On the Bipolar DC Flow Field-Effect-Transistor for Multifunctional Sample Handing in Microfluidics: A Theoretical Analysis under the Debye⁻Huckel Limit

Abstract

We present herein a novel method of bipolar field-effect control on DC electroosmosis (DCEO) from a physical point of view, in the context of an intelligent and robust operation tool for stratified laminar streams in microscale systems. In this unique design of the DC flow field-effect-transistor (DC-FFET), a pair of face-to-face external gate terminals are imposed with opposite gate-voltage polarities. Diffuse-charge dynamics induces heteropolar Debye screening charge within the diffuse double layer adjacent to the face-to-face oppositely-polarized gates, respectively. A background electric field is applied across the source-drain terminal and forces the face-to-face counterionic charge of reversed polarities into induced-charge electroosmotic (ICEO) vortex flow in the lateral direction. The chaotic turbulence of the transverse ICEO whirlpool interacts actively with the conventional plug flow of DCEO, giving rise to twisted streamlines for simultaneous DCEO pumping and ICEO mixing of fluid samples along the channel length direction. A mathematical model in thin-layer approximation and the low-voltage limit is subsequently established to test the feasibility of the bipolar DC-FFET configuration in electrokinetic manipulation of fluids at the micrometer dimension. According to our simulation analysis, an integrated device design with two sets of side-by-side, but upside-down gate electrode pair exhibits outstanding performance in electroconvective pumping and mixing even without any externally-applied pressure difference. Moreover, a paradigm of a microdevice for fully electrokinetics-driven analyte treatment is established with an array of reversed bipolar gate-terminal pairs arranged on top of the dielectric membrane along the channel length direction, from which we can obtain almost a perfect liquid mixture by using a smaller magnitude of gate voltages for causing less detrimental effects at a small Dukhin number. Sustained by theoretical analysis, our physical demonstration on bipolar field-effect flow control for the microfluidic device of dual functionalities in simultaneous electroconvective pumping and mixing holds great potential in the development of fully-automated liquid-phase actuators in modern microfluidic systems.

Keywords: bipolar DC field-effect flow control; counterionic Debye screening; flow field-effect-transistor; induced-charge electroosmosis; linear electroosmosis; simultaneous electroconvective pumping and mixing in microfluidics.

Figure 1

2D schematic diagrams of the microfluidic device for bipolar DC field-effect electroosmosis control. (a) Geometric configuration of a bipolar DC flow field-effect-transistor (DC electroosmosis (DCEO)), in which one or several pairs of face-to-face gate (G) terminals of counter voltage polarities are embedded in a straight microchannel on the external surfaces of both sidewalls. (b,c) A vivid illustration of the physicochemical mechanism responsible for causing simultaneous sample pumping and mixing with different discrete arrangements of the external gate electrode array; (b) in the structural configuration of one pair of face-to-face oppositely-polarized gate-electrode, an individual induced-charge electroosmotic (ICEO) vortex is induced across the channel width direction next to the two G terminals; and (c) in the microfluidic device of two neighboring sets of upside-down G terminal pairs, a pair of ICEO whirlpools in reversed rotating directions is induced in the vicinity of the four external gate electrodes. Interestingly, in (c) the pair of symmetric counter-rotating ICEO micro-vortices is induced by nonlinear electroosmotic slip on the surface of polarizable membranes, within which strong electric field leakage occurs due to the action of external G terminals, and the electrokinetics-driven turbulence adds effectively to the horizontal DCEO flow component in the forward direction to achieve simultaneous pumping and mixing of electroneutral chemical analytes in microfluidics.

Figure 2

Effect of the length of gate terminal L_G on the device performance in terms of dual functionalities. (a,b) An arrow and surface plot of the electroosmotic flow field and analyte concentration distribution in the straight microchannel. (a) Passive mixing of incoming samples carried by a forward electroosmotic pump flow rate of 47 μm/s under Vs = 30 V in the absence of gate voltage supplies, where merely the molecular diffusion effect in the vertical concentration gradient across the phase interface between the two co-flowing laminar streams occurs and is responsible for the passive mixing process, resulting in a poor mixing index of 27.8%. (b) Active mixing is actuated with all the DC voltage terminals turned on, in which the pump flow along the channel axial direction is caused by DC electroosmosis, and the lateral turbulent mixing flow is originated by ICEO from Bipolar DC Flow Field-Effect Transistor (B-DCFFET) with a GE length of L_G = 150 μm, for given values of V_S = 30 V, V_G1 = −V_G2 = 1500 V, giving rise to an enhanced mixing performance of γ = 72.81%. (c) L_G-dependent device mixing performance. (d) Electroosmotic pump and mixing flow velocity as a function of the width of the G terminal. (e) Distribution of the induced zeta potential at the solution/membrane interface adjacent to the gate electrode with different L_G; the negative sign indicates positive counterionic charges in the vicinity of the negatively-polarized G terminal.

