1. Introduction
The micro direct methanol fuel cell is a promising micro energy source with broad potential for application citing its advantages of high energy conversion efficiency, strong continuous power supply capability, being environmental-friendly, low temperature and fast start, high reliability, and easy integration [
1,
2,
3]. Direct methanol fuel cells (DMFCs) can be classified into two types according to the supply mode of the fuel and oxidant, that is, active cells and passive cells [
4]. Passive cells rely primarily on free diffusion to control the fuel and oxidant supply, and the cell output performance is relatively low. In active cells, the fuel and oxidant supply needs to be controlled by active auxiliary devices, such as pumps and valves, with particular flow rates and concentration, which is not conducive in portable applications of DMFC. Therefore, ascertaining how to combine the advantages of the two types of cells is of great significance to the practical application of DMFCs.
The liquid supply mechanism of the DMFC has been extensively studied, to improve the cell energy density and stability. Yang et al. [
5] investigated the effects of different anode flow fields and parameters on the cell performance, where the results showed that the single-serpentine flow field exhibited a significantly higher performance than the parallel flow fields. Similarly, in their research, Deng et al. [
6] reached the same conclusion. Adnan Ozden [
7] applied Murray’s Law to design two different bio-inspired, leaf-shaped flow fields. The serpentine, the lung, and the two leaf-shaped flow fields were used to form seven different anode–cathode combinations. For comparison, when patterning the serpentine flow field, the peak power density was 824 W/m
2.
Specifically, the working parameters have a significant and overlapping impact on the output performance of the μDMFC. These parameters include temperature, methanol solution concentration, flow rate, and the cell operating temperature. Given these factors, the internal temperature transport has been the focus of ongoing research [
8,
9]. A.A. Kulikovsky [
10] reported a model that considered fragment heating due to reactions and cooling by the fuel flow in the anode channel and by water evaporation. Y. Wang [
11] designed a spatial model of the DMFC, as well as a system model, including the air supply and the pump for the methanol supply. The results described the whole cell temperature distribution. In addition, the effect of the anode methanol flow rate on the performance of the μDMFC is complex, citing the need to control several key factors that affect cell performance, including reactant mass transfer, gas CO
2 emission, and methanol crossover. On the one hand, an increase in the flow rate leads to an increase in the mass transfer rate, which can effectively overcome the mass transfer resistance of the anode and increase the bubble CO
2 discharge velocity in the flow channel, so that the liquid flow in the flow channel becomes more stable. On the other hand, excessive flow rates increase the methanol crossover, resulting in cell performance degradation. Wei et al. [
12] prepared a direct methanol fuel cell and investigated the effects of temperature, cathode humidification temperature, methanol concentration, methanol flow rate, and air flow rate on the polarization curve of the direct methanol fuel cell. The results showed that the best working condition of the cell was a temperature of 80 °C. In fact, the low current density working region uses a lower concentration of the methanol solution, whereas a high concentration methanol solution is supplied to the cell in the high current density region. For an active methanol fuel cell, the actual concentration of the methanol solution reacted in the catalytic layer can be adjusted by changing the flow rate of the methanol fuel at the inlet. The traditional variable speed liquid supply generally uses a microprocessor to monitor the current output, and then it adjusts the operating frequency of the micro pump according to the current feedback signal, thereby realizing real-time control of the flow rate. Although this method obviously increases the size and power consumption of the system, it is detrimental to the μDMFC’s portable applications.
Based on above understanding, in this paper, we developed a novel self-adaptive speed supply method derived from the internal reaction, where the design concept considers that the heat dissipated is different when the DMFC is in different working states, and thus the fuel supply speed in the microvalve is automatically adjusted. A microvalve was designed at the back side of the cell anode flow channel. For the methanol solution, the supplied flow rate is influenced by the dynamic viscosity related to the temperature of the solution. By changing the temperature of the methanol solution, the viscosity can be altered, and the variable speed can finally be achieved. Under low current density working conditions, the temperature of the methanol solution in the microvalve is low, and the micro valve outlet flow rate, that is, the inlet flow rate of the cell is also low, and this can meet the slower reaction requirements of the cell. When the reaction in the cell is gradually intensified with the increase in the working current, the increased heat generation is then transferred to the methanol solution inside the microvalve, and the outlet flow rate is gradually increased to satisfy the severe chemical reaction. Therefore, the microvalve structure can achieve an adaptive speed liquid supply mode, which effectively increases the power and stability during the entire process of the μDMFC operation. To further illustrate the method, this paper built a three-dimensional full-cell structure diagram with micro-valve using the COMSOL simulation software. The first part involved simulating the single micro-valve and verifying the relationship between viscosity and the speed of solution. The full cell model was simulated to illustrate the effect of the solution flow rate on cell performance, and the role of the microvalve structure. In addition to the simulation, we conducted experimental verifications, and the experimental results showed that the micro-valve could effectively improve the cell performance.
2. Simulation Analysis
Figure 1 shows the three-dimensional full cell model with the microvalve. While studying the methanol solution state in the microvalve, to facilitate the calculation, a representative single channel was simulated with a cross-sectional area of 0.4 mm × 0.4 mm and a height of 10 mm. To study the mass transfer analysis and power density inside the μDMFC, we modeled the full cell calculation domain.
To simplify the calculation and model processing, some assumptions were made with regards to the mathematical model.
(1) The cell operates under stable state, single phase, and isothermal conditions.
(2) Since methanol reacts rapidly on cathode catalyst layer (CCL), it is assumed that the methanol reacts completely with anodic permeation.
