A Numerical Investigation of Enhancing Microfluidic Heterogeneous Immunoassay on Bipolar Electrodes Driven by Induced-Charge Electroosmosis in Rotating Electric Fields

A unique approach is proposed to boost on-chip immuno-sensors, for instance, immunoassays, wherein an antibody immobilized on the walls of a microfluidic channel binds specifically to an antigen suspended freely within a working fluid. The performance of these sensors can be limited in both susceptibility and response speed by the slow diffusive mass transfer of the analyte to the binding surface. Under appropriate conditions, the binding reaction of these heterogeneous immuno-assays may be enhanced by electroconvective stirring driven by external AC electric fields to accelerate the translating motion of antigens towards immobilized antibodies. To be specific, the phenomenon of induced-charge electroosmosis in a rotating electric field (ROT-ICEO) is fully utilized to stir analyte in the vicinity of the functionalized surface of an ideally polarizable floating electrode in all directions inside a tri-dimensional space. ROT-ICEO appears as a consequence of the action of a circularly-polarized traveling wave signal on its own induced rotary Debye screening charge within a bipolar induced double layer formed on the central floating electrode, and thereby the pertinent electrokinetic streamlines exhibit a radially converging pattern that greatly facilitates the convective transport of receptor towards the ligand. Numerical simulations indicate that ROT-ICEO can enhance the antigen–antibody binding reaction more effectively than convectional nonlinear electroosmosis driven by standing wave AC signals. The effectiveness of ROT-ICEO micro-stirring is strongly dependent on the Damkohler number as well as the Peclet number if the antigens are carried by a continuous base flow. Our results provide a promising way for achieving a highly efficient heterogeneous immunoassay in modern micro-total-analytical systems.


SI Appendix 1: Numerical modeling
A commercial software package, Comsol Multiphysics 5.5, is employed to obtain the complex electric field, ICEO vortex flow field, spatial-temporal delivery of antigen, and surface reaction by fully coupled finite-element simulation. Since ROT-ICEO involves outof-plane effect in essence, full scaled simulation modeling is conducted with a 3D computational domain (Fig.1 for the static case, and Fig.2 for the dynamic condition).
Firstly, we computed the AC potential within the fluid domain by using the Laplace equation for the complex voltage Eq.(1). All the electrodes are subjected to the Robin-type RC charging boundary condition Eq.(2), to describe the phenomenon of electrode polarization. Fixed potential phasor A, jA, -A, and -jA, are imposed to the four discrete DE metal strip along the clockwise direction in sequence with a 90° phase shift between neighboring electrodes, while the square FE in the field center floats in potential.
Insulation condition was imposed to all the channel walls due to the negligibly small polarizability of PDMS material.
Secondly, as for the mechanical problem governed by Eq.(4)(5), all the electrodes are subjected to the expression of ICEO slipping velocity Eq.(3), while we assume a no slip wall boundary condition on other insulating channel walls in the presence of a viscous boundary layer. The amplitude, frequency, and phase sequence of the AC voltage signal, as well as the discrete electrode arrangement, all exert an influence on the ICEO vortex flow profile on top of the FE. As a consequence, improvement of the bound antigen would depend sensitively on the selection of the above boundary conditions. Thirdly, the mass conservation of antigen concentration in the regime of dilute species was solved by using Eq. (6)(7)   Then a transient solver is adopted to compute both the analyte transport in the bulk and the binding reaction at the functionalized surface in a coupled way considering their timedependent nature.
As shown in the bi-dimensional phase diagram of ROT-ICEO (Fig.3) Fig.S4(a). As for case (ii), since the voltage phase was sequentially shifted by 180° for every two electrodes ( Fig.S1(a)(b)), the externally-applied electric field lines under the excitation of a such voltage sequence are inclined with respect to the central FE, as shown in Fig.S1(a), and just alternates in direction with time elapses (Fig.S1(b)). Even so, the converging ICEO flow pattern parallel to the field lines remains unchanged in slipping direction ( Fig.S1(a) All the above calculations of ICEO flow field are obtained at a voltage amplitude of V 0 =4V and respective optimum field frequency. According to the calculation results, the ICEO flow velocity shows strong frequency-dependence for all the three convection modes ( Fig.S2(b)), and the same also holds true for their ACEO counterpart on the DE array ( Fig.S2(a)). Both the ICEO and ACEO flow fields reach a single relaxation peak at an intermediate field frequency, regardless of the specific power supply modes ( Fig.S2(a)(b)). =800Hz serving as the low and high frequency threshold, respectively. As shown in Fig.S2(a), ACEO for both (i) and (ii) convection modes reaches a single relaxation peak at f ideal =200Hz, while case (i) possesses a much broader force plateau than case (ii). The ideal driving frequency of ACEO for case (iii) attains 300Hz, being higher than that for case (i) and (ii), and its maximum ACEO flow velocity is highest among the three convection modes.
As for ICEO, the opposite has happened. The (iii) powering scheme results in the weakest ICEO fluid motion than other two convection modes, with the typical ICEO flow velocity merely on the order of O(1)μm/s ( Fig.S2(b)), albeit its ACEO counterpart is strongest ( Fig.S2(a)). ICEO for case (i) and (ii) exhibits an identical frequency-dependent variation trend with a slightly larger flow speed of case (ii) than that of case (i). Even so, the convection mode of ROT-ICEO driven by case (i) is supposed to be able to engender better improvement of the antigen-antibody binding reaction due to its more favorable slip profile that the liquid medium is sucked at the electrode edge from all outer directions and is then ejected upward at the center of the electrode surface whatever the signal frequency is ( Fig.S4(a-d)), in stark contrast with the linear slipping fluid motion for case (ii) (Fig.S5(c)) and the vanishing ICEO flow field for case (iii) (Fig.S6(c)). In addition, in case (i), wherein a rotating electric field emits from the peripheral DE array, ACEO has a net counterclockwise rotating flow component in the direction of the rotating electric field ( Fig.S3(a)(d)). This large whirlpool induced in the field center dominates the global electrokinetic flow behavior at low frequencies, (Fig.S3(a)(d)(b)(e)), and diminishes as the field frequency further increases (Fig.S3(c)(f)). In this way, it is more beneficial to employ the convergent ICEO slipping pattern (Fig.S4)