Design and Analysis of a Valveless Impedance Pump for a Direct Sodium Borohydride–Hydrogen Peroxide Fuel Cell

Because of the general awareness of global warming in recent decades, fuel cells and other clean energy technologies have attracted considerable attention for many applications, including transportation, stationary power generation, and portable power electronics. Fuel cells can generate electricity with great efficiency and low levels of pollution and are on the brink of commercialization due to the availability and cost-competitiveness of practical system development.

As shown in Eq. (1), 1 mol of borohydride releases 8 mol of electrons.

Nevertheless, $BH4−$ is unstable in a neutral or acidic medium, so DBHPFCs work only in an alkaline environment. In addition, because a highly concentrated NaOH solution can inhibit the production of gaseous hydrogen from borohydride hydrolysis on the isolated catalyst particles, many researchers have used a borohydride fuel by dissolving NaBH₄ in an NaOH solution [7,9–11]. Similarly, on the cathode side, the use of acidified H₂O₂ as an oxidant in aqueous sulfuric acid (H₂SO₄) can inhibit oxygen generation and increase the output voltage of DBHPFC [6,9]. Because these aqueous anode and cathode fuels are generally circulated by pumps, the alkalinity of the $BH4−/NaOH$ solution and the acidity of the H₂O₂/H₂SO₄ solution pose great challenges to the pump’s anticorrosion requirement.

In general, mechanical pumps can be grouped into either displacement or dynamic types according to their operating principles. Displacement pumps can be further classified as reciprocating (diaphragm) or peristaltic pumps. Reciprocating pumps incorporate a pressure chamber driven by an actuator and inlet and outlet passive check valves [12]. However, these moving valves make the pumps prone to mechanical failure and corrosion, which can further induce fluid leakage at high operating pressures and high levels of acidity/basicity accordingly. To resolve these problems, a variety of valveless peristaltic pumps have been adopted in DBHPFCs [5–9], but such systems generally have large volumes.

In the past two decades, a novel valveless scheme based on the impedance mismatch effect has been introduced in engineering applications [12–16]. This valveless impedance pump has a simpler structure and can generate a higher flowrate than the peristaltic schemes. As shown in Fig. 1, the valveless impedance pump typically consists of a flexible section connected at both ends to rigid sections of different acoustic impedance. The flexible section is compressed periodically at a location asymmetrical from the ends with various actuation mechanisms, including electric motors [12,16], electromagnetic actuators [13–15,17–21], and piezoelectric (PZT) actuators [22]. A pair of pressure waves is emitted in opposite directions each time the tube is compressed. These waves travel along the line and reflect when they reach the end of the line or the compression site if it is in the closed configuration. The traveling waves combine with the reflected waves at the impedance-mismatched positions, yielding wave interference and a pressure gradient accordingly. The resulting pressure gradient generates a net flow within the fluid system, which is typically pulsatile. The pumping rate is closely related to the combination of flexible and rigid materials (concerning impedance mismatch) and the compression parameters, such as the waveform, offset, compression amplitude, and duty cycle [23–32]. In general, the valveless impedance pump exhibits two distinct features: it responds in a nonlinear manner to the actuating compression frequency, and it reverses the flow direction at certain actuating frequencies and locations. In contrast, the peristaltic pump produces flow only in the direction of compression, and the flowrate varies in a linear manner with the actuation frequency. It is therefore essential to characterize the impedance pump and determine its optimal operational parameters (i.e., compression position, amplitude, and frequency) to generate the maximum flowrate for pumping fuels in the DBHPFC. Notably, because of the valveless and external compression features, the impedance pump and the peristaltic pump can both avoid the corrosion problem caused by the high acidity/basicity of the DBHPFC fuels.

In this study, a compact valveless impedance pump is designed, analyzed, and applied in a DBPHFC. Its commercial feasibility as a pump for high-performance DBPHFC systems is demonstrated.

The impedance pump design of Wen et al. [16] was modified and further extended. As shown in Fig. 1, a circular amber latex rubber tube was chosen for the flexible section and two SS304 stainless-steel tubes were chosen for the rigid sections, because of their good anticorrosive characteristics in conditions of strong acidity and alkalinity. Meanwhile, the amber latex rubber tube possesses good wear-resistance and thermal aging characteristics. The length, outer diameter, and wall thickness of the rubber tube was 80 mm, 6 mm, and 1.0 mm, respectively. The stainless-steel tubes had a 0.5-mm wall thickness and an outer diameter of 5.0 mm. According to the earlier experimental studies of Wen et al. [16], actuating at x/L = 1/8 (see Fig. 1) and Δy/D = 1 (i.e., complete closure of the elastic tube) yields the maximum flowrate at any compression frequency f. A small direct control (DC) motor (FM-2088, Tricore Corp., Taiwan) was used to drive a cam and to compress the rubber tube at x/L = 1/8 and Δy/D = 1 at various f. The cam was made of lead solder because of its good lubrication characteristics under dry contact; its detailed dimensions are shown in the upper-right inset in Fig. 1. The corresponding duty cycle (i.e., the fraction of the time during which the cam is in contact with the elastic tube wall in an actuating period) is 36%. The dimensions of the motor are 16 × 8 × 6 mm (length × width × height, respectively), and its power requirement is 1.5 W. Notably, the electromechanical compression mechanism used in our study offers a quiet, simple, economical, and low power consumption actuation to pump the fuels.

