A direct formulation of electromagnetic scattering based only on scalar Helmholtz equations is given. The solution, expressed as coupled non-singular boundary integral equations for the field components, provides the benefits of the reduction of dimensionality. For perfect conductors, consideration of induced surface current densities, central to standard methods, is not required. This approach has utility in high aspect ratio electromagnetic problems, surface plasmon spectra and dis- persion force calculations of complex nano structures as near and far field values are given with equal precision. Extension to dielectric scatterers and elastic wave propagation in solids is immediate.
J. Oshitani, S. Hahashi, D. Y. C. Chan
Order from Chaos: Dynamics of density segregation in continuously aerated granular systems
Physical Review Letters [Submitted 6 Feb 2017]. pdf, supp
Under continual disturbance such as vibration, tumbling, flow or aeration, granular or powder systems can display solid or fluid like behavior. Using a well-mixed system of same size (0.2 mm) non-cohesive glass beads and iron powder, we show that gentle aeration can completely segregate the components thereby reducing the entropy of mixing to create near total order from an initially chaotic mixture. We quantify the time dependence of the segregation process and identify two dynamic pathways that dominate depending on the intensity of the aeration. Such findings can facilitate the search for energy efficient methods to process granular systems in pharmaceutical, mining and waste recovery industries.
D. Y. C. Chan, E. Klaseboer, Q. Sun
A stable zero frequency surface integral formulation for E and H
Progress in Electromagnetics Research Letters [17120307 Submitted 03 Dec 2017]. pdf
The frequency domain Maxwell's equations in linear homogeneous media are re-cast as 4 scalar Helmholtz equations: 3 for the Cartesian components of the electric field, E and 1 for the scalar function (r · E), with identical equations for the magnetic field, H. Their surface integral equation solution involves only the Green’s function, G(r, r') = exp(ik|r − r'|)/(4π|r − r'|) but can be written in a form with bounded integrands. Solving with the Nyström quadrature method with quadratic area elements gives a linear system for E and H on the boundary directly. Hypersingular dyadic Green's function and surface currents do not feature. This simpler direct approach is stable in the long wavelength limit, unaffected by the zero frequency catastrophe in the EFIE and MFIE formulations.
S. J. Flanders, Q. Sun, A. M. Siddiquee, D. Y. C. Chan, J. W. M. Chon
Analytical model for light scattering of plasmonic gold nanorods with size up to 200 nm
ACS Photonics [PH-2018-01196y Submitted 29 Aug 2018]. pdf, supp
Recently, various linear and nonlinear emission processes of shape-controlled plasmonic gold nanorods have been applied in biolabelling and photothermal cancer therapy. One of the most fundamental knowledge required for understanding these processes is the field around the nanorod. Here, we present a simple analytical theoretical model for calculating near- and far-fields around prolate spheroidal (PS) and hemispherically capped cylindrical (HCC) gold nanorods beyond the quasistatic limit, for rods up to 200 nm in length (ka ~ 1.13, corresponding to a wavelength ~ 500 nm) and aspect ratio 5, which encompasses the parameter range of most of the biolabelling applications. We achieve this by solving the field directly from classical electrostatic model for ellipsoids, and then by introducing correction factors for different size beyond quasistatic limit and then for the shape of HCC nanorods. We validate the model with numerical simulations and correlated single particle scattering cross-section measurements using confocal laser scanning microscopy (CLSM) and transmission electron microscopy (TEM). The simple and accurate expressions will be useful in determining efficiency in any linear or nonlinear emission processes for biolabelling application that require accurate knowledge of the field around these nanorods.
