A. Kouzoubo

Valorisation of lignin by depolymerisation and fractionation using supercritical fluids and conventional solvents

A procedure for Lignosulphonate valorisation is investigated. An attempt has been made to obtain diverse value-added products maximizing the atom economy. This procedure is carried in sequential steps starting with an oxidative depolymerization in supercritical water. Next, the reaction mixture is fractionated according to its solubility in water and in ethyl acetate. Several analytical methods - CHN elemental analysis, aqueous GPC and 31P-NMR - were used to determine the composition of these fractions and to assess their suitability for different applications. Water-insoluble fractions were converted to a lignin-derived hydrochar for the synthesis of active carbon of superior quality. Monomers were recovered from bio-oil fraction by supercritical carbon dioxide extraction and the remaining oil is proposed as a potential starting material for the synthesis of polyurethane foams

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all other cases an accurate semiclassical approximation is derived, based on the identification of the operators with a peculiar Schroedinger-like operator.Comment: 12 pages, 1 figure, amslatex, bibtex (added missing label eq.11

Towards a systematic understanding of the influence of temperature on glycosylation reactions

Glycosidic bond formation is a continual challenge for practitioners. Aiming to enhance the reproducibility and efficiency of oligosaccharide synthesis, we studied the relationship between glycosyl donor activation and reaction temperature. A novel semi-automated assay revealed diverse responses of members of a panel of thioglycosides to activation at various temperatures. The patterns of protecting groups and the thiol aglycon combine to cause remarkable differences in temperature sensitivity among glycosylating agents. We introduce the concept of donor activation temperature to capture experimental insights, reasoning that glycosylations performed below this reference temperature evade deleterious side reactions. Activation temperatures enable a simplified temperature treatment and facilitate optimization of glycosylating agent (building block) usage. Isothermal glycosylation below the activation temperature halved the equivalents of building block required in comparison to the standard ‘ramp’ regime used in solution- and solid-phase oligosaccharide synthesis to-date

On open venturis

Flow through an open converging-diverging channel, aimed at achieving maximum velocity at the throat.E. O. Tuc

Free-surface pressure distributions with minimum wave resistance

The wave resistance of distributions of excess pressure over a rectangular region on the surface of a steady stream is minimised by choice of spatial variation in pressure. Both unconstrained and constrained (non-negative) pressures are studied. Results with impressive resistance reductions are provided, both via discretisation to a large number of step pressures, and via optimisation within a low-order continuous family

Contact Line Instability and Pattern Selection in Thermally Driven Liquid Films

Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability of the flow can be altered, or patterns selected, using feedback control. We show that thermal perturbations of certain spatial structure imposed behind the contact line and proportional to the deviation of the contact line from its mean position can completely suppress the instability. Due to the presence of mean flow and a spatially nonuniform nature of spreading liquid films the dynamics of disturbances is governed by a nonnormal evolution operator, opening up a possibility of transient amplification and nonlinear instabilities. We show that in the case of thermal driving the nonnormality can be significant, especially for small wavenumber disturbances, and trace the origin of transient amplification to a close alignment of a large group of eigenfunctions of the evolution operator. However, for values of noise likely to occur in experiments we find that the transient amplification is not sufficiently strong to either change the predictions of the linear stability analysis or invalidate the proposed control approach.Comment: 13 pages, 14 figure

Steady two dimensional free-surface flow over semi-infinite and finite-length corrugations in an open channel

Free-surface flow past a semi-infinite or a finite length corrugation in an otherwise flat and horizontal open channel is considered. Numerical solutions for the steady flow problem are computed using both a weakly nonlinear and fully nonlinear model. The new solutions are classified in terms of a depth-based Froude number and the four classical flow types (supercritical, subcritical, generalised hydraulic rise and hydraulic rise) for flow over a small bump. While there is no hydraulic fall solution for semi-infinite topography, we provide strong numerical evidence that such a solution does exist in the case of a finite length corrugation. Numerical solutions are also found for the other flow types for either semi-infinite or finite length corrugation. For subcritical flow over a semi-infinite corrugation, the free-surface profile is found to be quasiperiodic in nature. A discussion of the new results is made with reference to the classical problem of flow over a bump

Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are encountered: a Stokes flow near a rough wall and the stress distribution on the rough interface of a material in uni-axial tension. We perform a complete numerical solution of these two-dimensional problems for any univalued rough surfaces. We present results for sinusoidal and self-affine surface whose slope can locally reach 2.5. Beyond the numerical solution we present perturbative solutions of these problems. We show in particular that at first order in roughness amplitude, the surface stress of a material in uni-axial tension can be directly obtained from the Hilbert transform of the local slope. In case of self-affine surfaces, we show that the stress distribution presents, for large stresses, a power law tail whose exponent continuously depends on the roughness amplitude