Improved algorithm of light scattering by a coated sphere

An efficient numerical algorithm for computing the light scattering by a coated sphere is proposed. The calculation of relevant functions by different recurrence algorithms is discussed. The new algorithm avoids the numerical difficulties, which give rise to significant errors encountered in practice by prior methods. Exemplifying results such as extinction efficiency, scattering efficiency, light scattering intensity as well as calculation speed are provided. The results show that this algorithm is efficient, fast, numerically stable and accurate.     

On establishing elastic–plastic properties of a sphere by indentation testing

Instrumented indentation is a popular technique for determining mechanical properties of materials. Currently, the evaluation techniques of instrumented indentation are mostly limited to a flat substrate being indented by various shaped indenters (e.g., conical or spherical). This work investigates the possibility of extending instrumented indentation to non-flat surfaces. To this end, conical indentation of a sphere is investigated where two methodologies for establishing mechanical properties are explored. In the first approach, a semi-analytical approach is employed to determine the elastic modulus of the sphere utilizing the elastic unloading response (the “unloading slope”). In the second method, reverse analysis based on finite element analysis is used, where non-dimensional characteristic functions derived from the force–displacement response are utilized to determine the elastic modulus and yield strength. To investigate the accuracies of the proposed methodologies, selected numerical experiments have been performed and excellent agreement was obtained.     

Creeping motion of a sphere in tubes filled with Herschel–Bulkley fluids

Previous numerical simulations for the flow of Bingham plastics past a sphere contained in cylindrical tubes of different diameter ratios are extended to Herschel–Bulkley fluids with the purpose of comparing them with experiments. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient as a function of the pertinent dimensionless groups. Good overall agreement is obtained between the numerical results and the experimental studies.     

Generalization of the Lamé problem for three-stage decelerated corrosion process of an elastic hollow sphere

The paper presents an analytical solution to Lamé's problem for a hollow sphere with unknown evolving boundaries. The double-sided uniform corrosion of a linearly elastic thick-walled spherical shell under internal and external pressure is considered. It is assumed that the corrosion rates are piecewise linear functions of the maximum principal stress on the related surface, and exponentially decaying with time. The corrosion process is supposed to be divided into three successive stages: constant rate double-sided corrosive wear, a stage of corrosion accelerated on only one of the surfaces of the shell, and a double-sided mechanochemical corrosion. Closed-formed expressions for all the consecutive stages are obtained with their junction points (corresponding to stress corrosion thresholds) being taken into account.     

Spherical Couette flow of a viscoelastic fluid – Part III: A study of outer sphere rotation

A study is carried out for the flow of viscoelastic fluid contained between a stationary inner sphere and a rotating outer sphere. A sequence of flow transitions that is unique to viscoelastic fluids is observed in the experiments. It is found that a `traveling cell', with roll-cell-like characteristics, is generated in the polar region, and then propagates toward the equatorial region when a dimensionless parameter (a measure of strength of the elasticity against the shear viscosity) is increased. In order to investigate the structure and mechanism of the traveling cell, a numerical analysis is performed using a constitutive equation of the Giesekus model. Results of the numerical simulation revealed that the elasticity of the fluid strongly influences the flow in the polar region, where the inertia effect of the outer sphere rotation is minimal, destabilizing the flow forming a pair of weak vortices at the polar region. It was further shown that the pair travel toward the equatorial region in a different manner depending upon the speed of rotation.     

The effect of sphere–wall interactions on particle motion in a viscoelastic suspension of FENE dumbbells

A new method for simulating the motion of particles in viscoelastic Boger fluids is extended to problems with bounded geometries. Viscoelasticity is incorporated into the Stokesian dynamics method by modeling a viscoelastic fluid as a suspension of finite-extension nonlinear-elastic (FENE) dumbbells. Wall–particle and wall–bead interactions are included by using the image system method of Blake; particle–particle and particle–bead interactions are also modified by the presence of the wall. The method of incorporating sphere–wall interactions is verified by doing calculations for several problems involving particle–wall interactions in Newtonian fluids. The method is then used to study particle–wall interactions in viscoelastic dumbbell suspensions by examining several problems of interest: the sedimentation of a spherical particle near vertical and tilted walls; the sedimentation of a nonspherical particle between two flat plates; and the migration of a neutrally buoyant sphere in plane Poiseuille flow. We find that a single sphere falling near a wall moves toward the wall and exhibits anomalous rotation. When the wall is tilted by an amount less than a few degrees, the sphere still moves toward the wall, but tilting the wall greater than an angle of approximately 1.5° results in the sphere falling away from the wall. A nonspherical particle settling in a channel exhibits an oscillatory motion, but ultimately becomes centered in the channel with its long axis parallel to gravity. Finally, it is shown that a neutrally buoyant sphere in plane Poiseuille flow migrates to the channel center in wide channels, but migrates to the walls when the sphere is sufficiently large relative to the channel width.