(3) The electrochemical reaction is completed when only water and CO2 are produced, without any other side effects.
(4) The temperature of the outer wall of the cell is the same as that of the environment, ignoring the Joule heat generated by the internal resistance of the cell.
(5) Contact resistances between each layer are ignored.
(6) There are no gas fluxes through the membrane.
The fluid in the microvalve single-channel and anode channels was considered as in-compressible flow Newtonian fluids, and the single-phase laminar flow was used to describe the velocity field and pressure field in simulation. Therefore, the Navier–Stokes equation can be used to describe the momentum transfer, which is expressed as follows:
where
represents the density of the fluid,
is the liquid phase transport velocity in the flow channel,
is the pressure of the flow channel,
is the dynamic viscosity coefficient of the fluid, and
T denotes the temperature. Similarly, the momentum of oxygen in the cathode flow channel can be described using the above equation.
In the anode channels, owing to the diffusion and convection effect, the methanol was transported into the anode diffusion layer. The transport equation in the channel is given as:
Both the anode diffusion layer and the cathode diffusion layer are composed of a porous carbon cloth, so the Darcy law can be used to describe the momentum transfer in the porous medium, which can be expressed as follows:
where
indicates the liquid phase transport velocity in the diffusion layer,
κ represents the absolute permeability of the diffusion layer, and
P represents the fluid pressure in the diffusion layer.
The mass transfer equation of liquid methanol in the anode diffusion layer is given by:
The mass transfer equation of O
2 in the cathode diffusion layer is given by:
The mass transfer phenomenon in the PEM includes methanol crossover and water penetration. Methanol mass transfer consists of diffusion, convection, and elector-osmosis, where the total molar flux can be simplified as shown in this model:
where
indicates the effective diffusion coefficient of methanol in the PEM,
indicates the concentration of the methanol solution in the PEM,
is the flux of the methanol crossover.
Both the anode oxidation reaction and the reduction reaction of the cathode in the model are obtained by concentration dependent kinetics.
The current density expressions of the anode and cathode catalytic layer are shown as:
where
is the anode reference exchange current density,
is expressed as the concentration of the methanol solution on the anode catalyst layer,
represents the reference concentration of methanol,
represents the transfer coefficient of the anode catalyst layer,
represents the cathode reference exchange current density, and
represents the oxygen concentration on the cathode catalyst layer.
indicates the reference concentration of oxygen,
represents the transfer coefficient of the cathode catalyst layer, whilst
and
are the over potential of the anode and cathode, respectively, which can be described as:
where
is the electron potential and
is the proton potential,
is the anode equilibrium voltage, and
is the cathode equilibrium voltage.
To obtain the effect of methanol crossover on the cathode overpotential, we assumed that the methanol permeated from the anode completed an electrochemical reaction on the cathode catalyst layer, and that the internal current
could be described as:
The viscosity of the liquid was mainly caused by the cohesive force between the molecules. As the temperature increased, the molecular thermal motion increased, and the inter molecular cohesion weakened, causing the decrease in liquid viscosity. The estimated viscosity of the methanol aqueous solution is as described in Reference [
13]:
where
is the viscosity of the aqueous methanol solution,
and
are the molar fractions of component 1 (water) and component 2 (solute), respectively.
and
are the viscosities of component 1 (water) and component 2 (solute), respectively. The parameters a and b are the binary interaction parameters, which are related to the species type and temperature, and can be expressed by a linear relationship of temperature, as shown in Equations (11) and (12):
where
5.37690,
−0.0115010,
−10.2113,
0.0286300.
Heat transfer is a key process in the μDMFC, where we consider the heat generated by the electrochemical reaction. The heat flux generated by the oxidation of methanol on the anode catalyst layer can be expressed as:
where
is the enthalpy change corresponding to the oxidation of methanol, and
represents the Gibbs free energy corresponding to the oxidation of methanol. In the above Equation, the first term on the right hand side represents the heat generated by the anode overpotential; whilst the second term represents the change in entropy corresponding to the anode methanol oxidation reaction.
Similarly, the heat flux corresponding to the reduction of oxygen on the cathode catalyst layer is shown as:
where, the first term on the right side of the Equation represents the mixed potential caused by methanol permeation and the heat generated by the cathode overpotential; whilst the second term represents the change in entropy corresponding to the oxygen reduction reaction; and the third term indicates the entropy change of oxygen and methanol which permeate into the cathode catalyst layer.
For the microvalve’s anode flow path and the cathode flow path, only the fluid heat transfer in the flow path needs to be considered. Therefore, the heat transfer equations in the anode and cathode channels can be expressed as follows:
where
is the specific heat capacity of the fluid, and
k is expressed as the heat transfer coefficient.
For the anode and cathode diffusion layers, these are composed of porous media. Therefore, the heat transfer in the anode and cathode diffusion layer is shown as:
The PEM is a solid perfluoro sulfonic acid type membrane, such that heat transfer therein can be considered to be transported in solids. The anode and cathode plates also experience heat transfer in solids. Therefore, the heat transfers in the PEM and the two plates can be expressed as follows, respectively:
where
indicates the thermal conductivity of the plate, and
is the thermal conductivity of the PEM.
In this study, the finite element analysis solver, COMSOL Multiphysics, was used to develop the above model. After constructing the above equations into the model, parameters and variables are added to the equation for physical domain setting, boundary setting, meshing, and solving.
Table 1 describes some of the parameters and variables used in the model solution.