Light-induced thermoosmosis about conducting ellipsoidal nanoparticles

Abstract

We consider the central problem of a non-spherical (ellipsoidal) polarizable (metallic) nanoparticle freely suspended in a conducting liquid phase which is irradiated (heated) by a laser under the Rayleigh (electrostatic) approximation. It is shown that, unlike the case of perfectly symmetric (spherical) particles, the surface temperature of general orthotropic particles exposed to continuous laser irradiation is not uniform! Thus, the induced surface slip (Soret type) velocity may lead to a self-induced thermoosmotic flow (sTOF) about the particle, in a similar manner to the electroosmotic flow driven by the Helmholtz-Smoluchowski slippage. Using the recent advancement in the theory of Lamé functions and ellipsoidal harmonics, we analytically present new solutions for two key physical problems. (i) Heat conduction and temperature distribution inside and outside a conducting laser-irradiated homogeneous tri-axial ellipsoid which is subjected to uniform Joule heating. (ii) Creeping (Stokes) sTOF around a fixed impermeable metallic ellipsoidal nanoparticle driven by a Soret-type surface slip velocity (i.e. proportional to the surface-temperature gradient).

Light-induced heat-conducting micro/nano spheroidal particles and their thermoosmotic velocity fields

“…The situation for non-spherical shapes is somewhat different. A general analytical solution for a triaxial ellipsoidal particle embedded in a medium with a uniform ambient temperature was recently derived by Miloh [15] using Làme functions. The non-spherical geometry was shown to cause a temperature variation along the surface of the particle and hence a thermoosmotic flow field was induced around it.…”

AC Electrokinetics of Polarizable Tri-Axial Ellipsoidal Nano-Antennas and Quantum Dot Manipulation

“…Our next task is to analytically solve the homogeneous Stokes equation (8) for the ACEO velocity field, which is subjected to the velocity-slippage Equation (9). For this purpose, let us assume the following expression for the velocity field trueu→false(nfalse)(u1false(nfalse),u2false(nfalse),u3false(nfalse)) that is induced by polarization due to uniform ambient electric excitation E0 acting along the xn direction [44] (n=1,2,3) uifalse(nfalse)(x1,x2,x3)=true∑k=13Ak(n)(xk∂ψk∂xi−δikψk)+a1Bfalse(nfalse)∂Φfalse(nfalse)∂xi…”

“…What remains now is to explicitly determine the velocity field by obtaining the coefficients Ak(n) in (21) and B(n) in Equation (25) using the boundary conditions Equation (9). Let us first note that by combining Equations (22) with (21), the ACEO velocity field can be expressed in a vector form as [44] trueu→(n)false(x1,x2,x3false)=a12true∑k=13Ak(n)xk2∇I1k(ρ)+a1Bfalse(nfalse)∇Φfalse(nfalse) which implies that the first term on the right hand side of Equation (27) does not have any tangential component along S, since by definition ∇tI1kfalse(ρfalse)=0 on ρ=a1. Thus, by virtue of Equation (23) and Equation (25), one gets Φ(n)(a1,…”

“…Our next task is to analytically solve the homogeneous Stokes equation (8) for the ACEO velocity field, which is subjected to the velocity-slippage Equation (9). For this purpose, let us assume the following expression for the velocity field that is induced by polarization due to uniform ambient electric excitation acting along the direction [ 44 ] such that both and are harmonic functions (namely ) which decay away from and denotes the Kronecker delta. Here, and are dimensionless geometric coefficients to be determined depending on the direction of the applied AC electric field.…”

“…What remains now is to explicitly determine the velocity field by obtaining the coefficients in (21) and in Equation (25) using the boundary conditions Equation (9). Let us first note that by combining Equations (22) with (21), the ACEO velocity field can be expressed in a vector form as [ 44 ] which implies that the first term on the right hand side of Equation (27) does not have any tangential component along , since by definition on . Thus, by virtue of Equation (23) and Equation (25), one gets and when combined together with Equations (7), (9), and (20), the coefficient can be finally resolved in terms of the parameter Equation (20), as …”