energies

Article
Influence of Stoichiometry on the T wo-Phase Flow
Behavior of Proton Exchange Membrane Electrolyzers
Olha Panchenko 1 , *, Lennard Giesenberg 1 , Elena Borgardt 1 , W alter Zwaygardt 1 ,
Nikolay Kardjilov 2 , Henning Markötter 2 , T obias Arlt 3 , Ingo Manke 2 , Martin Müller 1 ,
Detlef Stolten 1,4 and W erner Lehnert 1,4
1
Institute of Ener gy and Climate Resear ch—Electrochemical Pr ocess Engineering (IEK-3) Forschungszentrum
Jülich GmbH, Jülich 52428, Germany; lennard@giesenber g.de (L.G.); e.bor gar [email protected] (E.B.);
w .zwaygar [email protected] (W .Z.); mar [email protected] (M.M.); [email protected] (D.S.);
w [email protected] (W .L.)
2 Institute of Applied Materials, Helmholtz Zentrum Berlin, Berlin 14109, Germany;
[email protected] (N.K.); [email protected] (H.M.);
[email protected] (I.M.)
3 Institute of Applied Materials, T echnische Universität Berlin, Berlin 10623, Germany;
[email protected]
4 Faculty of Mechanical Engineering, R WTH Aachen University , Aachen 52062, Germany
* Correspondence: [email protected]
Received: 11 December 2018; Accepted: 19 January 2019; Published: 23 January 2019
      
  

Abstract:
In or der for electr olysis cells to operate optimally , mass transport must be impr oved.
The key initial component for optimal operation is the current collector , which is also essential for
mass transport. W ater as an educt of the r eaction must be evenly distributed by the curr ent collector
to the membrane electr ode assembly . As pr oducts of the r eaction, hydr ogen and oxygen must also
be dir ected quickly and ef ficiently thr ough the curr ent collector into the channel and r emoved fr om
the cell. The second key component is the stoichiometry , which includes the curr ent density and
water volume flow rate and repr esents the ratio between the water supplied and water consumed.
This study pr esents the corr elation of the stoichiometry , two-phase flow in the channel and gas
fraction in the por ous transport layer for the first time. The gas-water ratio in the channel and por ous
transport layer during cell operation with various stoichiometries was investigated by means of
a model in the form of an ex situ cell without electrochemical pr ocesses. Bubble formation in the
channel was observed using a transpar ent cell. The gas-water exchange in the por ous transport layer
was then investigated using neutr on radiography .
Keywords:
pr oton exchange membrane electr olysis; stoichiometry; neutr on radiography; two-phase
flow; flow r egime
1. Introduction
The ef ficient pr oduction of hydr ogen is vital to making the transition to a r enewable ener gy
system based on hydr opower , wind and photovoltaics. W ater electrolysis is an attractive option for
fully integrating such r enewable means of power generation. Pr oton exchange membrane (PEM)
water electr olyzers ar e consider ed especially pr omising due to their versatility in terms of curr ent
density and their high conversion ef ficiency . In the literatur e, several r eview papers [
1
–
3
] have given a
good overview of the state of the art in PEM electr olysis. A PEM electr olyzer consists of a membrane
electr ode assembly (MEA), curr ent collectors, bipolar plates with flow channels, distributors and
end plates. The current collector is a por ous medium between the MEA and bipolar plate, which is
placed on both sides of the electr ode. The two most important roles of a curr ent collector ar e electrical
Energies 2019 , 12 , 350; doi:10.3390/en12030350 www .mdpi.com/journal/energies

