A microfluidic wireless power system

Abstract

Electrical traces made using liquid metal can survive strains of tens or hundreds of percent without damage. Liquid metal is promising for creating the thick cross sections and low resistance necessary for power devices, while maintaining high stretchability. In this article, a stretchable wireless power receiver system is demonstrated featuring a liquid metal circuit board (galinstan traces embedded in silicone) to connect individual discrete components as well as to create the receiver inductor coil. The mechanical effects of embedding parts were also simulated using a numerical solver. The fluidic channels defining the liquid metal traces are built using a silicone molding and bonding process based on 3D printed molds. The system consists of an inductor-capacitor resonant tank, voltage-doubling diode rectifier for AC to DC conversion, and a representative load. Circuit operation was demonstrated up to 80% uniaxial mechanical strain.

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Introduction

The use of liquid metal in electrical systems dates to the very beginning of computing, from the drops of mercury used as inputs in punch card readers¹ to the fluidic delay line memories of early digital computers such as UNIVAC.² However, the toxicity of mercury has minimized widespread use in more recent years. Recently, liquid metals have made a resurgence in highly deformable devices for applications such as soft robotics and biomedical sensors,³ attracting interest due to their ability to stretch and bend without damage. One factor has been a shift toward the use of less toxic gallium alloys such as galinstan and eutectic gallium indium,⁴ more suitable for use on or near a user's skin. These alloys have the further advantage that the gallium forms a thin layer of oxide on its surface that resists leakage and creates a self-healing effect.⁵ From the initial demonstrations as electrical interconnects,⁶ the field has expanded to include pressure sensors,⁷ capacitors,^8,9 inductors,^9,10 resistive heaters¹¹ and tunable antennas.¹²

Liquid-metal-based systems, known as microfluidic electronics, are promising for stretchable devices because very large cross sections, on the order of millimeters, can be used while retaining deformability. This allows resistance to be kept far lower than stretchable alternatives such as serpentine traces¹³ and conductor loaded polymers.¹⁴ Fluidic devices are of particular interest for power devices such as inductors where increased resistance causes power losses and degraded efficiency. Stretchable electronics are commonly powered wirelessly to eliminate the need for fragile physical connections to the outside world. Although stretchable coils for wireless power have been demonstrated using thin serpentine traces,^15–17 the added length and small cross section, along with negative mutual coupling resulting from the interconnect geometry,¹⁸ result in poor electrical performance. This has led to interest in the use of liquid metal inductors for wireless power delivery to improve efficiency.^19,20

Although wireless power transfer can be demonstrated using an inductively coupled coil pair, most applications require additional components such as power conditioning circuitry as well as the desired load. A stand-alone stretchable system was recently demonstrated using a centimeter-scale flexible polyimide-based printed circuit board (PCB) embedded within an elastomeric substrate containing a fluidic inductor.²¹ The inductor alone was shown to maintain functionality up to a uniaxial strain of 50%, but the addition of the polyimide PCB resulted in system failure above 25% strain due to stress concentrations at the interface between the two materials. In this work, a self-contained wirelessly powered receiver is demonstrated using liquid metals for both the receiver coil and interconnects between embedded electrical components. Mechanical simulations were also performed to verify the stress concentrations of embedding piece parts with liquid metal traces. The system consists of a resonant inductor-capacitor (LC) tank, a single-ended diode rectifier and a representative load, consisting in total up to seven individual components. The system is able to operate for strains up to 80% uniaxial mechanical strain, more than a factor of three larger than previous work.

Fabrication

Forming electrical connections to discrete components was one of the earliest applications for liquid metal within stretchable electronics, and is typically done using one of two approaches distinguished by the timing of the liquid metal addition. In the first, liquid metal is patterned on a surface by a method such as tape transfer²¹ or screen printing.²² The components are arranged on the surface and then encapsulated by the addition of liquid elastomer precursors. Although this approach allows for high resolution patterning of parallel traces, issues with smearing or shifting of the liquid metal can cause shorting during the rigid component placement.²² Alternatively, components can be first embedded into an elastomer that contains pre-defined microchannels.²³ Liquid metal is then injected into the channels using a syringe, which eliminates the risk of shifting the liquid metal during the addition of parts. This method is serial in nature and therefore likely slower, and also requires additional area overhead for inclusion of the fluidic inlets and outlets. The latter method was used for this work but similar results could be obtained with either method. Sockets are defined within a fluidic network to orient and hold the components during the bonding process (Fig. 1(a)). Through-hole components are used with trimmed leads, which extend into the channels to make robust electrical contact after the addition of the liquid metal (Fig. 1(b)).

