Small-amplitude perturbations of shape for a nearly spherical bubble in an inviscid straining flow (steady shapes and oscillatory motion)

The method of domain perturbations is used to study the problem of a nearly spherical bubble in an inviscid, axisymmetric straining flow. Steady-state shapes and axisymmetric oscillatory motions are considered. The steady-state solutions suggest the existence of a limit point at a critical Weber number, beyond which no solution exists on the steady-state solution branch which includes the spherical equilibrium state in the absence of flow (e.g. the critical value of 1.73 is estimated from the third-order solution). In addition, the first-order steady-state shape exhibits a maximum radius at θ = 1/6π which clearly indicates the barrel-like shape that was found earlier via numerical finite-deformation theories for higher Weber numbers. The oscillatory motion of a nearly spherical bubble is considered in two different ways. First, a small perturbation to a spherical base state is studied with the ad hoc assumption that the steady-state shape is spherical for the complete Weber-number range of interest. This analysis shows that the frequency of oscillation decreases as Weber number increases, and that a spherical bubble shape is unstable if Weber number is larger than 4.62. Secondly, the correct steady-state shape up to O(W) is included to obtain a rigorous asymptotic formula for the frequency change at small Weber number. This asymptotic analysis also shows that the frequency decreases as Weber number increases; for example, in the case of the principal mode (n = 2), ω^2 = ω_0^0(1−0.31W), where ω_0 is the oscillation frequency of a bubble in a quiescent fluid

Bubble dynamics in time-periodic straining flows

The dynamics and breakup of a bubble in an axisymmetric, time-periodic straining flow has been investigated via analysis of an approximate dynamic model and also by time-dependent numerical solutions of the full fluid mechanics problem. The analyses reveal that in the neighbourhood of a stable steady solution, an O(ϵ1/3) time-dependent change of bubble shape can be obtained from an O(ε) resonant forcing. Furthermore, the probability of bubble breakup at subcritical Weber numbers can be maximized by choosing an optimal forcing frequency for a fixed forcing amplitude

Motion of a sphere in the presence of a plane interface. Part 2. An exact solution in bipolar co-ordinates

A general solution for Stokes’ equation in bipolar co-ordinates is derived, and then applied to the arbitrary motion of a sphere in the presence of a plane fluid/fluid interface. The drag force and hydrodynamic torque on the sphere are then calculated for four specific motions of the sphere; namely, translation perpendicular and parallel to the interface and rotation about an axis which is perpendicular and parallel, respectively, to the interface. The most significant result of the present work is the comparison between these numerically exact solutions and the approximate solutions from part 1. The latter can be generalized to a variety of particle shapes, and it is thus important to assess their accuracy for this case of spherical particles where an exact solution can be obtained. In addition to comparisons with the approximate solutions, we also examine the predicted changes in the velocity, pressure and vorticity fields due to the presence of the plane interface. One particularly interesting feature of the solutions is the fact that the direction of rotation of a freely suspended sphere moving parallel to the interface can either be the same as for a sphere rolling along the interface (as might be intuitively expected), or opposite depending upon the location of the sphere centre and the ratio of viscosities for the two fluids

The creeping motion of a spherical particle normal to a deformable interface

Numerical results are presented for the approach of a rigid sphere normal to a deformable fluid-fluid interface in the velocity range for which inertial effects may be neglected. Both the case of a sphere moving with constant velocity, and that of a sphere moving under the action of a constant non-hydrodynamic body force are considered for several values of the viscosity ratio, density difference and interfacial tension between the two fluids. Two distinct modes of interface deformation are demonstrated: a film drainage mode in which fluid drains away in front of the sphere leaving an ever-thinning film, and a tailing mode where the sphere passes several radii beyond the plane of the initially undeformed interface, while remaining encapsulated by the original surrounding fluid which is connected with its main body by a thin thread-like tail behind the sphere. We consider the influence of the viscosity ratio, density difference, interfacial tension and starting position of the sphere in deter-mining which of these two modes of deformation will occur

Buoyancy-driven motion of a deformable drop toward a planar wall at low Reynolds number

