An Approximate Analytical Solution for Counter-Current Spontaneous Imbibition

An approximate analytical solution is provided for one-dimensional, counter- current, spontaneous imbibition of a wetting phase (water) into a semi-infinite porous medium. The solution is based on the assumption that a similarity solution exists for the displacement process. This assumption, in turn, rests on the assumption that the set of relative permeability and capillary pressures curves are unique functions of saturation and do not depend on the nature of the displacement. It further rests on the assumption that the saturation at the imbibition face does not vary with time. It is demonstrated that the solution is in agreement with results obtained from experiments and also numerical analyses of these experiments. The experiments utilize cylindrical samples with the radial surface and one end-face sealed, and with counter-current imbibition occurring at the open end-face. The stage of the experiment that is modeled by the present solution is the period before the imbibition front contacts the sealed end-face. An important finding of the present analysis is that the pressure upstream of the advancing invasion front is a constant. A second, improved solution is also presented; this solution is an iterative, series solution of an integral-differential equation. It converges to a stable solution in very few terms.     

The investigation of the dynamic visco-elastic functions of printing inks

Summary Measurements of the dynamic rigidities and viscosties of some inks have been made in the frequency range 0.01 to 25 c. p. s. in the linear region. The dependency of the visco-elastic properties on concentration of pigment and added solvent is discussed. The dynamic mechanical properties of non-thixotropic inks are found to be distinct from those of thixotropic inks.

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Zusammenfassung Es wurden Messungen der dynamischen Steifigkeiten und Viskositäten verschiedener Tinten im Frequenzbereich zwischen 0,01 und 25 Hz im linearen Bereich durchgeführt. Es wird die Abhängigkeit der viskoelastischen Eigenschaften von der Pigmentkonzentration und dem Lösungsmittelgehalt diskutiert. Es zeigt sich, daß die dynamisch-mechanischen Eigenschaften nichtthixotroper Tinten sich deutlich von denen thixotroper Tinten unterscheiden.

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The cantilever strip plate under torision, bending or flexure at infinity

A homogeneous, isotropic plate occupies the region 0x ₁, |x ₂|a, |x ₃|h, where the ratio h/a is sufficiently small so that the classical theory of thin plate bending applies. The short end of the plate at x ₁=0 is clamped while the long sides are free. This cantilever plate is now loaded at x ₁=+ by an applied twisting moment, by a bending moment or by flexure. Despite the fundamental nature of these problems, and the long history of thin plate theory, no solutions are to be found in the existing literature that will determine (for instance) the important unknown resultants V ₁, M ₁₁ at the clamped end x ₁=0. The main reason for this is that this combination of boundary conditions leads to severe oscillating singularities of the field in the corners (0, ±a). The fact that such singularities must exist is widely known, but we present here for the first time a method of solution that takes these singularities fully into account.Our numerical results show that the values of M ₁₁, V ₁ on x ₁=0 bear little resemblance to those of the corresponding Saint-Venant solutions, which do not fully satisfy the boundary conditions at the clamped end. Indeed, significantly large values of these resultants were found at points far enough from the corners so as to be relevant in actual engineering applications. Also of interest are certain weighted integrals of M ₁₁, V ₁ which we calculate. These constants determine the effect of the clamping at large distances (greater than 4a, say) from the cla,ped end. At such distances, the effect of the clamping is merely to impose an additional rigid body deflection on the plate.Finally, we consider the plate of finite length. Provided that the aspect ratio is 2 or more, we give accurate approximate solutions for the torsion, bending or flexure of a finite plate clamped at both ends.     

Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials

We consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained, and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well-posed. For materials fulfilling the condition, we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system. As an application we determine the orthotropic materials for which the fundamental problems are well-posed in terms of their Young's moduli, shear moduli, and Poisson ratios. Finally, we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements. For a two-dimensional constrained material a further reduction to a single scalar equation is outlined.This paper is dedicated to Professor Joachim Nitsche on the occasion of his sixtieth birthday     

Biophysical implications of bubble dynamics

Evidence is reviewed, from theory and experiment, that biological systems can be affected by ultrasound at low levels, if resonant gas bodies are present. In a suspension of cells or other particles a pulsating gas bubble causes the particles to migrate toward its surface via radiation force. This motion, in addition to acoustic microstreaming, transports particles into the bubble near-field where they are subjected to highly localized stress fields. In plant leaves containing gas-filled channels, the ultrasonic intensity required to produce cell death varies with frequency, showing minima in ranges corresponding roughly to calculated frequencies for resonance of the channels.     