Fig. 1 (a) Addition of components to pre-defined channel network and (b) structure after filling with liquid metal.

Molds are first fabricated in acrylonitrile butadiene styrene (ABS) using a commercial 3D printer (Replicator 2X, Makerbot) (Fig. 2(a)). Liquid silicone precursors (Ecoflex 00-30, Smooth-on.com) are poured over the mold (Fig. 2(b)) and, after vacuum degassing, are allowed to cure completely at 85 °C on a hot plate. The cured silicone is peeled from the mold (Fig. 2(c)) and the components are arranged in the pre-defined sockets and glued into place using drops of uncured silicone (Fig. 2(d)). The channels are sealed by bonding to Ecoflex 00-30 that has been allowed to gel and partially solidify but not cure completely (Fig. 2(e)). This partial cure was done by curing for an hour and ten minutes at room temperature before bonding, rather than the four hours necessary for a complete cure. The bonded piece is then placed on a hot plate at 85 °C and baked until completely cured. Inlet and outlet holes are cored using narrow gauge syringe tips, followed by the injection of the liquid metal galinstan to form the inductor and interconnect traces (Fig. 2(f)). Drops of liquid silicone are then used to seal the injection holes and prevent leakage.

Fig. 2 Fabrication process for wireless power system: (a) 3D printed mold, (b) pouring of silicone precursors, (c) removing cured silicone from mold, (d) adding rigid components, (e) bonding to partially cured silicone and (f) injection of galinstan.

Electrical design

The wirelessly powered receiver developed in this work contains a total of seven embedded components along with a liquid metal inductor for use in an inductive power link (Fig. 3(a)). The circuit (Fig. 3(b), with list of component values given in Table 1) consists of three major blocks: a resonant LC tank, rectification circuitry and a representative load. While inductive wireless power transfer can operate over a broad frequency range, resonance improves energy transfer efficiency within the inductive link. In the LC tank, the capacitor C₁ is therefore shunted across the secondary coil terminals to resonate the receiver and allow improved coupling. The stretchable inductor was implemented as a single-turn circular planar coil (20 mm radius, 1 mm trace width and 1.5 mm trace thickness) with an approximate inductance and resistance of 101 nH and 79 mΩ respectively. A complete model of the effects of mechanical deformation on a similar type of coil was previously developed.²⁰ A capacitance of 0.22 μF resonates the stretchable coil at 1.24 MHz.

Fig. 3 (a) Wireless power system and (b) circuit schematic.

Table 1 Embedded components

Component	Value/type
C1	0.22 μF
C2	0.22 μF
C3	0.22 μF
D1	HP2826
D2	HP2826
D3	Avago HLMP-P156-EGO31
Rload	10 Ω

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A one-turn coil was chosen primarily for fabrication reasons. Creating a multi-turn inductor requires a more complicated fluidic network, since a second routing layer and vias between the two layers are necessary to create an overpass from the center of the coil. Creating and aligning these additional channel layers, although possible, add significantly to the fabrication complexity. Single turn samples can also be made thinner, again due to the elimination of the second routing layer. This does however come at a cost: multiple-turn inductors couple more strongly, allowing better energy transfer between the transmitter and receiver coils. To help quantify the tradeoff in using the single turn receiving coil, the field solver FastHenry was used to model the inductive coupling coefficients for both the single-turn as fabricated and an eight-turn coil with the same outer diameter and 1 mm line width and spacing, the resolution of the fabrication process used here. In both cases, the transmitter coil was modeled to simulate the one used in the experimental section of this work. The drop in coupling coefficient to the transmitter coil geometry by choosing a single turn coil was modest, approximately 12.5%. Although the multiple turn coil was found to couple more strongly, the inner turns contributed less strongly to the mutual coupling due to the increasingly smaller diameters. Therefore the modestly reduced coupling coefficient of the single turn coil was found to be an acceptable tradeoff in return for the significantly simplified fabrication process.