Energies 2019 , 12 , 350 2 of 12
conduction between the electr ode and bipolar plate and the ef ficient transport of water and gas
between the electr ode and flow channels. At the anode of a PEM electr olyzer , liquid water is fed
thr ough the curr ent collector to the MEA and dissociated into molecular oxygen. Any gas pr oduced is
dir ected thr ough the curr ent collector into the flow channel. Liquid water is the educt in the anode
r eaction, and simultaneously wets the membrane to maintain a high level of pr oton conductivity .
If the oxygen pr oduced cannot be r emoved quickly and ef ficiently , the channel is blocked, limiting
mass transport. The ef ficient mass transport of liquid (water) and gas (oxygen) thr ough the anode
curr ent collector is ther efor e decisive for the stable operation of a PEM electr olyzer . Many studies
have contributed to a better understanding of mass transport in electrolysis cells. Investigations by
Grigoriev et al. [
4
], for example, correlate electrical performance with the pr operties of the curr ent
collector , such as por osity , pore size, and hydr ophobicity . The optimal por e size of curr ent collectors
was determined to be 12–13
µ
m. However , a definitive correlation between cell performance and por e
size has not yet been clearly established. Hwang et al. [
5
] conducted electr olysis experiments with
unitized r eversible fuel cells that featur e dif fer ent T i-felt current collectors. The authors concluded that
if the mean por e diameter (MPD) of a por ous curr ent collector is smaller than appr oximately 60
µ
m,
then the electr olysis performance is not noticeably influenced by either the polytetrafluor oethylene
content or the por osity . For MPD > 100
µ
m, the cell performance decr eased at high curr ent densities
(> 0.5 A/cm
2
). In a study by Ito et al. [
6
], the flow pattern of the two-phase flow in the flow channel was
analyzed, and the relationship between the flow pattern and electr olysis performance was investigated.
In collaboration with Hackemüller et al. [
7
], we tested several titanium PTLs with dif fer ent
por osities and por e sizes. PTLs with por osity below 20% have mass transfer limitations. Depending on
the material pr operties (hydr ophilicity , contact angle) and the por e pr operties (capillary ef fects), some
por es will contribute to gas transport and the others to water transport. One of the tasks of this work is
to determine which por osity actually contributes to the measur ement transport of water and gas.
At the cathode, hydr ogen gas is pr oduced that then dif fuses thr ough the curr ent collectors to the
flow channel. In contrast to the anode r eaction, no liquid water is r equir ed for the cathode r eaction,
with water r eaching the cathode side thr ough osmosis. In this way , ther e is a two-phase flow on the
cathode side as well. The activation overpotential of the cathode r eaction is low [
7
], and so the ef fect of
the pr operties of the cathode curr ent collector on the cell performance is limited.
T o optimize the mass transport in an electr olysis cell, the dependence between the flow r egime
and cell performance must be understood. A number of studies have made key contributions to
characterizing the two-phase flow in the channel. For instance, Ito et al. [
8
] described the flow patterns
in the two-phase flow , as well as the bubble size dependence on the por e diameter of the por ous
transport layer (PTL). They observed that lar ger bubbles form at lar ge por es, which restricts water
supply . Mishima [
9
] investigated the flow r egime in vertical capillary tubes with a diameter of 1–4
mm. The Mishima-Ishii model has been verified and r epr esents a map of the flow r egimes that shows
bubble formation as a function of water -gas ratios. The average rise in velocity of slug bubbles was
corr elated with the drift flux model. A two-phase frictional pr essur e loss was measur ed. Using
an optically-accessible squar e micr ochannel, Cubaut et al. [
10
] tested various water-gas ratios and
two-phase flows and investigated bubble formation. In spite of the dif fer ent descriptions of flow
r egimes that can be found in the literatur e [
8
,
9
,
11
–
17
], the flow behavior in the two-phase flow in the
channel can be categorized as follows: “dispersed bubbly flow”—spherical, individual bubbles in the
channel; “plug flow”—the bubbles become larger than the channel cr oss section so that they assume an
elongated shape; “slug flow”—the bubbles ar e much longer than they ar e wide; “churn flow”—longer
bubbles ar e interspersed with smaller ones; “annular flow”—a flow in which the gas phase forms a
monobubble that is rar ely interrupted.
One parameter that characterizes the water -gas ratio in an electr ochemical cell is the stoichiometry .
This is defined as the mass ratio between water that has been split to water that has been added.
When the stoichiometry is 1, the added water is completely split. Unfortunately , the literature pr ovides
little information on the stoichiometry used. Olesen et al. describe mass transport models investigated

Energies 2019 , 12 , 350 3 of 12
using a cir cular cell with inter digitated channels [
18
]. The authors specified a stoichiometry of
λ
= 350
without explaining why they selected this particular stoichiometry . Our previous study [
19
] describes
cell operation at thr ee stoichiometries (
λ
= 100, 350, 600). During the measur ements, the gas-water
distribution in the current collector , also called porous PTL, and in the channel was observed using
neutr on radiography . At higher stoichiometries, the gas is quickly and efficiently r emoved fr om
the PTL and channel. At a stoichiometry of appr oximately 100, a short-term gas accumulation
was observed in the PTL. The gas-blocked the por es in the PTL for several seconds (3–5 s), during
which time newly-pr oduced gas also accumulated and could no longer be transported into the
channel. After several seconds, this blockage dissolved and the gas-water exchange functioned
again. This earlier study was primarily concerned with electrochemical characterization and only
thr ee dif fer ent stoichiometries wer e investigated (
λ
= 100, 350, 600). In or der to supplement this
investigation, the present study was conducted. Her e, the focus was primarily on investigating smaller
stoichiometries with the aim of mor e accurately defining the point at which mass transport limitations
occur . These measur ements wer e carried out with neutr on radiography . The examined stoichiometry
range was
λ
= 120–160. Another objective was to clarify the extent to which the two-phase flow regime
in the channel influences mass transport in the PTL. These measur ements wer e carried out with a
transpar ent cell. The examined stoichiometry range was λ = 95–1035.
2. Materials and Methods
2.1. Cell and Sample
An ex situ cell was designed for the investigations r eported her e. The cell was not an actual
electr olysis cell, but a model that served to simulate the two-phase flow in the channel of an electrolysis
cell. It had two straight channels (15
×
2
×
2 mm
3
). These wer e separated by a titanium sinter ed
body with a por osity of 48.99% (17
×
4
×
0.8 mm
3
). The sintered body was placed in a matching
r ecess in the components between the two channels. The plates and edge of the sinter ed body wer e
glued together using instant adhesive (Loctite 408). Each channel had an inlet and outlet for the media
supply . A pr essur e measuring unit was also installed in fr ont of the inlet to measur e the pr essur e
dr op, as each medium flowed through the sinter ed body . T wo cells were assembled accor ding to
the schematic shown in Figur e 1 : one transpar ent cell made of acrylic glass and one stainless steel
cell. The transpar ent cell was used to investigate bubble formation and agglomeration in the channel.
The stainless steel cell, meanwhile, was used for neutr on radiography due to its lower absorption.
Energies 2019 , 12 , 350 3 of 12