Figure 3

Effect of the magnitude of gate voltage V_G on the device performance, for given values of L_G = 150 μm and Vs = 30 V. (a) An arrow and surface plot of electroosmotic streamlines and the resulting molar concentration distribution of electroneutral chemical analyte (unit: mol/m³) under V_G = 2000 V of γ = 82.42%. (b) V_G-dependent mixing performance. (c) Electroosmotic flow velocity in terms of pumping and mixing as a function of the magnitude of gate voltage V_G. (d) Distribution of the non-uniform induced zeta potential along the channel sidewall adjacent to the negatively-polarized gate electrode for distinct V_G, in which the negative sign implies a positive charge cloud within the Debye layer above the right-side G terminal.

Figure 4

Effect of source voltage magnitude Vs on the efficiency of device bifunctionality, for given values of V_G = 2000 V and L_G = 150 μm. (a) An arrow and surface plot of the electroosmotic flow field and resulting analyte mass distribution (unit: mol/m³) under Vs = 70 V with γ = 73.03%. (b) Vs-dependent device mixing performance. (c) Characteristic pumping and mixing flow velocity of electroosmosis as a function of the source voltage Vs. (d) Distribution of inhomogeneous induced zeta potential at the sidewall/medium interface next to the negatively-polarized G terminal for varying Vs; the minus sign means positive charge cloud is induced inside the diffuse double layer above the right-side G terminal.

Figure 5

In an improved device configuration with two neighboring sets of gate electrode pairs, a numerical analysis of the effect of electrode separation L_GG between adjacent G terminals for given values of Vs = 70 V, V_G1 = −V_G2 = 2000 V and L_G = 150 μm. (a,b) An arrow and surface plot of DCEO fluid motion and resulting analyte concentration distribution (unit: mol/m³) for different combinations of external gate polarities; (a) for a neighboring GE pair of identical voltage polarity, two sequential ICEO vortexes of the same rotating directions are produced in the vicinity of the four G terminals, so that a non-ideal mixing efficiency of γ = 83.66% is obtained at the channel exit; and (b) for two external sets of gate electrodes of an upside-down polarity combination, an alternation in the rotating direction of the forward sample motion trajectory within the mixing region enables a much higher mixing performance of γ = 92.43% at the outlet port, which is named ‘double-inverted B-DCFFET’. (c–e) For double-inverted B-DCFFET, (c) the mixing index as a function of interelectrode gap width L_GG, (d) L_GG-dependent electroosmotic pump and mixing flow velocity and (e) distribution of non-uniform induced zeta potential along the planar channel sidewall adjacent to the left two gate electrodes of opposite voltage polarities for different interelectrode separations L_GG, in which the left-side positive and right-side negative zeta potential represent the negative and positive induced counterionic charges next to the side-by-side positively- and negatively-polarized G terminals, respectively.

Figure 6

Simultaneous pumping and mixing of microflows in the device configuration with different sets of inverted B-DCFFET. (a–e) For given values of Vs = 70 V, V_G1 = −V_G2 = 900 V, L_G = 150 μm and L_GG = 100 μm, an arrow and surface plot of the DCEO flow field and resulting sample concentration distribution (mol/m³) in the integrated device design of a distinct number of G terminals; (a) single-inverted B-DCFFET of γ = 49.83%, (b) double-inverted B-DCFFET of γ = 74.38%, (c) triple-inverted B-DCFFET of γ = 85.71%, (d) quadruple-inverted B-DCFFET of γ = 88.87%, (e) quintuple-inverted B-DCFFET of γ = 92.45% and (f) sextuple-inverted B-DCFFET of γ = 94.79%. It is noteworthy that the highly-integrated electroosmotic pump and mixer embedded with twelve gate terminals of alternating voltage polarities exhibits optimum performance for fully-automated electrokinetics-driven analyte treatment (f), which makes it possible for us to receive almost perfect liquid mixture in the channel outlet port.

