Stephen Pennell

Internal solitary waves in a two-fluid system

A ninth‐order perturbation solution describing the solitary wave at the interface of a two‐fluid system is found by means of a symbolic manipulation software package. The coefficients in the general solution are evaluated for 37 values of the density and depth ratios σ and R, yielding the first nine terms in the series expansions for the wave profile, wave speed, mass, and potential energy in powers of the wave amplitude a. A maximum in the ninth‐order partial sum for the wave speed is found in each case for which the sum is judged to be an acceptable approximation to the infinite series for all a less than or equal to Af=(R−(σ)1/2 )/(1+(σ)1/2). Furthermore, this maximum occurs for a value of a very close to the value of Af. In all 37 cases, the [5,4] Pade approximant for the wave speed has a maximum, and in almost all cases the maximum occurs close to Af. No maximum is found in the ninth‐order partial sums for mass or potential energy in the range of values of a for which these sums are judged to be valid.

Multi-Wavelength Fluorescence-Quenching Model for Determination of Cu2+ Conditional Stability Constants and Ligand Concentrations of Fulvic Acid:

In this work, a multi-wavelength model (MWM) is developed. It uses fluorescence bands in the fulvic acid (FA) spectrum that quench upon binding of inorganic Cu2+ to FA. Quenching data at pH values of 5, 6, and 7 are placed in sets, containing fluorescence measures at select wavelengths versus added copper (CM). Intensity data of wavelength set 1 are obtained from 25 nm constant offset synchronous fluorescence spectra (SyF), in which are observed distinct peaks (λex = 415 nm, λem = 440 nm; and λex = 471 nm, λem = 496 nm). Wavelength set 2 intensity data are obtained from the FA fluorescence excitation and emission maxima (λex = 335 nm, λem = 450 nm; and λex = 471 nm, λem = 496 nm). Application of MWM shows that the multi-wavelength data sets characterize ligands of different binding strength (log Kx) and concentration (CLx). Corresponding to pH values of 5, 6, and 7, mean and standard deviation values for wavelength set 1 are log K415/440 = 4.66 (0.12), 5.03 (0.12), and 5.05 (0.08), log K471/496 = 4.93 (0.06), 5.27 (0.11), and 5.39 (0.09), C415/440 = 3.1 (1.5), 10.9 (4.5), and 7.9 (3.9) μM, C471/496 = 14.3 (3.0), 1.7 (0.6), and 1.4 (0.5) μM. And for wavelength set 2, log K335/450 = 4.50 (0.03), 4.96 (0.27), and 5.22 (0.08), log K471/496 = 5.02 (0.04), 5.42 (0.32), and 5.71 (0.09), C335/450 = 8.8 (0.5), 21.9 (7.9), and 18.7 (0.3) μM, C471/496 = 21.0 (2.5), 7.17 (1.2), and 7.09 (0.3) μM. The ability of the 415/440 nm SyF transect to characterize the main excitation and emission maximum of FA at 335/440 nm is evaluated. Relatively low concentration values returned by the model for this transect (415/440 nm) suggest that it is not entirely illustrative of the maximum. The model predictive capability is verified at pH 6 with two fluorescing Cu2+ chelating organic compounds, L-tyrosine and salicylic acid. This test confirms that the model is capable of providing good estimates of equilibrium binding parameters from multi-wavelength measurements of a mixed ligand system.

Contact angle calculations from the contact/maximum diameter of sessile drops

We present two algorithms for computing the contact angle of sessile liquid drops given data about the drops. The first yields the contact angle given the volume, surface tension and maximum diameter (or contact diameter) of a single drop. This algorithm is an extension of existing algorithms based on knowledge of the maximum diameter or of the contact diameter of a drop. A sensitivity analysis is included for this algorithm, allowing estimates to be made of the error in computed contact angle caused by errors in the measurement of the volume and/or diameter. The second algorithm requires only the volume and maximum or contact diameter of two different drops as input, and it produces both the contact angle and surface tension as output. Both algorithms are based on Newtons method applied to a function whose value is computed by solving a system of ordinary differential equations obtained from the Laplace equation of capillarity. The techniques are applicable to both hydrophobic and hydrophilic surfaces

On Inertial Motion on a Rotating Sphere

Abstract An explicit solution is derived for the trajectory of a particle in an inertial flow on a rotating sphere. This solution explains many of the features of inertial trajectories that have been presented in the literature.

