LOC microsystems have grown quickly in sophistication and number over the last ten years. This development is tightly linked to the growing field of digital microfluidics (DMF) systems. Indeed, DMF has emerged as a promising technology to manipulate droplets and bio-components at will on a 2D surface using, in most cases, EWOD forces. In such digital microfluidic circuit devices, most fluidic operations can be carried out on a chip using discrete droplets rather than usual continuous flows. Droplets creation and displacement using EWOD or LDEP allows for elementary microfluidic operations [1-5] and complex biological assays [5-9] with high precision in terms of displacement, reproducibility and low power consumption.

EWOD transduction mechanism is based on capillary forces modification at the interface in-between conductive liquid on top of an insulating layer. This modification occurs while applying an AC voltage to either underneath electrodes (in case of open microfluidic) or opposite-sides facing electrodes (in case of parallel-plate microfluidic). This concept has been widely studied [10-14] and benefits from its inherent effectiveness at the microscale and simplicity in terms of implementation. However, according to the literature, EWOD transduction is generally efficient unless the displaced liquids are conductive, and thereof could not be used to move organic solvents and dielectric solutions that may be required to carry complex biological protocols. Nevertheless, some articles show that low-conductive liquids and organic solvents can be manipulated by EWOD transduction [9,15]. Liquid actuation by Liquid DiElectroPhoresis (LDEP) is considered as an alternative solution, since it is more suitable for dielectric liquids. According to Jones et al. [16,17], EWOD and LDEP transduction can be modeled using frequency dependent electromechanical forces: in particularly above a critical frequency f_c, a given liquid is displaced by LDEP transduction, and reversely below f_c the EWOD transduction dominates. References [16,17] describe the LDEP as an electromechanical response of a liquid deposited onto two coplanar electrodes and polarized using an AC voltage. The electrodes create a non-uniform electrical field under AC voltage and the DEP force attracts the polarizable liquid into regions of higher electrical field. One of the identified issues related to LDEP actuation is the required actuation voltage which is usually above 200 V_RMS for a single-plate open microfluidic device, together with a frequency range of 1 kHz to 1 MHz [18-20]. Such high voltages may lead to the chip dielectric layer breakdown and liquid electrolysis. Consequently, a current challenge is to lower the actuation voltage, to fit also the specifications of standard characterization equipments and enable future co-integration with the CMOS signal processing circuit to provide a complete μTAS system onto a single chip.

To achieve this goal, this paper is proposing some guidelines and design tools for a reliable LDEP actuation with low voltage and low frequency actuation. This study is based on the electromechanical models presented in References [21] and [22]. By integrating the effects of the geometry and the impact of the materials on the actuation voltage, this study gives key rules to minimize both threshold actuation voltage V_th and critical frequency f_c. The paper is organized as follows: first we introduce the LDEP theory. Next section describes the parameters of the LDEP experimental setup. Theoretical and experimental results are finally compared in the last section.

A model for LDEP was developed in [16,17,21,23]. This model assumed that an electrostatic force is able to break the capillary equilibrium of a droplet. Recently, Reference [22] has completed the model by introducing a global electromechanical energy paradigm to describe both EWOD and LDEP transduction. According to [22], the liquid displacement is generated thanks to a unified electromechanical force, which is the sum of the LDEP force and the EWOD force. Depending on the liquid properties and the applied frequency, one force becomes preponderant beyond the other. For low frequencies, the EWOD force is assumed to be preponderant, while for higher frequencies the LDEP force becomes higher. The frequency limit between the two forces has to be determined. In the literature, two LDEP device configurations can be found: the parallel-plate closed microfluidic device [Figure 1(b)] [24,25] and the single-plate open microfluidic device [Figure 1(a)] [26-28]. In order to clearly establish the advantages and drawbacks of both systems, those configurations will be compared in this study. On the one hand, the single plate device features two coplanar electrodes, separated by a gap g, patterned onto a substrate [Figure 1(a)]. The electrodes are covered by a dielectric layer and a thin hydrophobic layer (the dielectric layer can be itself hydrophobic preventing from an additional coating). The hydrophobic layer minimizes the effects of contact angle hysteresis and the static friction [20]. The electric field constrains the liquid in a semi circular profile centered in the inter-electrode gap [23]. On the other hand, the parallel-plate closed microfluidic device consists in applying a voltage between an electrode patterned onto the bottom substrate and a facing electrode located on the above plate [Figure 1(b)]. A hydrophobic layer covers a dielectric layer in both plates.