been add e d. When the sto i chiometry is 1, the ad de d wat e r is co mplet e ly spli t . Unfort un at ely, t h e
lit er at ure pr ovides lit t l e inform at ion on t h e st oi c h iometry used. Olesen e t al. desc rib e mass
t r ansport models invest ig at ed us ing a circu l a r cel l wit h int e rdig it at ed chann e ls [ 1 8]. The a u t h ors
specif ied a st oichiomet r y of λ = 350 wi thout expl a i ni ng why they sel e cted thi s pa rti c ula r
st oichiomet r y . Ou r prev iou s st u d y [ 1 9 ] d e scribe s ce ll o p erat ion at t h ree st o i chiom e t r ies ( λ = 1 00, 3 5 0 ,
6 00) . Duri ng the mea s urements, the ga s- wa ter dist ribut i on in t h e c u rrent collect or, al s o ca ll ed
porous PT L, and in the ch annel was ob served using neutron radio g raphy. At h i gher stoich io metries,
the gas is quick l y and e f ficiently re moved from t h e PTL and channel . At a st oichio m e t r y of
a pproxi m a t ely 100 , a short- term gas a c cumula ti on was observe d in the PTL . The g a s-bloc ked the
pores in the PTL for se veral second s (3–5 s ) , d u ring wh ich time newly - produce d g a s als o
a ccum u la ted a n d coul d no l o nger be tra n sported i n to the cha nnel. Af ter several seconds, thi s
blockage d i s s o lved and th e gas-w a ter e x change func tioned ag ain. This ear l ier s t udy w a s pr imarily
concerned w i th e l ectroch e mical ch a r acteri za ti on and onl y three di ff erent stoi chi o metri e s were
invest ig at ed ( λ = 1 0 0 , 35 0, 6 0 0 ). In o r d e r t o s u p p l e m ent t h is inv e st ig at ion, t h e p r esent st u d y w a s
conduct e d. H e re, t h e foc u s wa s prim ar il y on invest i g at ing sma l l e r st oich iomet r ies wit h t h e a i m of
more acc u r a t e ly def i nin g t h e point at w h ich ma ss t r a n sport lim it at ions occ u r. T h ese me as ure m ent s
were carrie d out with neutron rad i ogr a ph y. The ex amined stoichiometry ran g e was λ = 120– 160 .
Another objecti v e wa s to cl a r i f y the extent to whi c h the two- pha s e f l ow regime i n the cha nnel
i n f l uences m a ss tra n sport i n the PTL. T h ese mea s ur ements were ca rri e d out with a tra n spa r ent cel l .
The exam ine d stoich iometry r a nge w a s λ = 95 –10 35 .
2. Ma t e ri als a nd M e th ods
2. 1. C e l l an d S a mpl e
An ex s i t u ce ll wa s d e si gn ed fo r t h e in vest ig at ions r e port ed here . The ce ll w a s not an act u a l
el ectrolysis cel l , but a m o del tha t served to si mula te the two-pha s e f l ow in the cha nnel of a n
elect r ol ysi s c e ll . It had t w o st ra ight cha nnels (1 5 × 2 × 2 m m 3 ) . These were sep a ra ted by a tita ni um
sint ered b o d y wit h a p o r o sit y of 4 8 . 9 9 % (1 7 × 4 × 0. 8 m m 3 ). Th e sintered bo dy was place d in a
ma tchi ng recess i n the components between the two channe ls. Th e plates and edge o f the sintered
body wer e glued together usin g inst ant adhes i ve (L oc t i t e 4 0 8 ) . E a c h chann e l ha d an inlet an d out l e t
for t h e med i a supp ly. A pr essu re me as u r ing un it w a s a l so in st al le d in f r ont of t h e in let t o meas ure
the pressure drop, as e a ch medium flo w ed thro ugh the sintered body. Two c e lls were assembled
accord ing t o t h e schem a t i c shown in F i gure 1: one t r ansp arent ce ll m a de of ac ryli c gl as s an d one
st ain l es s st eel cel l . The t r an sp arent cel l was u s ed t o i n v e st ig at e b u b b l e form at io n an d ag glom erat io n
in t h e chann e l. The st ain l ess st ee l ce ll , meanwhi l e, was used for neutron r a diography due to its
lower absorpt i on.

Figure 1. ( a ) El ements of the cell design; ( b ) 3D mo d e l o f t h e c e ll .

Figure 1. ( a ) Elements of the cell design; ( b ) 3D model of the cell.
A PTL sample was investigated. This PTL was sinter ed fr om HDH titanium powder (i.e., produced
using the hydride-dehydride pr ocess [
20
]) with a particle fraction below 45
µ
m. The pore size
distribution and por osity wer e measur ed using mer cury por osimetry . The average por e size was