Applying a sinusoidal current to the transmission coil produces time varying magnetic fields that in turn induce a sinusoidal voltage at the receiver input. The induced AC voltage can be used to power a system directly, but in many cases rectification of the sinusoidal signal is required to provide a steady DC voltage. A single-ended voltage doubler is used as the rectifier structure to rectify and boost the AC signal at the input into a larger DC voltage. While multiple stages can be cascaded to increase the rectified voltage, a single stage is implemented for simplicity within the stretchable receiver. The load consists of a light emitting diode (LED) (1.6 V turn-on voltage) with current-limiting resistor to allow for visual verification of the circuit operation without a need for direct electrical connection.

A commercial inductive coil with magnetic backplane (Wurth Electronics 760308111, 6.3 μH nominal inductance) was used to wirelessly transmit energy to the stretchable system and turn on the LED (Fig. 4(a)). The transmitter coil was driven at the measured unstrained resonance of the system (1.29 MHz, 4% higher than calculated due to component tolerances), requiring a minimum of 7 V peak-to-peak sinusoidal signal on the transmitter to turn on the light emitting diode (Fig. 4(b)). During electrical testing, the voltages across the receiver coil and load were measured using copper wires that were connected to the liquid metal traces at each node. Due to the turns ratio between the transmitter and receiver coil (eight turns, as opposed to one turn in the receiver), the voltage drops to 2.4 V peak-to-peak across the liquid metal coil. A single-turn inductor could be used for transmission to minimize this reduction in voltage, but a larger, multi-turn inductor was chosen to simplify the needed power circuitry on the transmitter side. This rectifier topology has an expected output voltage of 2V_in − 2V_diode, where V_in is the single sided amplitude applied to the input of the rectifier and V_diode is the forward conducting drop across an individual rectifier diode. The receiver circuitry rectifies the signal to 1.65 V with 100 mV (6%) ripple, consistent with the measured forward conduction drop on each rectifier diode of 0.35 V.

Fig. 4 (a) Wireless power demonstration and (b) measured transient voltages.

Mechanical characterization

Unlike a rigid inductor, a stretchable system is dynamic and able to deform freely during operation. However, the inductance of a coil is geometry dependent, with wire self and mutual inductance varying with wire length and spacing between neighboring wires respectively. The resistance also varies based on the length and cross section dimensions. This effect is typically undesirable in wireless power transfer, although both resistance and inductance variation of liquid metal traces has been used for hyperelastic strain sensing.^7,9 The inductor used in this work was characterized using a custom uniaxial strain testing setup¹⁰ to extract the deformed electrical behavior. Testing of the inductor was performed without the additional embedded power circuitry, and copper wires were used to make electrical contact to the liquid metal traces. After subtracting away the analytically estimated the inductance of the copper lead wires, the inductance of the liquid metal coil was found to vary from 75 nH at 0% strain to 124 nH at 80% strain (Fig. 5(a)), the maximum strain reached by the full system before failure. The resistance varied from 62 mΩ to 323 mΩ for 0% and 80% respectively (Fig. 5(b)).

Fig. 5 Liquid metal coil (a) inductance (b) resistance and (c) coupling to rigid transmit coil during (c) stretching and (d) bending across 3D printed pieces with different radii of curvature.

In addition to the change in the electrical properties of the inductor itself, the electromagnetic coupling to the rigid coil is also affected by the change in geometry. At 0% strain, the liquid metal coil is similar in size to the rigid transmitter coil, as seen in Fig. 4(a). During stretching, the inductor is elongated along the axis of mechanical strain, becoming elliptical in shape. A portion of the trace will extend past the outer dimensions of the rigid coil, resulting in weaker coupling between the two coils. In a two-coil system, the strength of the magnetic coupling can be characterized by the coupling coefficient k:

where L₁ and L₂ are the inductance of the two individual coils and M is the mutual inductance resulting from the coupling between them. The coupling coefficient varies from negative one for perfect negative coupling to positive one indicating perfect positive coupling, with zero for no coupling at all between the coils. The coupling coefficient between the liquid metal coil and the rigid transmitter coil was measured across strain (Fig. 5(c)). During testing, the rigid coil was placed in contact with the surface of the encapsulating silicone, leading to a separation of approximately 1.5 mm between the two coils. The coupling was found to drop with higher strain, from 0.37 for 0% strain to 0.31 for 80%, due to the change in the stretchable coil geometry. The inductor was also curved across 3D printed pieces with different radii of curvature to measure the change in coupling to a flat rigid inductor as the stretchable inductor bends (Fig. 5(d)). Since the rigid transmission coil is unable to conform to the curved silicone surface, the curvature of the liquid metal inductor results in a modest reduction of the coupling between the two.¹⁵ The coupling drops from 0.37 unbent to 0.32 for a 30 mm radii of curvature.