In order to calculate the electromechanical force, the system is modeled as an equivalent electrical circuit. The equivalent circuit is described in Figure 2(a). Each dielectric/hydrophobic layer is considered as a pure capacitance. The liquid, as an imperfect conductor, is modeled using a resistance and a parallel capacitance. Z_d, Z_h, Z_liq and Z_air represent respectively the impedance of the dielectric layer, of the hydrophobic layer, of the liquid and of the air in the case of a single-plate open microfluidic device. The model described in this paragraph is related to the single-plate open microfluidic device configuration. A comparison between both configurations is presented later on.

The equivalent RC electrical circuit model is illustrated on the Figure 2(a) where ε₀, ε_d, ε_h, ε_liq and σ_liq, are respectively the vacuum permittivity, the dielectric layer permittivity, the hydrophobic layer permittivity, the dielectric constant and the conductivity of the liquid. d, h, w and g represent respectively the dielectric layer thickness, the hydrophobic layer thickness, the electrode width and the inter-electrode gap. K(k) is the complete elliptic integral of the first kind [20] and its modulus is k = g g + 2 w. Lastly, the liquid is defined by a capacitance value C_liq and a conductance value g_liq.

Based on the equivalent circuit model [Figure 2(a)], the electric potentials across each layer can be evaluated as a function of the RMS applied tension V and the complex impedances of the system. The total energy inside the system is deduced from the sum of each potential energy stored by each capacitance of the device [22]: (10) U = ∑ i 1 2 C i V i 2 (11) V i = Z i ∑ j Z j Vwhere C_i is the capacitance and V_i the voltage at the terminals of the i^th circuit element.

Considering all the capacitances inside the device, the total electromechanical force can now be expressed from the total energy derived with respect to the displacement direction (here according to the y-axis), and is given by: (12) F E M = ∂ U ∂ y = ε 0 C d ( V d / liq 2 − V d / air 2 ) + ε 0 C h ( V h / liq 2 − V h / air 2 ) ︸ F EWOD + ε 0 2 ( C liq V liq 2 − C air V air 2 ) ︸ F LDEPwhere V_d/liq, V_d/air, V_h/liq, V_h/air, V_liq and V_air represent the voltage across the dielectric layer at the liquid filled side and the air filled side, the voltage across the hydrophobic layer at the liquid filled side and the air filled side, the voltage of the liquid and the voltage of the surrounding air respectively [Figure 2(a)]. Chaterjee et al. [22] assume the total force to be the sum of the EWOD force acting at the three-phase contact line and the LDEP force acting on the liquid-air interface advancing side.

An important parameter of LDEP actuation is the threshold frequency f_c of the AC electric field. Since liquids conductivity varies according to the applied voltage AC frequency, f_c represents a transition in the liquid behavior. When f ≪ f_c, the liquid behaves as a conductor (the liquid is isopotential) and is predominantly moved by EWOD forces. On the contrary if f ≫ f_c, the liquid behaves as a dielectric (electric field lines entering the liquid) and is moved using the LDEP forces. Literal expression of f_c is thereby written as the ratio of the overall capacitance of the liquid filled side over its total conductance [left branch of equivalent electric circuit in Figure 2(a)].

Given the expression of both the electromechanical force and the other forces acting on the liquid (e.g., the capillary force F_cap and the viscous force F_visc), the fundamental dynamic principle leads to a literal expression describing both the position and velocity of the liquid finger as a function of time [29] (14) ρ π ( w + g 2 ) 2 2 d d t [ y d y d t ] = F EM + F cap + F visc ( y , t )

At t = 0, in order to enable the liquid to move along the y direction, the electromechanical force must overcome the capillary forces: F_EM > F_cap. This condition is theoretically satisfied as soon as the RMS applied voltage V is higher than a threshold voltage V_th given by Equation (15).

The expression (15) is associated to a typical stack composed of a dielectric layer (dielectric constant ε_d, thickness d) and a hydrophobic layer (dielectric constant ε_h, thickness h). The characteristic length α is introduced hereafter (17), and refers to the global dielectric/hydrophobic layer stack properties. As α is increasing, V_th is increasing satisfying the following Equation (16): (16) V th = 2 F cap ( 2 α ε 0 w + 1 C liq * ) ( 2 α ε 0 w + 1 C air * ) 1 C liq * − 1 C air * (17) α = h ε d + d ε h ε d ε hwhere C_liq * and C_air * are respectively the capacitance of liquid and air derived with respect to the liquid displacement direction.