Energies 2019 , 12 , 350 4 of 12
5 ± 0.45 µ m
and the por osity was 48.99
±
0.41%. Permeability was also measured for this sample.
The permeability measur ed with air was 4.5
×
10
− 12
m
2
and the permeability measur ed with water
was 8 × 10 − 12 m 2 .
2.2. Acrylic Glass Cell T est
Bubble formation in the channel was recor ded using a Panasonic DHC-SD66 camera at a video
r esolution of 1080i. An image pr ocessing pr ogram was then used to quantify the r ecor ded videos and
a total of 10 images wer e analyzed for each stoichiometric state. In turn, the edges of the bubbles were
marked and their ar ea calculated.
In the optically accessible cell, bubble formation was observed and the gas fraction in the channel
calculated. As the PTL was not transparent and the por es of the PTL wer e no longer located in the
optically accessible portion, neutr on radiography was used.
2.3. Neutr on Radiography T est
Using neutr on radiography , the PTL was observed in situ and changes in the gas-water content in
the por es wer e detected at a r esolution of 100 µ m.
The measur ement was conducted at the CONRAD (COld Neutr on RADiography) station in
BER II at the Helmholz-Zentrum, Berlin [
21
,
22
]. A nuclear fission reaction pr oduced neutr ons that
wer e decelerated by a moderator and then guided to dif fer ent measuring stations. The wavelengths
of the neutr ons ranged from 0.1 nm to 1.1 nm, with a maximum of 0.25 nm. The temperatur e of
the neutr ons was appr oximately 152 K and their ener gy was 13 meV [
23
]. For optimal resolution,
the sample was placed as close to the scintillator as possible, with an exposure time of 5 s. The field of
view of the detector was 16
×
13.5 mm
2
at a r esolution of 2562
×
2160 pixels and a lateral r esolution
of 100
µ
m. The cell was mounted on a translational table with a r otational table top, which permits
pr ecise adjustment and positioning.
Image pr ocessing was based on the Lambert-Beer law , which states that the beam intensity is
attenuated during transmission through the material. The attenuation depends on the material’s
attenuation coef ficient and thickness (Equation (1)). T o calculate the material thickness, Equation (1)
was solved for z (Equation (2)):
I t = I 0 · e − ∑ z µ · z (1)
z = − 1
µ l n  I t
I 0  (2)
wher e I
0
is the original beam intensity , I
t
is the transmitted beam intensity ,
µ
is the material-specific
attenuation coef ficient and z is the material thickness.
Every image contains two-dimensional information as a pr ojection of the irradiated material on
the detector . W ater absorbs large amounts of radiation, so the channel or PTL filled with water appear
dark. When the channel or PTL are empty , less radiation is absorbed. In this case, the transmitted
radiation has mor e ener gy and the image is brighter .
An i m a g e o f t h e ce l l i n t h e d r y st a t e w a s u s e d as a r ef e r en c e i ma g e . T o de t e rm i n e t h e t h ic k n e s s o f t he
wa t e r l a y er i n t h e c e l l , ea c h i m a ge w a s d i v i d ed u s i n g a r ef er en c e i m a g e, t h e n l o g ar i t h m i z ed , inverted,
and divided by the water absorption coef ficient (Equation (2)). This r esulted in the two-dimensional
mapping of the water content of the cell. The Lambert Beer law is the standar d means to edit the
neutr on and synchr otr on images. Because we ultimately divide the images of the cell in the humidified
state thr ough the images of the cell in the dry state, the artifacts and deviations ar e shortened out.
2.4. Operating Pr ograms and T ests
The cell was positioned so that the channel was horizontal, while the lower channel outlet was
closed of f. The medium added to the lower channel was for ced to pr opagate through the sinter ed

Energies 2019 , 12 , 350 5 of 12
body . Meanwhile, the upper channel outlet had a horizontal extension wher e the water was collected
in a container .
The medium was supplied by a syringe pump, which enabled the flow rate to be set with
µ L/min pr ecision.
A schematic of the experimental pr ocedur e is shown in Figur e 2 . The images show the central
part of the cell, i.e., the porous sinter ed body and the two parallel channels. At the beginning of the
measur ement, the cell was dry (see Figur e 2 a). After 10 min, water was fed into the lower channel at a
flow rate of 20
µ
L/min. W e observed how the water penetrated (“imbibition”) in the PTL (Figure 2 b).
At the same time, the pr essur e r equir ed to conduct water thr ough the PTL was measur ed. The thir d
step was to investigate the dr oplet formation on the PTL surface (Figur e 2 c). In step 4, the entir e
cell was wet (Figure 2 d). For a certain time period, we observed how the water permeated the PTL,
and whether the gas fraction in the PTL changed. In step 5 (Figur e 2 e), air was fed in thr ough the lower
channel (drainage). W e then measured the pr essur e r equir ed for the gas to penetrate the water -filled
por ous medium. At the same time, how the gas penetrated in the PTL was observed, as was subsequent
gas bubble formation on the PTL surface. In step 6 (Figur e 2 f), air was fed in fr om below , and water
simultaneously fr om above, to simulate the cell in operation at various stoichiometries.
The calculation of the water -gas ratios for the simulation of pr ocesses that take place in an
electr olysis cell can be found in the section outlining the calculations.
Energies 2019 , 12 , 350 5 of 12