D. Y. C. Chan, A. J. Yuffa, E. Klaseboer, Q. Sun
Efﬁcient Field-Only Surface Integral Equations for Electromagnetics
IEEE Transactions on Antennas and Propagation [AP1812-2322 Submitted 19 Dec 2018]. pdf
In a recent paper, Klaseboer et al. (IEEE Trans. Antennas Propag., vol. 65, no. 2, pp. 972-977, Feb. 2017) developed a surface integral formulation of electromagnetics that does not require working with integral equations that have singular kernels. Instead of solving for the induced surface currents, the method involves surface integral solutions for 4 coupled Helmholtz equations: 3 for each Cartesian component of the electric E ﬁeld plus 1 for the scalar function (r·E) on the surface of scatterers. Here we improve on this approach by advancing a formulation due to Yuffa et al. (IEEE Trans.Antennas Propag., vol. 66, no. 10, pp. 5274-5281, Oct. 2018) that solves for E and its normal derivative. Apart from a 25% reduction in problem size, the normal derivative of the ﬁeld is often of interest in micro-photonic applications.
I. U. Vakarelski, F. Yang, Y. S. Tian, E. Q. Li, D. Y. C. Chan, S. T. Thoroddsen
Mobile-surface bubbles and droplets coalesce faster but bounce stronger
Science Advances [aaw4292 Submitted 19 Dec 2018]. pdf, Supp
Enhancing the hydrodynamic interfacial mobility of bubbles and droplets in multiphase systems is expected to reduce the characteristic coalescence times and hence affect the stability of gas or liquid emulsions that are of wide industrial and biological importance. However, by comparing the controlled collision of bubbles or water droplets with mobile and immobile liquid interfaces that have been designed to have the same interfacial tension in a pure fluorocarbon liquid, we demonstrated that collisions involving mobile surfaces result in a significantly stronger series of rebounds prior to the rapid coalescence event. The stronger rebound is explained by the lower viscous dissipation during collisions involving mobile surfaces. We present direct numerical simulations confirming that the observed rebound is enhanced with increased surface mobility. Good quantitative agreement between simulation and experiments substantiates the prediction that, in contrast to the intuitive expectation of surface mobility decreasing colloidal stability, there is a dynamic regime in which mobile surface droplets will bounce apart, whereas immobile surfaces droplets coalesce. These novel observations require a reassessment of the role of the surfaces mobility and open new avenues for controlling of the dynamics stability of gas or liquid emulsion systems relevant to a wide range of processes from microfluidics and pharmaceuticals to food and crude oil processing.
E. Klaseboer, F. D. E. Charlet, B.-C. Khoo, Q. Sun, D. Y. C. Chan
Eliminating the ﬁctitious frequency problem in BEM solutions of the external Helmholtz equation
Engineering Analysis with Boundary Elements [EABE_2019_44 Submitted 29 Jan 2019]. pdf
The problem of the spurious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green's function is replaced by a modiﬁed Green's function, it is shown that these spurious frequencies do not necessarily have to correspond to the internal resonance frequency of the object. Together with a recently developed fully desingularized boundary element method that confers superior numerical accuracy, a simple and practical way is proposed for detecting and avoiding these ﬁctitious solutions. The concepts are illustrated with examples of a scattering wave on a rigid sphere.
A. S. Jayaraman, E. Klaseboer, D. Y. C. Chan
The unusual ﬂuid dynamics of particle electrophoresis
Journal of Colloid and Interface Science [JCIS-19-2201 Submitted 11 Apr 2019]. pdf
The classical problem of the electrophoretic motion of a spherical particle has been treated theoretically by Overbeek in his 1941 PhD thesis and almost 40 years later by O'Brien & White. Although both approaches used identical assumptions, the details are quite diﬀerent. Overbeek solved for the pressure and velocity ﬁelds as well as the electrostatic potential whereas O’Brien & White were able to obtain the electrophoretic mobility without the need to consider the pressure and velocity explicitly. In this paper, we establish the equivalence of these two approaches which allow us to show that the tangential component of the ﬂuid velocity has a maximum near the surface of the particle and outside the double layer, the velocity decays as 1/r³, where r is the distance from the sphere, instead of as 1/r in normal Stokes ﬂow. Associated with this behavior is that the outer ﬂow ﬁeld is irrotational. This behavior is consistent with the fact that a sphere moving with a constant electrophopretic velocity experiences zero net force. These results are important in situations in which interparticle interaction is considered, for instance, in electrokinetic deposition.