The mechanical behavior of the wireless power system was also analyzed. The addition of rigid components into the soft silicone results in local stress concentrations within the elastomer and earlier system failure. The larger the embedded parts, the greater the effect the parts will have in concentrating stress and affecting the rigidity of the overall system. The through-hole components used in this work have dimensions ranging from two to four millimeters on a side. To examine the effects on the overall system performance of parts on this size scale, a uniaxial strain of 30% was modeled using the finite element solver COMSOL (Fig. 6). The position of the parts within the simulation was estimated using the slots in the 3D printed mold defining the channels. Locally, the maximum principal strain within the silicone was found to reach 70% near the components, more than twice the strain on the overall system. Although liquid metal inductors have been demonstrated to survive up to 200% uniaxial mechanical strain,⁹ with the rigid components the system is likely to fail at a lower overall strain, likely less than half this value.

Fig. 6 Mechanical simulation for 30% applied uniaxial strain; the black outlines show the original positions of the components prior to stretching.

To test the failure point, mechanical testing was performed on the full system after the addition of the rigid components. As long as sufficient power is coupled to the inductor and the rectifier is providing at least 1.6 V of DC voltage, the red LED will turn on. The system was first tested by bending the stretchable sample across 3D printed pieces of different radii of curvature down to 30 mm (Fig. 7(a)). The minimum spacing set by the silicone thickness results only at the point of actual contact, the center of the inductor, while farther from that point the spacing is significantly wider, resulting in the weaker coupling. Due to the reduced coupling, the required transmission voltage to turn on the LED increased to 8.5 V peak-to-peak at 30 mm radius of curvature from the 7.0 V peak-to-peak required for the static case.

Fig. 7 Wireless power system (a) curved to 30 mm radius of curvature, stretched to (b) 40% and (c) 80% uniaxial mechanical strain and (d) resonant frequency with strain.

A sample was also stretched using the uniaxial strain testing setup (Fig. 7(b) and (c)). The system continued to function and turn on the LED up to 80% strain. Since the inductor dimensions and resulting inductance change during stretching, the resonant frequency also changes. The brightness of the LED with frequency was used to estimate the approximate resonant frequency of the system. Since the inductance increases with stretch, the resonant frequency drops to a minimum of 0.97 MHz for 80% strain. The required input voltage on the transmitter to turn on the LED also increases with strain, an increase of about 13% in voltage for 80% mechanical strain, due both to the higher resistance of the stretchable inductor and the reduction in coupling between the two coils. Above 80% strain, voiding within the liquid metal traces resulted in system failure and loss of connectivity. At high strains microfluidic channels can partially or completely collapse²⁴ or become pinched off by protrusions left by imperfections in the molds used.⁹ These effects result in re-distribution of the liquid conductors and loss of electrical connection. Once squeezed out of the channel, the viscous fluid resists flow back to its initial position,²⁴ preventing the contact from being restored after the applied strain is removed without re-filling the device.

To verify survivability during cycling, the uniaxial strain testing setup was also used to repeatedly stretch the system. The wireless power system was stretched 100 times to 50% uniaxial strain without loss of electrical connection or appreciable reduction in LED brightness during wireless power coupling.

Conclusion

In this work, a wireless power system consisting of liquid metal traces for both an inductor for power coupling and interconnects between embedded components for signal conditioning is demonstrated. The system is based on mm-scale through-hole components embedded with a silicone matrix and connected by channels filled with galinstan. Using individual piece parts, rather than an embedded flexPCB as in past work, allows for greater stretchability due to the smaller individual rigid part sizes. The system demonstrated here has a maximum strain of 80%, more than three times the flexPCB method. The fabrication technique could be easily scaled up to more complicated circuitry, either by incorporation of additional circuitry or by using a previously developed multi-layer liquid metal inductor process in a similar technology.¹⁰

Notes and references

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