2.4. Operatin g Programs a n d Tests
The cell w a s posit i oned so t h at t h e channel wa s hori z o nt al, wh ile t h e lower ch a nnel out l et w a s
closed o f f. The medium ad ded to the lower channe l was fo rced to propagate th rough the sin t ered
body. Mea n while, the upper cha nnel outlet ha d a horizontal extension w h ere the wat e r was
collected in a container .
The medium was supp lie d by a sy rin g e pump, w h ich en abled the flow rat e to be set w i th
µl/ m in prec is ion.
A s c he ma ti c of the e x pe rime nta l pr oc ed u r e is s h own i n Fi gu r e 2. The i m a g e s show the ce ntr a l
part of the cell, i.e., the por o us sinter ed body an d the two p a ral l el cha nnels . At t h e beginning of th e
measurement , the cell w a s dry (see Fi gure 2a ) . Af ter 10 mi n, wa ter wa s fed i n to the l o wer channel a t
a flow rate of 20 µ l /min. We ob served how the w a t e r penetra t ed (“ i m b i bi ti on” ) i n the PTL (Fi g ure
2 b ) . At the same ti me, the pressure requi r ed to conduct wa ter through the PTL wa s measured. The
t h ird st ep w a s t o invest ig a t e t h e d r ople t form at ion o n the PTL surfac e (F igure 2c). In step 4, the
enti re cell was wet (Fi g u r e 2 d ). For a certa i n ti me period, we ob served how the wa ter permeated the
PTL, and wh ether the g a s fract i on in the PTL ch ang e d. In step 5 (Fig ure 2e ), air was fed in t h rough
the lower ch annel (dr a inag e). We then measured the pressur e r e quire d for the gas to penetr ate the
wa ter-f i l l e d p o rous medium. At the same ti me, how the g a s penet r ated in the P T L was ob ser v ed, as
was subs equ e nt gas bubble form ation o n the PTL sur f ac e . In st ep 6 (Fi g ure 2f ), air wa s fed i n from
below, and wat e r s i mult aneou s l y fro m above, t o simu lat e t h e cell in op erat ion at vario u s
stoichiometries.
The cal c ula t ion of the water- gas ra ti os f o r the si m u l a ti on of processes tha t take pla c e i n an
elect r ol ysi s ce ll c a n be fo un d in t h e sect io n out lin ing t h e ca lcu l at ions .

Figure 2. Schematic experim e nt plan: ( a )–dry cell; ( b )–im bibition; ( c )–b u bble formatio n; ( d )–wat e r
penetration through PTL; ( e )– drainage; ( f )–b u bble formatio n.
2 . 5 . Stoich iometry Calculations
In thi s experiment, no a c tua l cell wi th an el ectrochemi cal rea c ti on wa s used. Si mpl e cell s wi th
few compon ents can be more easily positioned re l a ti ve to the detector, a c hievi n g better spa t ia l
resolution in neutron rad i ogr a phy. It was assu med tha t the ga s f e d i n to the l o wer cha n nel was
p r o d u c e d b y a n M E A . I n b o t h c a s e s , i n a n e l e c t r o l y s i s c e l l a n d a m o d e l , g a s w o u l d f l o w t h r o u g h t h e
PTL and exit int o t h e cha nnel. This m o del w a s use d t o inve st ig at e t w o-ph as e f l ow in t h e channe l
and PTL as a funct i on of st oichiom e t r y . It was a s s u m e d t h at t h e e l ect r olys is cel l us ed h a d an act i v e
sur f ace are a of 0. 3 cm 2 . It was f u rt her a ssum e d t h at t h e cell wor ke d at a cu rrent densit y of 2 A/ cm 2 ,
which i s a t y pica l oper at in g point .

Figure 2.
Schematic experiment plan: (
a
)–dry cell; (
b
)–imbibition; (
c
)–bubble formation; (
d
)–water
penetration through PTL; ( e )–drainage; ( f )–bubble formation.
2.5. Stoichiometry Calculations
In this experiment, no actual cell with an electrochemical r eaction was used. Simple cells with few
components can be mor e easily positioned r elative to the detector , achieving better spatial resolution
in neutr on radiography . It was assumed that the gas fed into the lower channel was pr oduced by
an MEA. In both cases, in an electr olysis cell and a model, gas would flow thr ough the PTL and exit
into the channel. This model was used to investigate two-phase flow in the channel and PTL as a
function of stoichiometry . It was assumed that the electr olysis cell used had an active surface ar ea of
0.3 cm
2
. It was further assumed that the cell worked at a curr ent density of 2 A/cm
2
, which is a typical
operating point.
The stoichiometry is the ratio between the volume of the water that has been added (educt) and
the volume of the water used in the r eaction.
Stoichiometry is defined as follows:
λ =
.
V
.
V v
(3)