Figure 2 depicts the DBHPFC used in our research. A membrane electrode assembly (MEA, a CCM Nafion^® 212 membrane with catalyst loading of anode and cathode: Pt 1.0 mg/cm² and Au 1.0 mg/cm², Yangtze Energy Technologies, Inc., Taiwan) sandwiched between two standard carbon cloths (W0S1002, CeTech, Co., Ltd., Taiwan) as gas diffusion layers was placed in the middle of two flow channel plates. The active area of MEA was 25 cm². The selection of Pt and Au as the catalysts for the anode and cathode, respectively, was based on the early experimental observations that a quasi-8e-reaction occurs at the Pt anode when an NaBH₄ alkaline solution (<1 M) was used as the anolyte [33] and that Au tends to minimize the decomposition of H₂O₂ [7]. Moreover, Au is resistant to corrosion and is easily applied. Both graphite bipolar plates (80 × 58 × 4 mm; Homytech, Taiwan) on the cathode and anode sides have three-parallel-channel serpentine flow fields, with channel widths and heights of 2 mm and 1 mm, respectively. The rib width is 1 mm. The DBHPFC was clamped between two aluminum alloy (6061T651) end plates (80 × 80 × 10 mm), with four bolts tightened with a uniform torque of 8 N m. Silica gel insulation plates (films) and copper current collectors were placed between the end plates and the cell. The DBHPFC temperature was controlled at 75 °C with two thin flexible heaters attached to end plates. The DBHPFC has no external thermal insulation.

Figure 3 illustrates the combined test scheme for the pumps and the fuel cell. The liquid fuels of the DBHPFC comprised an anode of an alkaline borohydride aqueous solution (5 wt% NaBH₄ and 15 wt% NaOH) and a cathode of an acidic hydrogen peroxide aqueous solution (2.0 M H₂O₂ + 1.0 M H₂SO₄). When pumped into the serpentine channels at the anode and cathode, respectively, the NaBH₄ and H₂O₂ solutions further diffused through the diffusion layers and then reacted under the anode and cathode catalysts. The heaters inside the polytetrafluoroethylene fuel tanks (500 ml each) heated both the anode and cathode electrolytes to 75 °C. This temperature was maintained with a control system using the proportional–integral–derivative (PID) control scheme; the temperatures of the fuels and the cell were tracked with K-type thermocouples.

A computer-controlled Arbin fuel cell test system (Arbin Instruments, BT2000, 1 kW), which comprises an electrical load and a data acquisition system, was used to control and record the current and voltage of the fuel cell unit under operation to obtain the I–V curves. With the DBHPFC connected to the electrical load, the I–V curves were measured in a constant-current model. The I–V curves of the DBHPFC pumped by peristaltic pumps (Great Tide Instrument Co., Ltd. Tp-100) and impedance pumps (as seen in Fig. 4) were compared. The impedance pumps shown in Fig. 4(b) are simple devices that are easily attached to the case wall of the entire fuel cell unit, which thus reduces the DBHPFC’s operating weight and size.

As a preliminary step, the pumping performance of the impedance pump was calibrated both with and without the DBHPFC. As shown in Fig. 4(b), the pump alone (i.e., not connected to the DBHPFC) was connected to a fuel tank at one end, and the other end was left open to drain the fuel; this configuration was used to measure the flowrate profiles at various actuation frequencies. A DC power supply (MOTEH Co., Taiwan, LPS-305) was applied to an electric motor to drive the cam that compresses the elastic tube. The actuation voltage was monitored by a digital oscilloscope (Tektronix, TDS 2014). At the beginning of each experiment, the pump was filled with fuels. The correlation between the voltage applied to the motor, V, and the actuation frequency, f, under a load was initially calibrated with a stroboscope (Strobotac 1546). The pulse length of the flash is approximately 1.2 µs, which is short enough to freeze the motion of the cam as the correct flashing frequency is set. A linear regression analysis revealed a relationship between f and V: f = 5V–2, for 11 V ≤ V ≤ 15 V, with a high correlation coefficient (R² value of the fit) of 0.998.