The slow viscous motion of a deformable drop moving normal to a planar wall is studied numerically. In particular, a boundary integral technique employing the Green's function appropriate to a no-slip planar wall is used. Beginning with spherical drop shapes far from the wall, highly deformed and ‘dimpled’ drop configurations are obtained as the planar wall is approached. The initial stages of dimpling and their evolution provide information and insight into the basic assumptions of film-drainage theory

Treatment of bimodality in proficiency test of pH in bioethanol matrix

The pH value in bioethanol is a quality control parameter related to its acidity and to the corrosiveness of vehicle engines when it is used as fuel. In order to verify the comparability and reliability of the measurement of pH in bioethanol matrix among some experienced chemical laboratories, reference material (RM) of bioethanol developed by Inmetro - the Brazilian National Metrology Institute - was used in a proficiency testing (PT) scheme. There was a difference of more than one unit in the value of the pH measured due to the type of internal filling electrolytic solutions (potassium chloride, KCl or lithium chloride, LiCl) from the commercial pH combination electrodes used by the participant laboratories. Therefore, bimodal distribution has occurred from the data of this PT scheme. This work aims to present the possibilities that a PT scheme provider can use to overcome the bimodality problem. Data from the PT of pH in bioethanol were treated by two different statistical approaches: kernel density model and the mixture of distributions. Application of these statistical treatments improved the initial diagnoses of PT provider, by solving bimodality problem and contributing for a better performance evaluation in measuring pH of bioethanol.Comment: 20 pages, 6 figures, Accepted for publication in Accreditation and Quality Assurance (ACQUAL

Low-Reynolds-number flow past cylindrical bodies of arbitrary cross-sectional shape

A numerical implementation of the method of matched asymptotic expansions is proposed to analyse two-dimensional uniform streaming flow at low Reynolds number past a straight cylinder (or cylinders) of arbitrary cross-sectional shape. General solutions for both the Stokes and Oseen equations in two dimensions are expressed in terms of a boundary distribution of fundamental single- and double-layer singularities. These general solutions are then converted to integral equations for the unknown distributions of singularity strengths by application of boundary conditions at the cylinder surface, and matching conditions between the Stokes and Oseen solutions. By solving these integral equations, using collocation methods familiar from three-dimensional application of ‘boundary integral’ methods for solutions of Stokes equation, we generate a uniformly valid approximation to the solution for the whole domain. We demonstrate the method by considering, as numerical examples, uniform flow past an elliptic cylinder, uniform flow past a cylinder of rectangular cross-section, and uniform flow past two parallel cylinders which may be either equal in radius, or of different sizes

Modelling of epitaxial film growth with a Ehrlich-Schwoebel barrier dependent on the step height

The formation of mounded surfaces in epitaxial growth is attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growth using a ES barrier explicitly dependent on the step height. Our model has an intrinsic topological step barrier even in the absence of an explicit ES barrier. We show that mounded morphologies can be obtained even for a small barrier while a self-affine growth, consistent with the Villain-Lai-Das Sarma equation, is observed in absence of an explicit step barrier. The mounded surfaces are described by a super-roughness dynamical scaling characterized by locally smooth (faceted) surfaces and a global roughness exponent $\alpha>1$. The thin film limit is featured by surfaces with self-assembled three-dimensional structures having an aspect ratio (height/width) that may increase or decrease with temperature depending on the strength of step barrier.Comment: To appear in J. Phys. Cond. Matter; 3 movies as supplementary materia

A Geometric Approach to Massive p-form Duality

Massive theories of abelian p-forms are quantized in a generalized path-representation that leads to a description of the phase space in terms of a pair of dual non-local operators analogous to the Wilson Loop and the 't Hooft disorder operators. Special atention is devoted to the study of the duality between the Topologically Massive and the Self-Dual models in 2+1 dimensions. It is shown that these models share a geometric representation in which just one non local operator suffices to describe the observables.Comment: 26 pages, LaTeX. The discussion about the equivalence between the Proca model and two seldual models, with opposite spins, was eliminated. Typos correcte