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The formation of pairs and trains of particles in inertial microfluidics is an important consideration for device design and applications, such as particle focusing and separation. We study the formation and stability of linear and staggered pairs of nearly rigid spherical particles of different sizes in a pressure-driven flow through a straight duct with a rectangular cross section under mild inertia. An in-house lattice-Boltzmann-immersed-boundary-finite-element code is used for three-dimensional simulations. We find that the stability and properties of pairs of heterogeneous particles strongly depend on particle sizes and their size ratio, while the formation of the pairs is also determined by the initial lateral position and the axial order of the particles. Our findings imply that perturbations of particle trajectories caused by other particles, as they are expected to happen even in dilute suspensions, can be important for the formation of stable pairs in inertial microfluidics.

Abstract. Staggered and linear multi-particle trains constitute characteristic structures in inertial microfluidics. Using lattice-Boltzmann simulations, we investigate their properties and stability, when flowing through microfluidic channels. We confirm the stability of cross-streamline pairs by showing how they contract or expand to their equilibrium axial distance. In contrast, same-streamline pairs quickly expand to a characteristic separation but even at long times slowly drift apart. We reproduce the distribution of particle distances with its characteristic peak as measured in experiments. Staggered multi-particle trains initialized with an axial particle spacing larger than the equilibrium distance contract non-uniformly due to collective drag reduction. Linear particle trains, similar to pairs, rapidly expand toward a value about twice the equilibrium distance of staggered trains and then very slowly drift apart non-uniformly. Again, we reproduce the statistics of particle distances and the characteristic peak observed in experiments. Finally, we thoroughly analyze the damped displacement pulse traveling as a microfluidic phonon through a staggered train and show how a defect strongly damps its propagation. Graphical abstract

With the development of nanotechnology, many new optical phenomena in nanoscale have been demonstrated. Through the coupling of optical waves and collective oscillations of free electrons in metallic nanostructures, surface plasmon polaritons can be excited accompanying a strong near field enhancement that decays in a subwavelength scale, which have potential applications in the surface-enhanced Raman scattering, biosensor, optical communication, solar cells, and nonlinear optical frequency mixing. In the present article, we review the Green's matrix method for solving the surface plasmon resonances and near field in arbitrarily shaped nanostructures and in binary metallic nanostructures. Using this method, we design the plasmonic nanostructures whose resonances are tunable from the visible to near-infrared, study the interplay of plasmon resonances, and propose a new way to control plasmonic resonances in binary metallic nanostructures.

Metallic nano-structures characterised by multiple geometric length scales support low-frequency surface-plasmon modes, which enable strong light localization and field enhancement. We suggest studying such configurations using singular perturbation methods, and demonstrate the efficacy of this approach by considering, in the quasi-static limit, a pair of nearly touching metallic nano-spheres subjected to an incident electromagnetic wave polarized with the electric field along the line of sphere centers. Rather than attempting an exact analytical solution, we construct the pertinent (longitudinal) eigen-modes by matching relatively simple asymptotic expansions valid in overlapping spatial domains. We thereby arrive at an effective boundary eigenvalue problem in a half-space representing the metal region in the vicinity of the gap. Coupling with the gap field gives rise to a mixed-type boundary condition with varying coefficients, whereas coupling with the particle-scale field enters through an integral eigenvalue selection rule involving the electrostatic capacitance of the configuration. By solving the reduced problem we obtain accurate closed-form expressions for the resonance values of the metal dielectric function. Furthermore, together with an energy-like integral relation, the latter eigen-solutions yield also closed-form approximations for the induced-dipole moment and gap-field enhancement under resonance. We demonstrate agreement between the asymptotic formulas and a semi-numerical computation. The analysis, underpinned by asymptotic scaling arguments, elucidates how metal polarization together with geometrical confinement enables a strong plasmon-frequency redshift and amplified near-field at resonance., 13 pages, 7 figures

Investigation on the interplay of plasmonic resonances in binary nanostructures indicated that, at a fixed wavelength, with a variation in the difference permittivity ratio eta=(epsilon(2)-epsilon(0)/epsilon(1)-epsilon(0)), resonances exhibit the dielectric effect, resonance chaos, collective resonance, resonance flat, and new branch regions. This means that plasmonic resonances can be controlled by material parameters epsilon(1) and epsilon(2). In this work, using the Green's matrix method of solving the surface plasmon resonances, we first study the resonance combination of symmetrical binary three-nanostrip systems. Several resonance branches extend across the above mentioned regions. Near fields within the gaps and at the ends of nanostrips are greatly enhanced due to the influence of neighboring metallic material. Then, along each resonance branch, resonances in the dielectric permittivity region are mapped into the wavelength region of gold. Through adjusting material parameters epsilon(1) and epsilon(2), the resonance wavelength is tuned from lambda(R)=500 to 1500 nm, while for a single nanostrip it is only at lambda(R)=630 nm. We also find that comparable permittivity parameters epsilon(1) (or epsilon(2)) and epsilon(Au)(omega) can control resonance wavelength and intensity effectively. High dielectric permittivity of the neighboring metal has also an advantage in a giant enhancement of the near field. These findings provide new insights into design of hybrid plasmonic devices as plasmonic sensors. (C) 2010 American Institute of Physics. [doi:10.1063/1.3407527]

By introducing the difference permittivity ratio eta=(epsilon (2)-epsilon (0))/(epsilon (1)-epsilon (0)), the Green matrix method for computing surface plasmon resonances is extended to binary nanostructures. Based on the near field coupling, the interplay of plasmon resonances in two closely packed nanostrips is investigated. At a fixed wavelength, with varying eta the resonances exhibit different regions: the dielectric effect region, resonance chaos region, collective resonance region, resonance flat region, and new branches region. Simultaneously, avoiding crossing and mode transfer phenomena between the resonance branches are observed. These findings will be helpful to design hybrid plasmonic subwavelength structures.