Energies 2019 , 12 , 350 6 of 12
Accor ding to Faraday’s law , stoichiometry can be calculated as follows:
m = M · Q
z · F (4)
It ther efor e follows:
ρ · .
V v = M · A · j · t
z · F (5)
λ =
.
V · z · F · ρ
M · A · j · t (6)
λ : stoichiometry
.
V : educt of the r eaction (mL/min)
.
V v : water used (mL/min)
A : active surface ar ea of cell (cm 2 )
M : molar mass (g/mol)
m : mass (g)
j : curr ent density (A/cm 2 )
z : char ge number
F : Faraday constant
n : amount of substance
Q : total electric char ge
ρ : density (kg/L)
Once the stoichiometry has been determined for a specific volume flow , the volume of water
converted per unit of time
.
V v
can be calculated. When the volume of converted water is known,
the r eaction equation can be used to calculate the volume of oxygen pr oduced. At this point, only the
amount of oxygen is inter esting because we ar e investigating mass transport on the anode side. Let the
converted water .
V v be X. It follows that the mass of converted water is:
m ( H 2 O ) = .
V v $ t = X ( g ) : (7)
n(H 2 O) = m(H 2 O)/M(H 2 O) = X/18 (mol) (8)
with the following r eaction equation:
1 H 2 O → 1
2 O 2 +1H 2 (9)
n(O 2 ) = n(H 2 O)/2 = X/36 (mol) (10)
with Vm = 22.4 L/mol (ideal gas), the volume of oxygen pr oduced is:
Vm(O 2 ) = 22.4 × X/36 = 0.622 × X (11)
The volume of oxygen pr oduced is independent of the stoichiometry and of the water volume
flow; It depends only on the curr ent density .
T able 1 shows the investigated stoichiometries and water -gas ratios.
The gas volume flow is constant at 2.09 mL/ min.
T able 1. Experimental parameters.
W ater V olume Flow
[mL/min] 0.320 0.405 0.442 0.480 0.530 0.632 1.057 2.089 3.482
Stoichio-metry 95 121 134 142 158 188 315 622 1037
W ater-gas ratio 0.153 0.194 0.212 0.230 0.254 0.302 0.506 1.000 1.667

Energies 2019 , 12 , 350 7 of 12
The stoichiometry variation was investigated in the optical experiment. The ratio between water
(in the upper channel) and air , which was fed into the lower channel and flows through the PTL into
the upper channel, varied.
3. Results
The bubble formation and water -gas ratio in the channel wer e observed using a transpar ent cell.
The image series in Figur e 3 shows the characteristic bubble pattern in the channel for the r espective
stoichiometry . Using an image processing pr ogram, ten images wer e analyzed for each stoichiometry .
The edges of the bubbles wer e marked and the bubble ar ea calculated. The bubble volume was
calculated fr om the cr oss-sectional ar ea. Bubbles still adhering to the PTL were distinguished fr om
fr eely moving bubbles and analyzed separately . The size of the bubbles still adhering to the PTL was
independent of the stoichiometry and varied between 0.02 mm
3
and 0.2 mm
3
. The bubbles always
left the PTL at the same spot. As soon as a bubble exceeded a critical size, it detached from the
surface. A new bubble then formed immediately at the same location. This effect is also described
in the literature: larger por es r esult in lar ger bubbles [
9
]. Smaller bubbles agglomerate into larger
bubbles in the channel. At the same time, bubbles in the channel ar e carried away with the water flow .
The faster the water flow (higher stoichiometry), the faster the bubbles ar e moved in the channel and
the less time they have to agglomerate. Figure 3 a shows bubble size as a function of stoichiometry .
At a stoichiometry of 1000, the bubbles have an average size of 1 mm
3
. At a stoichiometry of 300,
the bubbles have an average size of 9 mm
3
. At a stoichiometry of 134, the bubbles have an average size
of 34 mm
3
, i.e., half the entire channel volume. Bubbles at a stoichiometry of 94 could not be measur ed.
In this case, ther e was only one single bubble, and since both ends of the bubble cannot be viewed in
one image, the actual size of the bubble could not be measur ed. Figur e 3 b shows bubble volume as a
function of stoichiometry . All measur ed bubbles ar e depicted in black, while the mean values ar e r ed,
and the maximum bubble volume for each stoichiometry is shown in blue.
At smaller stoichiometries, some of the bubbles pushed against the water flow into the inlet ar ea.
This can be seen in the image depicting
λ
= 188: a single bubble is located in the left-hand inlet channel.
Energies 2019 , 12 , 350 8 of 12

Figure 3 . ( a ) B u bble siz e s in the channel ch aracte risti c of each sto i chiom e try ; ( b ) bubble siz e and
mean bubble size as a func t i on o f s t oi c h i o met r y.
The st udi e s of C u b a ud et al . [ 1 0] and Mish im a et a l . [1 ] p r ov id e im p o rt ant in sight s int o t h e
flow reg i mes of cert ain w a t e r-g a s ratios.

Figure 4. Flow regimes in the two-phase f l o w according t o Cubaud et al. (2004) [10] and Mishima et
al. (1996) [1] , a n d in compar ison to our own results.
The measur ing proced ur es for invest igating the two-phase flo w desc ribed in the literat u re
inv o lv e e i t h er m i xing c e rt ain r a t i o s of wat e r an d g a s b e fore t h e r e achin g chan nel or s i m u lt aneou s l y
feed ing w a te r and gas int o the channe l. In our m e thod, the ga s wa s di rected through the PTL f r om
the l o wer cha nnel to ensure tha t the experi ment was des i gne d t o ap p r ox i m at e a re al e l ect r oly s i s
cell . De spit e t h is import ant di ff erence, t h e t w o-ph ase f l ows observe d in t h e exper i ment were si mil a r
to the effects describe d in the liter atur e. Fig u re 4 shows the li tera t u re v a lues p l otted together wi th

Figure 3.
(
a
) Bubble sizes in the channel characteristic of each stoichiometry; (
b
) bubble size and mean
bubble size as a function of stoichiometry .
The studies of Cubaud et al. [
10
] and Mishima et al. [
1
] pr ovide important insights into the flow
r egimes of certain water -gas ratios.

