### Glossary

### 1. Introduction

### 2. Theoretical Background

*F*

*, that is equal to the force of adhesion between the water and the supporting surface,*

_{drop}*F*

*. In equation form, the basis for water removal may the expressed as:*

_{adh}*ω*= 2Rsin(

*ϕ*

_{0}).

*F*

*must actually be greater than*

_{drop}*F*

*. However, once initiated, movement at a constant velocity require only that Eq. (1) be satisfied and that equality will be taken as the benchmark for realizing water droplet removal.*

_{adh}*ϕ*

_{0}and the radius of the assumed sphere (R), both of which are shown in Fig. 1. The contact angle is a property of the surface on which the droplet rests. The bipolar plate is generally coated with a hydrophobic material (such as Teflon) to make water removal easier. The contact angle for a surface made of Teflon is around 105° [13]. The percentage of the spherical volume that makes up the droplet increases with the droplet angle. For example, the extreme case of

*ϕ*

_{0}= 180° would imply a perfect sphere resting on top of a surface. The effective volume

*V*

*and surface area*

_{eff}*S*

*of the spherical droplet cap may be calculated using the relations [14].*

_{eff}*π*/

*λ*is the wave number,

*λ*the corresponding wave length,

*ρ*the liquid density and

*ω*is the excitation frequency in rad/s. The parameters

*B*and

*A*are non-linear effect constants with the ration

*B*/

*A*=5.2 for liquids,

*u*the vibration amplitude in meters and

*x*is the direction of propagation of the flexural wave. The equation of capillary pressure is derived according to Laplace Law, explained in Reference [18]. In this equation,

*σ*is the surface density of the liquid droplet and

*R*

*and*

_{x}*R*

*are the radii of curvature on the horizontal surface of the plate in the respective directions. For a spherical droplet,*

_{y}*R*

*=*

_{x}*R*

*=*

_{y}*R*.

*F*

*exerted on the droplet by radiation pressure can then be calculated by integrating the radiation pressure over the angles*

_{x}*ψ*and

*θ*, shown in Fig. 1, as:

*P*

*can then be used with Eq. (8) to solve for the minimum vibration amplitude required to generate flexural waves that will cause droplet movement according to:*

_{or}*u*has been obtained, the corresponding vibration energy required for droplet movement using this method can also be calculated. This is given by [13]

*U*is velocity amplitude of vibration,

*ρ*

*the water density = 1,000 kg/m*

_{ω}^{3}and

*V*

*is the effective volume of the droplet given by Eq. (3).*

_{eff}### 3. Experimental

### 3.1 Experimental apparatus

### 3.2 Experiment conditions

Performance variation according to variation of frequency in the piezo-actuator.

Performance variation according to variation of relative humidity.

### 3.3 Piezo-Actuator

### 4. Results and Discussion

### 4.1 Variation of performance according to variation of piezo-actuator frequency

### 4.2 Evaluation of performance to variation of relative humidity

### 4.3 Performance evaluation with respect to variation in reacting gas temperature

### 4.4 Flexural wave reliability experiment

### 5. Conclusions

Observing results of the PEM fuel cell performance experiment, it can be seen that fuel cell performance improves as relative humidity increases. However at high-current density, cell voltage is unsteady due to flooding phenomenon and performance decreases rapidly.

It is verified through the frequency variation experiment that performance is improved the most at 20 percent at 50 Hz, which is the limit frequency of piezo-actuator.

The piezo-actuator is operated at optimal frequency of 50 Hz, and relative humidity is varied while the performance measuring experiment is conducted. As a result, the flooding phenomenon was removed by the flexural wave and rapid decline of fuel cell performance was prevented.