Dielectrophoretically assembled particles: feasibility for optofluidic systems

Abstract

This work presents the dielectrophoretic manipulation of sub-micron particles suspended in water and the investigation of their optical responses using a microfluidic system. The particles are made of silica and have different diameters of 600, 450, and 250 nm. Experiments show a very interesting feature of the curved microelectrodes, in which the particles are pushed toward or away from the microchannel centerline depending on their levitation heights, which is further analyzed by numerical simulations. In doing so, applying an AC signal of 12 V_p–p and 5 MHz across the microelectrodes along with a flow rate of 1 μl/min within the microchannel leads to the formation of a tunable band of particles along the centerline. Experiments show that the 250 nm particles guide the longitudinal light along the microchannel due to their small scattering. This arrangement is employed to study the feasibility of developing an optofluidic system, which can be potentially used for the formation of particles-core/liquid-cladding optical waveguides.

Appendices

Appendix 1

See Fig. 7.

Fig. 7

The variation of Re[f _CM] for silica particles of 250, 450, and 600 nm particles suspended in DI water

Appendix 2

The electro-convective force induced by Joule heating effect is ignored due to application of a low conductivity medium, which produces a small temperature rise of 0.012 K in the medium, as (Morgan and Green 2003):$\Updelta T \approx {\frac{{\sigma_{\text{m}} V_{\text{rms}}^{2} }}{k}} = {\frac{{2 \times 10^{ - 4} \times 6^{2} }}{0.6}} = 0.012\;K,$, where k is the thermal conductivity of water. Similarly, the electro-convective force induced by light heating is ignored due to the low power of the incident beam, which produces a small temperature rise of 0.014 K in the medium as below:$\Updelta T \approx {\frac{{{\text{power}}_{\text{light}} }}{{\rho_{\text{m}} QC_{\text{m}} }}} = {\frac{{1 \times 10^{ - 3} }}{{10^{3} \times 1.66 \times 10^{ - 8} \times 4.18 \times 10^{3} }}} = 0.014\;K,$ where Q is the flow rate, and C _m is the thermal capacity of water. Finally, the optical radiation pressure force is ignored due to the low power of the incident beam, which induces a small electric field of 18.5 kV/m in the microchannel, as (Paschotta 2008): $E_{\text{light}} = \left( {{\frac{2I}{{c\varepsilon_{0} n_{\text{d - core}} }}}} \right)^{0.5} = \left( {{\frac{{2 \times 6.6 \times 10^{5} }}{{3 \times 10^{8} \times 8.85 \times 10^{ - 12} \times 1.475}}}} \right)^{0.5} = 18.5\;{\text{kV/m}},$ where I is the intensity of light, and c is the speed of light. The I is calculated assuming that all energy is concentrated along the core region with an approximated dimensions of 30 × 50 μm².

Appendix 3

See Fig. 8.

Fig. 8

a Increasing the applied voltage to 20 V_p–p while operating at 5 MHz, increased the negative DEP force and pushed the particles toward the sidewalls. b Increasing of medium flow rate to 2 μl/min destabilized the funneling of particles and caused the width of the narrow band to harmonically change between the consequent pairs.

Appendix 4

The scattering efficiency of particles varies with respect to the influential parameters of an optical system, including the refractive indexes of particles and surrounding medium, the diameter of particles, and the wavelength of the incident light. It can be calculated using the Mie scattering theory (Bohren and Huffman 1983; Hahn 2009), as follows:

$$ \sigma_{\text{scattering}} = {\frac{{\lambda^{2} }}{2\pi }}\sum\limits_{n = 0}^{\infty } {(2n + 1)} \left( {a_{n}^{2} + b_{n}^{2} } \right) $$

(5)

where λ is the relative scattering wavelength, defined as:

$$ \lambda = {\frac{{\lambda_{\text{light}} }}{{n_{\text{d - m}} }}} $$

(6)

In which, λ_light is the wavelength of the incident light, and n _d-m is the refractive index of the medium (or cladding for an optical waveguide). On the other hand, a_n and b_n are defined as below:

$$ a_{n} = {\frac{{\Uppsi_{n} (\alpha ) \cdot \Uppsi_{n}^{\prime } (\alpha \cdot n_{\text{d - p}} ) - n_{\text{d - p}} \Uppsi_{n} (\alpha \cdot n_{\text{d - p}} ) \cdot \Uppsi_{n}^{\prime } (\alpha )}}{{\xi (\alpha ) \cdot \Uppsi_{n}^{\prime } (\alpha \cdot n_{\text{d - p}} ) - n_{\text{d - p}} \Uppsi_{n} (\alpha \cdot n_{\text{d - p}} ) \cdot \xi_{n}^{\prime } (\alpha )}}} $$

(7)

$$ b_{n} = {\frac{{n_{\text{d - p}} \cdot \Uppsi_{n} (\alpha ) \cdot \Uppsi_{n}^{\prime } (\alpha \cdot n_{\text{d - p}} ) - \Uppsi_{n} (\alpha \cdot n_{\text{d - p}} ) \cdot \Uppsi_{n}^{\prime } (\alpha )}}{{n_{\text{d - p}} \cdot \xi (\alpha ) \cdot \Uppsi_{n}^{\prime } (\alpha \cdot n_{\text{d - p}} ) - \Uppsi_{n} (\alpha \cdot n_{\text{d - p}} ) \cdot \xi_{n}^{\prime } (\alpha )}}} $$

(8)

where Ψ and ξ are the Ricatti–Bessel functions (Kerker 1969), n _d-m is the refractive index of the particles (or core for our case), which is the cladding for an optical waveguide, and α is the size parameter defined as:

$$ \alpha = {\frac{{2\pi r \cdot n_{\text{d - m}} }}{{\lambda_{\text{light}} }}} $$

(9)

From the above equations, it is clear that the scattering efficiency varies with respect to refractive indexes of particles and surrounding medium, the diameter of particles, and the wavelength of the incident light.