Implementation and examination of a new drop shape analysis algorithm to measure contact angle and surface tension from the diameters of two sessile drops

The performance of a new algorithm developed to measure contact angle and surface tension of sessile drops is examined. To calculate the contact angle and surface tension, the new algorithm (ADSA-TD) requires the radius (contact or equatorial) and volume of two sessile drops of different sizes that are placed on the same surface. Initially, the algorithm was tested using synthetic drops (synthetic or theoretical drops are produced by numerical integration of the Laplace equation). The radii and volumes of synthetic drops were used as ADSA-TD inputs. The calculated contact angle (θ) and surface tension (γ) by ADSA-TD matched perfectly the assumed values of θ and γ used to produce the synthetic drops, confirming theoretically the validity of the new algorithm. In the next step, the sensitivity of the algorithm to input errors was examined. It was shown experimentally that both calculated contact angle and surface tension are affected by the errors in volume and radius. Besides the error in input values, it was shown that the size difference between the paired drops and the differences in their contact angles would affect the output of ADSA-TD. As it turns out, the calculated surface tension is so sensitive to the above factors that ADSA-TD does not appear to be promising as a surface tension measurement technique. However, ADSA-TD produced acceptable contact angle values as compared to measurements made by other proven techniques such as axisymmetric drop shape analysis-profile. Thus, ADSA-TD may be of interest as a contact angle measurement technique which does not require the liquid surface tension as input.

A note on exact relations for solitary waves

Free‐surface solitary waves and interfacial solitary waves in a two‐fluid system with a rigid lid are known to satisfy certain exact relations involving integral quantities (mass, kinetic and potential energy, etc.). It is shown here that similar relations are satisfied by interfacial solitary waves in a two‐fluid system with a free upper surface and by surface solitary waves in a three‐dimensional one‐fluid system.

Computing the Projected Area of a Cone

Techniques from linear algebra and calculus are used to compute the projected area of an arbitrarily oriented right circular cone. This type of computation is important in the design of interceptor missile systems, which use infrared sensors to distinguish between warheads and decoys

Weak oblique collisions of interfacial solitary waves

Abstract A third order perturbation solution is developed to describe the interaction between two solitary waves approaching each other at an angle close to 180 ° on the interface between two immiscible inviscid homogeneous fluids. The solution is steady in the frame of reference moving with the point of intersection of the waves. To lowest order, the solution consists simply of the superposition of the undisturbed solitary waves. Second-order collision effects include interaction terms localized near the point of intersection and a phase shift in the solitary waves. In addition to corrections to the phase shift and localized interaction terms, third order effects are found to include a wave train that is stationary in the frame of reference moving with the point of intersection of the solitary waves. The amplitudes of the wave train and localized interaction terms diminish with distance from the point of intersection, and the solitary waves recover their initial shape asymptotically long after the collision. Thus, the only long-term effect of the collision is a phase shift.

Modelling smectite illitization in earthen barriers of buried radioactive wastes

The textural characteristics of engineered clay barriers of deeply buried radioactive waste repositories are likely to change in response to hydro-thermo-mechanical stresses during the 10 000-year service and risk analysis period. Expected textural changes stem from a combination of processes, the most significant of which is smectite illitization. To pose significant risks of radionuclide release from buried waste canisters, illitization must, as a minimum, produce barrier textural changes that are significant within the timeframe in which radioactive activity is still significant. Besides, the canister must be damaged, principally through corrosion by substance-laden infiltrating moisture. In the current paper, simulations of three scenarios of illitization of a clay barrier that is initially 100% smectite under a temperature regime that does not exceed 150°C indicate that the accumulation of potassium ions ( ) borne by infiltrating water close to the waste canister is likely to be insignificant within the first 1000 years of waste entombment. Some are extracted from the infiltrating moisture to feed the illitization reaction which is herein assumed to occur with an activation energy of 1.17 × 10−5 J/mole.