Energies 2019 , 12 , 350 8 of 12
Energies 2019 , 12 , 350 8 of 12

Figure 3 . ( a ) B u bble siz e s in the channel ch aracte risti c of each sto i chiom e try ; ( b ) bubble siz e and
mean bubble size as a func t i on o f s t oi c h i o met r y.
The st udi e s of C u b a ud et al . [ 1 0] and Mish im a et a l . [1 ] p r ov id e im p o rt ant in sight s int o t h e
flow reg i mes of cert ain w a t e r-g a s ratios.

Figure 4. Flow regimes in the two-phase f l o w according t o Cubaud et al. (2004) [10] and Mishima et
al. (1996) [1] , a n d in compar ison to our own results.
The measur ing proced ur es for invest igating the two-phase flo w desc ribed in the literat u re
inv o lv e e i t h er m i xing c e rt ain r a t i o s of wat e r an d g a s b e fore t h e r e achin g chan nel or s i m u lt aneou s l y
feed ing w a te r and gas int o the channe l. In our m e thod, the ga s wa s di rected through the PTL f r om
the l o wer cha nnel to ensure tha t the experi ment was des i gne d t o ap p r ox i m at e a re al e l ect r oly s i s
cell . De spit e t h is import ant di ff erence, t h e t w o-ph ase f l ows observe d in t h e exper i ment were si mil a r
to the effects describe d in the liter atur e. Fig u re 4 shows the li tera t u re v a lues p l otted together wi th

Figure 4.
Flow regimes in the two-phase flow accor ding to Cubaud et al. (2004) [
10
] and Mishima et al.
(1996) [ 1 ], and in comparison to our own results.
The measuring pr ocedur es for investigating the two-phase flow described in the literatur e involve
either mixing certain ratios of water and gas before the r eaching channel or simultaneously feeding
water and gas into the channel. In our method, the gas was directed thr ough the PTL fr om the
lower channel to ensur e that the experiment was designed to appr oximate a r eal electr olysis cell.
Despite this important dif fer ence, the two-phase flows observed in the experiment wer e similar to the
ef fects described in the literatur e. Figur e 4 shows the literatur e values plotted together with our data.
The data fit the entir e flow r egime distribution well and even expand it towards smaller volume flows.
The experiment only shows one small cell or the inlet ar ea of a lar ge cell. In a r eal electr olysis cell,
mor e oxygen will always exit the PTL into the channel. If the cell had a lar ger surface ar ea, ther e would
be lar ge slugs close to the channel outlet. The ratios between the stoichiometry and bubble size only
apply to the inlet ar ea. Depending on the surface ar ea of the cell and channel geometry , the channel
length can r each several hundr ed millimeters. Depending on the curr ent density , the flow at the outlet
ar ea is only annular .
Using neutr on radiography , not only could the bubble formation in the channel be determined,
but also the gas fraction in the PTL. For this purpose, the ar ea of the image in which the PTL is located
was marked and the average transmission intensity determined. The transmission served to determine
the water volume accor ding to Equation (1). Figur e 5 shows the water content in the PTL over time as
a per centage of the por e volume.
Images 1–6 in Figur e 5 a show the water distribution in the cell at dif fer ent operating conditions.
Figur e 5 b shows the r elevant water fraction over time in the PTL and in the upper and lower channels.
During the first phase, the cell was dry and the water fraction at zero. The second phase shows the
wetting of the cell. The blue curve in Figur e 5 b shows the water fraction in the PTL. As soon as water
had filled the lower channel, the water fraction in the PTL abruptly incr eased to 26%. At this time,
the water filled the por es that wer e easily accessible fr om the surface. The first transport pathways
thr ough the PTL wer e then cr eated, and the first dr oplets formed on the surface. The water fraction in
the upper channel also incr eased, while the pr essur e in the lower channel r ose to 0.3 bar . The pressur e
of 0.3 bar , which established itself in the lower channel, was a characteristic value for the PTL used
her e. It was the pr essur e needed to push a volume flow of 40
µ
L/min thr ough the PTL. Over the next

Energies 2019 , 12 , 350 9 of 12
10 min, further transport pathways opened up and the water fraction in the PTL increased to 63%.
W ithin 30 min, the water content in the PTL incr eased by another 3% as water flowed thr ough it.
Energies 2019 , 12 , 350 9 of 12

our da ta . The da ta fi t the enti re fl ow regi me di stri b u ti on well a n d even expa nd i t towa rds sma l l e r
volume flow s.
The experim e nt only show s one sm al l c e ll or t h e inle t are a of a lar g e ce ll . In a r e al e l ect r oly s i s
cell , more ox ygen w i l l al ways exit t h e PTL int o t h e channe l. I f t h e cel l h a d a la rger su rf ac e are a ,
there would be large slug s close to the channe l outlet. The rat i os between the stoichiometr y and
b u b b l e si ze o n ly ap p l y t o t h e in let are a . Dep e nd ing on t h e sur f ac e are a o f t h e cel l and ch a nnel
geometry, th e channel length can reach several h u ndred m i llimeters. Depending on the current
densi t y, the flow a t the outl et are a is on ly ann u l a r.
Usin g neutro n radio g raphy, not only co uld the bubble forma t ion in the cha nnel be determined,
but a l so the ga s f r a c ti on in the PTL. For thi s pu rpo s e, the ar ea o f the image in which the PTL is
located was marked an d t h e aver ag e tr ansmission in tensi t y determi n ed. The tra n smissi on served to
determi n e the wa ter vol u me a ccordi n g to Equa ti on 1 . Fi gure 5 shows the wa ter content i n the PT L
over time as a percentage o f the pore vo lume.