Figure 7

Effect of the number of gate electrode terminals (n) on the dual functionalities of the integrated device configuration, for given values of Vs = 70 V, V_G1 = −V_G2 = 900 V, L_G = 150 μm and L_GG = 100 μm. (a) n-dependent mixing performance. (b) Pump and mixing electroosmotic flow velocity as a function of the number of gate electrode pairs. (c) The largest value of induced zeta potential at the polarized liquid/membrane interface for a distinct number of G terminal pairs.

Figure 8

Effect of liquid conductivity σ_f on the device performance for sextuple-alternated B-DCFFET, for given values Vs = 70 V, V_G1 = −V_G2 = 700 V, L_G = 150 μm and L_GG = 100 μm. (a) An arrow and surface plot of the electroosmosis flow field and resulting molar concentration distribution of chemical analyte (unit: mol/m³) with σ_f = 0.005 S/m. (b) σ_f-dependent mixing efficiency. (c) Electroosmotic flow velocity in terms of pump and mixing fluid motions at varying liquid conductivities σ_f. (d) A quantitative comparison between the magnitude of native zeta potential $\left|{\zeta }_{\mathrm{fixed}}\right|$ and maximum induced zeta potential ${\zeta }_{\mathrm{induced}}^{\mathrm{maximum}}$ at the membrane/solution interface, as a function of the medium conductivity σ_f.

Figure 9

Effect of the absolute value of fixed surface charge density $\left|{\sigma }_{\mathrm{free}}\right|$ on the dual functionalities of the sextuple-alternated B-DCFFET device, for given values of Vs = 70 V, V_G1 = −V_G2 = 700 V, L_G = 150 μm, L_GG = 100 μm and σ_f = 0.005 S/m. (a) An arrow and surface plot of electrokinetic streamlines and analyte concentration distribution (unit: mol/m³) with ${\sigma }_{\mathrm{free}}$ = –0.0002 C/m². (b) $\left|{\sigma }_{\mathrm{free}}\right|$ -dependent device mixing performance. (c) Electroosmotic pumping and mixing flow velocity for varying values of $\left|{\sigma }_{\mathrm{free}}\right|$. (d) A quantitative comparison between the magnitude of native zeta potential $\left|{\zeta }_{\mathrm{fixed}}\right|$ and the maximum induced zeta potential ${\zeta }_{\mathrm{induced}}^{\mathrm{maximum}}$ at the membrane/electrolyte interface, as a function of the magnitude of the fixed surface charge density $\left|{\sigma }_{\mathrm{free}}\right|$ on channel sidewalls.

Figure 10

A simulation analysis of the influence of the thickness of dielectric membrane W_ins on the device performance of sextuple-alternated B-DCFFET, under given values of Vs = 70 V, V_G1 = −V_G2 = 700 V, L_G = 150 μm, L_GG = 100 μm, σ_f = 0.005 S/m and ${\sigma }_{\mathrm{free}}$ = –0.0002 C/m². (a) An arrow and surface plot of DCEO streamlines and analyte molar concentration distribution (unit: mol/m³) with W_ins = 20 μm. (b) W_ins-dependent device mixing efficiency. (c) Electroosmotic pumping and mixing flow velocity at different membrane thicknesses. (d) A quantitative comparison between the magnitude of native zeta potential $\left|{\zeta }_{\mathrm{fixed}}\right|$ and maximum induced zeta potential ${\zeta }_{\mathrm{induced}}^{\mathrm{maximum}}$ at the membrane/electrolyte interface, as a function of the membrane thickness W_ins of the dielectric coating layer.

Figure 11

Calculation results of the influence of the dielectric permittivity of the insulation membrane ε_ins on the device performance of the sextuple-alternated B-DCFFET, under given values of Vs = 70 V, V_G1 = −V_G2 = 700 V, L_G = 150 μm, L_GG = 100 μm, W_ins = 20 μm, σ_f = 0.005 S/m and ${\sigma }_{\mathrm{free}}$ = –0.0002 C/m². (a) An arrow and surface plot of electroconvective streamlines and analyte molar concentration distribution (unit: mol/m³) with ε_ins = 20ε₀. (b) ε_ins-dependent device mixing performance. (c) Electroosmotic pumping and mixing flow velocity for distinct membrane dielectric permittivity. (d) Comparison between the native zeta potential $\left|{\zeta }_{\mathrm{fixed}}\right|$ and maximum induced zeta potential ${\zeta }_{\mathrm{induced}}^{\mathrm{maximum}}$ at the sidewall/medium interface, as a function of the relative permittivity of the dielectric layer.