The previous expression is valid for chips composed of either two independent layers (an hydrophobic layer onto a dielectric layer) or a single layer featuring both dielectric and hydrophobic properties. The characteristic length α influence on the threshold voltage is inspected in Section 4.2.

The voltages across each layer, and therefore the electric fields contained in the layers or in the liquid, can be extracted from the previous LDEP model. Dielectric material has an inherent breakdown field. In order to prevent from dielectric breakdown voltage, the best matching in between dielectric and hydrophobic thicknesses can be adjusted by incorporating the electric field E_h (electric field across the hydrophobic layer) into the LDEP model. Indeed a linear relationship exists between thicknesses d and h as a function of E_h and the capacitances of the system. The relation (18) is valid for V = V_th and the hydrophobic layer potential in the air filled side is neglected in regard with its potential in the liquid filled side.

Z_h* represents the hydrophobic layer impedance per unit of length and is expressed in Ω.m⁻¹. The threshold voltage used to optimize the LDEP device is exposed in Equations (15) and (16) for a frequency threshold written in (13). Similarly to the work of Saeki et al. [30] about voltage reduction for EWOD actuation, the next section deals with the influence of the parameters to be optimized in order to achieve LDEP actuation with low voltage and low frequency.

In order to benchmark this model, the effect of the geometry has been studied experimentally, with the electrode width w ranging from 3 to 20 μm and the inter-electrodes gap g ranging from 2 to 20 μm. Since the model discussed previously focuses on protrusion generation and not on its break up into droplets, simple parallel coplanar electrodes have been designed (Figure 3).

Chips have been manufactured by patterning 170 nm thick aluminum electrodes on a Si wafer (Pyrex), the latter being coated by a 100 nm Teflon-like passivating layer (on which DI water makes a contact angle θ = 110°).

The parent DI-water droplet is delivered with a manual 5 μL pipette directly on the electrodes. The experimental protocol consists in monitoring the threshold voltage which leads to a protrusion generation. All experiments have been done at 100 kHz.

This section presents results towards the minimization of the threshold required voltage V_th. We present in Section 4.1 theoretical and experimental results showing the electrodes geometry effects onto V_th, in Section 4.2 the theoretical effect of materials on V_th (i.e., the effect of the characteristic length α), in Section 4.3 the tradeoff in between the isolating layer(s) thickness reduction, and its electrical breakdown prevention is considered; and in Section 4.4 a comparison is carried out for both device microfluidic configurations.

Based on existing electromechanical models, this article suggests some design key rules to reduce both applied voltage and frequency for a LDEP actuation. The chip microfluidic configuration, its constituent layers dielectric properties, and the electrode design are the most important parameters to tune in order to reduce the actuation threshold voltage. Regarding the chip materials, numerical simulations highlighted that the layers should feature high dielectric constant together with low thickness, while preventing material dielectric breakdown and therefore electrolysis phenomenon. As an example, standard stacked layers composed of a 300 nm thick SiOC layer onto a 300 nm thick SiN layer leads to an expected actuation threshold voltage higher than 150 V_RMS, while it is smaller than 50 V_RMS for a single 50 nm thick Al₂O₃ or ZrO₂ layer. These stacked layers theoretically prevent dielectric breakdown field since the electric fields across the layers do not exceed 2 MV cm⁻¹ (see Table 3). In other words, the threshold voltage can be decreased by a factor of 2/3. Besides the constituent chip material influences, LDEP model highlighted that there are also optimized electrode design parameters (w,g) which reduce the threshold voltage. Some electrode design examples have been compared experimentally and theoretically, based on a single 100 nm thick Teflon-like passivating layer, in a single plate open microfluidic configuration. The experiments have shown fair agreement between the measured threshold voltage and the expected theoretical value. The maximum error is less than 40%. As far as the comparison between the fluidic configurations (open single-plate or closed parallel-plate) is concerned, the numerical results predict lower threshold voltages associated to the parallel-plate closed microfluidic device compared to the single-plate open microfluidic device.