Highly radiating hydrogen flames: Effect of toluene concentration and phase

Adapting hydrogen as a carbon-free fuel for industrial applications requires new, innovative approaches, especially when radiant heat transfer is required. One possible option is to dope hydrogen with bio-oils, containing aromatics that help produce highly sooting flames. This study investigates the potential doping effects of toluene on a hydrogen-nitrogen (1:1 vol) flames. Flames with 1–5% toluene, based on the mole concentration of hydrogen, are measured using a combination of techniques including: still photographs and laser-based techniques. Toluene was mixed with hydrogen-nitrogen fuel mixture as either a vapour carried by nitrogen, or as a dilute spray. Spray flames are found to produce substantially more polycylic aromatic hydrocarbons, with significantly more soot near the nozzle exit plane, than the prevaporised flames. Increasing the dopant concentration from 1 to 3% of the hydrogen has a marked effect on soot loading in the flame, although the further increasing the dopant concentration to 5% has a far smaller effect on the soot produced in the flame. Simulations of laminar flames using detailed chemical kinetics support the above findings and reveal details of the competition between soot precursor formation and hydrocarbon oxidation. Correlations of formation rates are non-linear with toluene concentration in cases where toluene represents less than 10% of the fuel, although expected linear relationships are noted beyond this regime up to 1:1 toluene/hydrogen blends. The study provides insight and explanation into effects of toluene as a dopant, comparison between flame doping in gaseous or liquid phases and suggests that flame doping and blending should be treated as different regimes for their global effect on flame sooting characteristics.     

Singlet and Triplet State Properties and Singlet Oxygen Yield of an Amino-Acyl-Quinoxalinone Yellow Dye

Amino-acyl-quinoxalinone yellow dyes are cyclised analogues of the yellow azomethine dyes developed for, and still used in, silver halide colour photography. Unlike image azomethine dyes, which are rapidly deactivated in their excited states by torsion about the azomethine bond, amino-acyl-quinoxalinone dyes have an interesting photophysics because torsion is not possible due to their cyclised structure. We report results from studies on singlet and triplet state properties, and singlet oxygen yields, of the yellow dye, 7-diethylamino-3-(2,2-dimethyl-propionyl)-5-methyl-1-phenyl-1H-quinoxalin-2-one, in polar and nonpolar solvents. The dye photophysics is characterised by a weak fluorescence, with a solvent dependent emission yield (Φ_F?≈?0.002–0.004), and short singlet state lifetime (τ_expt?≈?20–50 ps), both increasing by a factor of ≈2 in going from polar acetonitrile to non-polar dioxane as solvent. DFT ZINDO calculations show a transition involving significant electron transfer from the diethyl-amino group into the carbonyl region of the molecule. In solution, in the presence of oxygen, the triplet state decays almost exclusively by oxygen quenching, and singlet oxygen is produced in high yield (Φ_??≈?0.5–0.55). The triplet state absorbs across the 450–750 nm region with maxima around 480 and 650 nm, and moderate molar absorption coefficients (ca. 6000–8000 M^?1 cm^?1). In a glass at 77 K, triplet decay gives a red phosphorescence, with λ_max?≈?640–650 nm, and a ?≈?0.25 s lifetime. If singlet oxygen yields are a good indication of triplet yields, then internal conversion and intersystem crossing occur with roughly equal efficiency.

     

Diphospha-Ureas from the Phosphaketene Ph3GePCO

The phosphaketene Ph₃GePCO is shown to react with the phosphide KP(tBu)₂ to generate the anion [Ph₃GePC(O)P(tBu)₂]⁻ 1 . This species reacts with CH₃I or ClGePh₃ to give the dissymmetric diphospha-ureas (tBu)₂PC(O)P(GePh₃)(CH₃) 2 and (Ph₃Ge)₂PC(O)P(tBu)₂ 3 respectively. Sequential treatment of 2 with a base and CH₃I affords a route to (tBu)₂PC(O)P(CH₃)₂ 5 . These species are products of the first modular diphospha-urea synthesis. The subsequent thermal and photochemical reactivity of these species was also probed and described.     

Erratum: The average degree of an edge-chromatic critical graph II

In the article “The average degree of an edge-chromatic critical graph II” by Douglas R. Woodall (J. Graph Theory 56 (2007), 194-218), it was claimed that the average degree of an edge-chromatic critical graph with maximum degree $\mathrm{\Delta }$ is at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+1\right)$ if $\mathrm{\Delta }⩾2$, at least $\text{◂+▸}\frac{2}{3}\mathrm{\Delta }+1$ if $\mathrm{\Delta }⩾8$, and at least $\text{◂⋅▸}\frac{2}{3}\left(\mathrm{\Delta }+2\right)$ if $\mathrm{\Delta }⩾15$. Unfortunately there were mistakes in the proof of the last two of these results, which are now proved only if $\mathrm{\Delta }⩾18$ and $\mathrm{\Delta }⩾30$, respectively.