The relevance of the pump flowrate to the actuation frequency was then measured. First, the fuel tank and the pump tubing were suffused with fuels and blocked with a ball valve at the end. To minimize the initial pressure head, the water level in the reservoir was 2.0 cm above the pump. The pump was then activated and the valve was opened. The fuel that exited from the fuel cell was collected in a sink for a few seconds to estimate the flowrate. The fuel flowrate was measured at every 1-V interval of the DC power supply change. Note that the ball valve and the sink are not shown in Fig. 4(b).

To obtain flowrate profiles for the pump with connection to the DBHPFC, the pump was connected to a fuel tank at one end and to the fuel cell at the other. The fuel flowrate was calculated by measuring the volume of fuel collected in the sink for a few seconds.

Figure 5 shows the measured impedance pump flowrates in response to the compression frequencies, actuating at x/L = 1/8 and Δy/D = 1 (complete closure of the elastic tube). The pump’s performance was observed to depend in a nonlinear fashion on the actuation frequency for both the fuel cell-connected scenario (i.e., the dashed line in Fig. 5) and the pump alone (i.e., the solid line in Fig. 5). For the DBHPFC-connected scenario, the variation of the flowrate with the actuation frequency exhibited a broadly similar trend to that of the pump alone. No flow-reversal effect was induced beyond the limited applied frequency range. The unique frequency-dependence of the net flowrate indicates an impedance-driven flow. Note that the flowrate measurements have a very high degree of repeatability. For each experimental condition, 0.5% uncertainty was obtained via five repeated measurements for the flowrate. A maximum pump flowrate of Q = 715 ml/min was obtained for the pump alone scenario when the actuation force was applied at a frequency of 68 Hz (corresponding to an applied voltage of 14 V at the motor). Significant shrinkage of the flowrate at various compression frequencies was induced by the large head losses in the three-parallel-channel serpentine flow fields of the graphite bipolar plate. The maximum pump flowrate reduced to Q = 30 ml/min when the DBHPFC was connected to the impedance.

As the working mechanism of the impedance pumps mentioned in the “Introduction section,” a pair of pressure waves is emitted in opposite directions with each periodic compression of the tube. These waves travel along the tube and are then partially reflected when they reach the ends. The relative impedances of the two materials determine the proportion of the reflected wave energy to the total wave energy when they propagate through the intersection. The waves are delivered from a soft latex rubber tube to a very hard stainless-steel tube. The start time, travel distance, travel time, directions, amplitudes, and positions for each wave pair emitted are dependent upon the compression period and the cycle to which it belongs. Because the wave speed (estimated to be around 50–60 m/s [26]) in the latex rubber tube is much slower than the normal speed of sound (1500 m/s through water) inside the stainless-steel tubes, the pressure waves inside the pumping section that propagate to both ends are almost entirely reflected. As each wave crosses a reflection site, its pulse shape is reflected in a similar manner. All waves are eventually summed along the length of the compressed pliable tube. Once equilibrium is reached, a net pressure head is accordingly generated at the ends of the piping to impel the flow within the flow channel. The pump curve thus depends primarily upon the specific piping configuration and actuation parameters. Variations in the materials, the length of the pliable tube, the actuating wave pulse shapes, the actuating positions, and the actuating frequencies all affect the pump’s performance [13]. Therefore, the head losses in the stainless-steel tube, bends, and the flow channel plate of the fuel cell system result in the nearly constant decrease of the flowrates in Fig. 5.

At an actuation frequency of 68 Hz and actuation position x/L = 1/8 (see Fig. 5), the total pump head is determined by H_pump = Q_pump × R_pump = Q_fuelcell × (R_pump + R_fuelcell), where Q_pump is the flowrate of the pump alone, Rpump is the internal pump flow resistance, Q_fuelcell is the flowrate of the pump with connection to the DBHPFC, and R_fuelcell is the total flow resistance of the stainless-steel tube, bends, and flow channel plate of the fuel cell system. Accordingly, the ratio of the total flow resistance of the fuel cell system to the internal pump flow resistance can be ascertained by R_fuelcell/R_pump = Q_pump/Q_fuelcell–1 = 715 (ml/min)/30 (ml/min)–1 ≈ 23. Marked flow resistance of the flow channel plate emerged in the current study. To mitigate pressure head loss, the DBHPFC will require optimum flow channel plates for future practical applications.

As illustrated in Fig. 6, this section focuses on performance testing of the fuel cell system, that is, the influence of the anode and cathode flowrates on the output power of the DBHPFC with the fuels, both oxidizer and reducing agents, circulated by the peristaltic pumps. Because the constant voltage of 0.7 V is close to the corresponding voltages at the maximum powers for all flowrates (see typical I–V curve in Fig. 7), the fuel cell power was measured while maintaining a constant voltage of 0.7 V. In addition, the flowrates were kept the same for the anode and the cathode, ranging from 30 to 150 ml/min with the increments of 40 ml/min. Note that increases in the anode and cathode flowrates gradually improve the DBHPFC performance. The measured output power was enhanced from 13 W (520 mW/cm²) at 30 ml/min to 15.2 W (610 mW/cm²) at 150 ml/min, but this increase stopped when the flowrates exceeded 110 ml/min. A further increase in the flowrates would increase the pumping power without accelerating fuel cell power generation. The current DBHPFC can achieve a maximum power density of 650 mW/cm², which is comparable to the value of 680 mW/cm² obtained by Gu et al. [9].

