As stated earlier, water is present in three phases in a PEM fuel cell. Depending on local thermodynamic and fluid dynamic conditions, mass transfer may occur between the three phases. For example, since PEM fuel cells operate under relatively low temperature (<100° C), the water vapor may condense to liquid water, especially at high current densities. Dissolved water is generated by cathode-side reactions, and, depending on the local state of deviation from equilibrium, part of it may convert to either the liquid or gas phase. The dissolved phase can also be transported across the membrane from cathode to anode, or from anode to cathode.
While the presence of water keeps the membrane hydrated (which is necessary for PEM fuel cell operation), the liquid water blocks the gas diffusion passage and decreases the diffusion rate and the effective reacting surface area hence reducing the cell performance. Therefore, water formation and transport should be considered when modeling PEMFC systems. In this section, the modeling approaches adopted in Ansys Fluent are described.
The dissolved phase exists in the catalyst layers (ionomers) and the membrane. The generation and transport of dissolved water is described by [718]:
 | (20–25) |
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 = porosity of porous media. = 1 if the membrane is solid. | |
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 = osmotic drag coefficient. | |
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The 
and 
are expressed as ([586]):
 | (20–26) |
 | (20–27) |
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where | |
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The 
, 
and 
are user-specified parameters.
The equilibrium water content is computed as ([586]):
 | (20–28) |
where 
is the water activity defined as:
 | (20–29) |
where 
is the water vapor partial pressure, and 
is the saturation pressure.
Both 
and 
in Equation 20–28 are user-specified parameters.
Liquid water is present in all the porous electrodes and gas channels.
The driving force of the liquid water transport is the liquid pressure gradient
([586]):
 | (20–30) |
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where | |
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 = absolute permeability | |
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In the porous gas diffusion and micro-porous layers, the relative permeability is computed as:
 | (20–31) |
where 
is liquid saturation, and 
is a user-defined constant.
In the membrane, the relative permeability 
is expressed as:
 | (20–32) |
Replacing 
in Equation 20–30 with the sum of the capillary pressure
and the gas pressure 
, Equation 20–30 can be rewritten as:
 | (20–33) |
The mass transfer rate between the gas and the liquid phases is computed based on the unidirectional diffusion theory [42] and [586]:
 | (20–34) |
where 
is the porosity, 
is the evaporation rate coefficient, 
is the is the condensation rate coefficient, and 
has the following form:
The Ansys Fluent PEMFC module solves for the capillary pressure 
(Equation 20–33). Then, because capillary pressure is a
function of saturation, liquid saturation can be computed. Note that even though the capillary
pressure is continuous across various porous zones, liquid saturation can be discontinuous at
the zone interfaces.
Equation 20–33 is solved in regions located in between the anode GDL-channel interface and the cathode GDL-channel interface (gas-diffusion layers, microporous layers, catalytic layers, and membrane). Inside the membrane, the transient term is zero. At GDL-channel interfaces, the liquid water flux is assumed to go out of the GDL and into the gas channel only. No backflow is allowed. The flux is assumed to be driven by the capillary pressure ([586]) and the dynamic pressure in the gas channel:
 | (20–35) |
where 
is the coefficient of liquid water removal, and 
is the local dynamic head in the gas channel.
Once the capillary pressure is obtained by solving Equation 20–33, liquid saturation is computed from the following Leverett function (except in the membrane that is non-porous to gas species transport):
 | (20–36) |
 | (20–37) |
where 
is the surface tension (N/m), 
is the contact angle, and 
, 
, and 
are the user-specified Leverett function coefficients with the following
default values:
Liquid water will reduce the effective active surface area in the catalyst layers. This is modeled by modifying the transfer currents as follows:
 | (20–38) |
where 
is a user-specified constant.
Liquid water leaves the gas diffusion layers and enters the gas channels. The main purpose of modeling the presence of liquid water in gas channels is to predict the pressure drop increase. In the PEMFC model, liquid water in the channels is tracked using the following correlation:
 | (20–39) |
where 
is the liquid water diffusion coefficient in the gas channel, and
is the liquid velocity which is assumed to be a fraction of the gas velocity
:
 | (20–40) |
where 
is the liquid to gas velocity ratio.
At the anode and cathode flow inlets, liquid saturation 
= 0. The liquid flux calculated from Equation 20–35 is
used as a boundary condition at the GDL-channel interfaces for Equation 20–39. Since it is reasonable to assume that the flow is
convection-dominated, the phase change in the gas channel is not considered here. With some
meaningful level of saturation in the gas channels, momentum resistance can be constructed to
model the pressure drop using the UDF function resistance_in_channel (real
sat) in pemfc_user.c.
When a PEMFC is started in an extremely cold environment, ice may form inside the fluid zone, and especially in porous zones [223]. To predict the formation of ice and the effects of ice on the performance of the PEMFC, the ice phase can be accounted for in the PEMFC model. The ice phase is modeled in all porous electrodes, but is not considered in gas channels.
The ice formation is governed by the following equation:
 | (20–41) |
where
 = porosity |
 = volume fraction of the ice phase |
 = density of ice |
 = mass source for the ice phase |
Due to the nature of Equation 20–41, the ice phase can be considered only in transient simulations. Only the mass transfer between the gas phase and the ice phase is considered, and the mass sources for the ice phase is calculated as:
 | (20–42) |
where
 = local water vapor concentration |
 = local water saturation concentration |
 = freezing temperature |
 and  = water desublimation and sublimation rate parameters |
In Ansys Fluent, when the ice phase is considered the in PEMFC model, the relative permeability in Equation 20–31 can be expressed as:
 | (20–43) |
The ice phase reduces the effective active surface area in the catalyst layers as well. Therefore, Equation 20–38 can be written as:
 | (20–44) |