Figure 5. ( a ) Water–gas fractions in the ce l l (neutron radi ographs) co rresponding to Figure 2; ( b )
Water fraction over time in th e upper and lower channels and PTL.
Im ages 1– 6 in Fig u re 5a show t h e wat e r dist r i b u t i on in t h e cel l at d i f f e rent op er at i n g
condit ions . F i gure 5b show s t h e r e lev a nt wat e r fr ac ti on over ti me in the PTL a n d i n the upper a n d
l o wer cha nnel s . Duri ng the fi rst pha s e, the cell wa s dry and t h e wat e r fr act i o n at zero . Th e secon d

Figure 5.
(
a
) W ater–gas fractions in the cell (neutr on radiographs) corr esponding to Figur e 2 ; (
b
) W ater
fraction over time in the upper and lower channels and PTL.
In phase 4, the lower channel was filled with air . The air was accumulated and compressed
for as long as it took for the necessary pr essur e to be achieved to push it thr ough the wet PTL.
The titanium PTL was hydr ophilic and a certain pr essur e was r equir ed to displace the water fr om
the por es (drainage). The water fraction in the PTL r emained unchanged at 44% of the por e volume.
Por es close to the surfaces that contributed to the roughness wer e filled with air . At an air volume flow
of 300
µ
L/min, the pr essur e r eached 150 mbar in 40 min. After this, the first bubbles wer e visible in
the upper channel.
Phase 5 began when the water in the upper channel was displaced by air . The PTL was then
permeated by air . During this phase, the water content in the PTL decreased to 19%. During the next
10 min, the water in another 4% of the por e volume was displaced by air .
In phase 6, water was added to the upper channel and air to the lower channel at the same time.
The volume flows and stoichiometries of 120–160 wer e simulated. The water -gas ratio in the PTL
did not change. Her e, water took up 37% of the PTL por e volume, irr espective of the stoichiometry .

Energies 2019 , 12 , 350 10 of 12
The figur e also shows r egular peaks, which occurred when the syringe pump was exchanged and
contribute no additional information.
4. Conclusions
A transpar ent ex situ cell was designed, repr oducing two-phase flow in an electr olysis cell.
The two-phase flow r egime was investigated for the first time as a function of stoichiometry
and compar ed to findings r eported in the literatur e. Specifically , stoichiometries of 95–1037 were
investigated. Furthermore, neutr on radiography was used to observe bubble formation in the channel
and to determine the gas and water fractions in the PTL. The following conclusions can be drawn on
the basis of this study:
•
Bubbles always exit the PTL at the same location. Preferr ed pathways exist for gas transport
thr ough the PTL.
•
Observations of two-phase flows in the literatur e wer e also made in this PTL. The Mishima model
was expanded for smaller volume flows.
• Using neutr on radiography , the water -gas fraction in the por es of the PTL wer e determined.
•
During the imbibition and penetration of the por ous medium with water , the breakthr ough point
occurr ed at a por e water fraction of 26%.
•
While water flowed thr ough the PTL (imbibition), 37% of the por e volume was occupied by air
and did not contribute to the transport of water .
•
When air flowed thr ough the PTL (drainage), 15% of the por e volume was blocked with water
and did not contribute to the transport of air .
•
During the stoichiometry experiment, replicating a two-phase flow thr ough the PTL, the water
fraction in the por es was 37%.
The values determined her e ar e material-specific and characterize a PTL made of HDH particles at
a por osity of 48.99% and an average por e size of 5
µ
m (value determined using mercury por osimetry).
It shows that the 37% of all por es contribute to water transport and the other 63% contribute to
gas transportation. This is an important finding, since even for samples with higher porosity , the
por e constitution and hydr ophobe/hydr ophile material pr operties could lead to limitations in the
water/gas transport. The method presented her e could be used in turn to compar e materials for
curr ent collectors.
Author Contributions:
Conceptualization, O.P . and W .L.; Methodology and carrying out measurement in HZB,
O.P ., L.G., E.B., W .Z.; Consulting, technical and scientific support in HZB, N.K., H.M., T .A.; Software, O.P .;
V isualization, O.P .; W riting—original draft pr eparation, O.P .; W riting—review and editing, W .L.; Supervision,
M.M. and W .L.; Project administration, I.M. and M.M.; Funding acquisition, D.S. and W .L.
Funding:
This resear ch was funded by NestPEL pr oject pr ovided fr om the German Federal Ministry for Economic
Affairs and Ener gy (BMW i, funding refer ence number: 03ET6044A) is highly appr eciated.
Acknowledgments:
The authors would like to thank the HZB for the beam time and numerous scientific
discussions. W e would also like to thank Richard W egner , Christian Bordin, Roger Keller , Norbert Commerscheidt,
and Juri Romazanov (all at Forschungszentrum Jülich).
Conflicts of Interest: The authors declare no conflict of inter est.
Abbreviation
(PEM) Proton exchange membrane
(MEA) membrane electrode assembly
(MPD) mean pore diameter
(PTL) porous transport layer (PTL)
CONRAD COld Neutron RADiography

Energies 2019 , 12 , 350 11 of 12
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©
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(CC BY) license (http://creativecommons.or g/licenses/by/4.0/).

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