The fuel cell performance was further investigated by comparing two fuel pumping configurations at anode and cathode flowrates of 30 ml/min (i.e., the optimal flowrates for the current impedance pumps). Figure 7 shows the fuel cell I–V and power density curves using a pair of impedance pumps and a pair of peristaltic pumps (Fig. 4), respectively. Little disparity is observed in the DBHPFC performance between the two pumping mechanics. At anode and cathode flowrates of 30 ml/min, the DBHPFC has a maximum power density of about 530 mW/cm² and an OCV of 1.75 V.

For quantitative evaluation of the performance of the DBHPFC with these two pumping configurations, the specific power (power-to-mass ratio), volumetric power density, and back work ratio were defined as follows:

• $Specificpower≡PproducedMtotal$

• $Volumetricpowerdensity≡PproducedVtotal$

• $Backworkratio≡PpumpingPproduced×100%$⁠,

Based on impedance pumping, a new valveless pump was successfully developed and applied to the fuel pumping of an all liquid-fueled direct borohydride–hydrogen peroxide fuel cell. The pump comprises a simple, quiet, economical, and energy-efficient actuation mechanism that combines a small DC motor, a cam, and an amber latex rubber tube, connected at both ends to rigid stainless-steel tubes with various acoustic impedances. At locations asymmetrical from the rigid ends, the net flow was generated by periodic compression of the pliable rubber tube to pump the fuel successfully. The pump flowrate was found to vary in a nonlinear manner with the actuation frequency, for a fixed actuation position (x/L = 1/8), waveform, duty cycle (36%), and input excitation amplitude (Δy/D = 1). The primary outcomes of this research are concluded as follows:

1. The measured maximum flowrate of the impedance pump is 715 ml/min at the zero pump head at a motor actuation voltage range of 11–15 V (corresponding operation frequency, 53–73 Hz). The flowrate achieves the optimal performance at an actuation frequency of 68 Hz.

2. The variation in the flowrate with the actuation frequency for the fuel cell-connected scenario exhibits a trend that is broadly similar to that of the pump alone (Fig. 5). When the DBHPFC is connected to the impedance, the large head losses in the three-parallel-channel serpentine flow fields of the graphite bipolar plate can induce enormous diminution of the maximum pump flowrate to Q = 30 ml/min.

3. Our DBHPFC successfully uses an alkaline borohydride aqueous solution (5 wt% NaBH₄ and 15 wt% NaOH) and an acid hydrogen peroxide aqueous solution (2.0 M H₂O₂ + 1.0 M H₂SO₄) as the liquid fuels for the anode and the cathode, respectively. The maximum power and current of about 13.0 W and 12.6 A were observed at anode and cathode flowrates of 30 ml/min.

4. The combination of impedance pumps and the DBHPFC showed remarkable advantages in reducing the fuel cell system weight and volume while enhancing the specific power, volumetric power density, and back work ratio. In addition, the valveless characteristics of this pump are capable of preventing pump corrosion.

Impedance-based pumping provides an exciting new option for liquid fuel pumping systems. The feasibility of its application to pump fuel for liquid-fueled fuel cells is demonstrated by our experimental results. Although it is conceptually simple, further work is necessary to optimize its performance in practical applications, including (1) the proper choice of the flexible tube material to extend the pump life and reduce the resistance to friction from the compressing cam and (2) maximization of the impedance mismatch and flowrate accordingly. In addition, the optimal length of the flexible tube, the actuation frequency, and the position must be considered for the new combination of the impedance pump to expand the flowrate range. In the meanwhile, the stability of the Nafion membrane and the corresponding DBHPFC cell performance by pumping the basic fuel and the acid oxidant with valveless impedance pumps will be investigated.

• National Science Council (Grant No. NSC 99-2221-E-006-050-MY2; Funder ID: 10.13039/501100001868), Taiwan, the Republic of China.

• Research Grants Council, Hong Kong (Grant No. GRF 526913).

f =

actuation frequency, Hz

D =

average diameter of the elastic tube, mm

H =

water head, Pa

I =

current, A

L =

length of the elastic tube, mm

P =

power, W

Q =

flowrate, ml/min

R =

flow resistance, Pa·min/ml

V =

voltage, V

M_total =

total mass of the fuel cell, kg

V_total =

total volume of the fuel cell, m³

E⁰ =

standard equilibrium cell voltage, V

x,y =

coordinates