# Experimental study of symmetry breaking in premixed flame propagation in narrow gaps

Cristian Mejía-Botero, Christophe Almarcha

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Cristian Mejía-Botero, Christophe Almarcha. Experimental study of symmetry breaking in premixed flame propagation in narrow gaps. Combustion and Flame, 2026, 286, pp.114837. 10.1016/j.combustflame.2026.114837. hal-05452513v3

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# Experimental study of symmetry breaking in premixed flame propagation in narrow gaps

Cristian Mejía-Boteroª, Christophe Almarchaª,

ªAix Marseille Univ, CNRS UMR7342, Centrale Marseille, IRPHE, Marseille, France

## Abstract

This study presents an experimental analysis of the critical conditions governing symmetry breaking in premixed flame propagating within the gaps of narrow Hele-Shaw cells. Fluid dynamic analysis was performed using hydrogen/air mixtures with equivalence ratios $\phi \in [0.5, 1]$, focusing on gaps of thickness $h = 2, 2.6$, and $3.7$ mm. The particle image velocimetry (PIV) technique was employed to measure the velocity field of the fresh gas. A glycerol/propylene glycol aerosol was used as a PIV tracer, and its influence on flame behavior was assessed. The study focuses on two key parameters: the dimensionless fresh gas velocity ($m$) and the gap-to-flame-thickness ratio ($a$). Results show that while $m$ strongly influences both the flame propagation speed and its symmetry, it is not sufficient on its own to predict symmetry breaking. Instead, a critical boundary $m = f(a)$ is shown to accurately separate symmetric and asymmetric flame regimes across a wide range of experimental conditions. These findings demonstrate that the combined effect of $m$ and $a$ governs the transition between symmetric and asymmetric flame shapes, and establish a reliable experimental methodology for future studies of confined premixed flame behavior. Finally, to further analyse the physics underlying symmetry breaking, the roles of the Péclet ($Pe$) and Damköhler ($Da$) numbers were examined. It is shown that flame symmetry is governed primarily by the combined effects of both parameters: low $Da$ promotes symmetric flames through strong diffusive smoothing regardless of $Pe$, whereas high $Da$ leads to pronounced asymmetry. In the intermediate $Da$ range, symmetry is found to depend on $Pe$, with advection-dominated conditions favouring symmetric structures provided that the flow is co-propagating with the flame.

**Keywords:** Flame propagation, Hele-Shaw cells, Symmetric/asymmetric flames, Hydrogen safety, Narrow channel

## 1. Novelty and significance statement

This work experimentally demonstrates, for the first time, the effect of fresh gas velocity and channel size on flame symmetry in narrow channels. The results are valuable because, until now, the only way to analyze the combined effect of these parameters on flame symmetry has been numerically, making it possible to demonstrate the validity of numerical results widely used in the literature. This paper advances the understanding of flame asymmetries in narrow channels and proposes an experimental methodology that may prove valuable for future studies on flame propagation within millimeter-scale gaps ($h \ge 2$ mm)—an accomplishment not previously reported at this scale to our knowledge.

## 2. Introduction

Hydrogen ($H_2$) is a promising alternative to conventional fossil fuels in sectors such as transportation and energy generation. However, its use presents significant challenges in storage, handling, and combustion due to its broad flammability limits, high flame temperatures, and rapid flame propagation speeds [1, 2, 3]. Compared to most hydrocarbons, such as methane, gasoline, or diesel, $H_2$ flames are more unstable and prone to oscillations [4, 5]. The common types of flame instabilities observed include thermal-diffusive, thermo-acoustic, and hydrodynamic instabilities [6, 7]. Investigating these instabilities is critical, as they significantly impact safety, efficiency, performance, and environmental outcomes in various combustion applications within confined environments, including internal combustion engines, gas turbines, and rocket engines [8, 9, 10].

One of the experimental devices frequently employed for studying flame instabilities is the Hele-Shaw cell [11, 12, 13, 14]. This device consists essentially of a narrow, confined space formed between two flat, parallel plates separated by a small gap, typically

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<footnote>*Fluid dynamic study in the gap</footnote>

<footnote>e-mail:</footnote>

<footnote>cristian-camilo.MEJIA-BOTERO@univ-amu.fr</footnote>

<footnote>(Cristian Mejía-Botero)</footnote>
on the order of millimeters. Because the gap is several orders of magnitude smaller than the plates' width and height, a stationary, symmetric flame shape across the thickness is generally assumed, allowing the problem to be treated as quasi-2D [15, 16]. This simplification offers several advantages when comparing experimental results with numerical simulations, as it permits the use of Navier-Stokes equations averaged over the gap, usually reducing the momentum equation within the thickness to a Darcy's law formulation [17, 18]. From a practical standpoint, the study of flame dynamics in confined, narrow channels is fundamental to the design of microcombustors, microscale propulsion systems, and portable power generators, where characteristic dimensions fall within the millimeter or sub-millimeter range [19, 20, 21, 22].

Some works have studied the experimental conditions under which the quasi-2D simplification breaks down by analyzing flame asymmetries in the gap. Radisson et al. [23] analyzed propane/air flames at various equivalence ratios ($\phi$) in Hele-Shaw cells with thickness $h \in [2, 6]$ mm. They found that for $h \le 5$ mm, flames remained symmetric, while at $h = 6$ mm, flames exhibited either symmetric or asymmetric shapes, with transitions between these states during propagation. Similar behaviors were observed for propane and methane flames propagation in tubes [24]. Veiga-Lopez et al. [25] studied oscillatory methane, propane, and dimethyl ether flames in a $900 \times 500 \times 10$ mm$^3$ Hele-Shaw cell, showing that flames remain parabolic and symmetric under primary acoustic instability but become flatter and asymmetric before secondary instability. Regarding H$_2$ propagation, Ballossier et al. [26] investigated H$_2$/air flames with $\phi \in [0.32, 2.68]$ in Hele-Shaw cells with $h \in [1.5, 4.2]$ mm. They observed both symmetric and asymmetric flame shapes and mapped the $\phi-h$ range where the quasi-2D assumption holds. Chen et al. [27] later reproduced these results numerically. For $h < 2.3$ mm, flames were symmetric for all $\phi$, while asymmetry increased with $h$ and was more pronounced for lean mixtures. To our knowledge, no other experimental studies investigating H$_2$ flame asymmetry in Hele-Shaw cells have been reported.

While the aforementioned experimental studies qualitatively identify the conditions under which the quasi-2D simplification breaks down, they do not explain the underlying causes of these asymmetries nor quantify key parameters such as the fresh gas (reactants) velocity upstream of the flame. To address this, numerical investigations in confined spaces have been conducted, revealing both symmetric and non-symmetric flame solutions. These studies assessed the influence of heat losses [28, 29, 30], Lewis number (Le) [31], and flame/acoustic interactions [32] on flame symmetry using various numerical approaches. A more comprehensive study was performed by Dejoan et al. [33], who examined the critical conditions for the emergence of non-symmetric flame

shapes, taking into account Le, thermal expansion, heat losses, and fresh gas velocity. They demonstrated that for a mixture propagating in a channel characterized by the gap-to-flame-thickness ratio $a = h/\delta_f$, there exists a critical dimensionless fresh gas velocity, $m = v_{fg}/s_L$, above which the flame transitions from symmetric to asymmetric shapes, where $v_{fg}$ and $s_L$ denote the fresh gas velocity and the laminar flame speed, respectively. By parameterizing $m$ under various conditions, they established a correlation between $m$, the dimensionless flame velocity $v_f = V_f/s_L$, and the flame shape factor $S$ (with $S = 0$ corresponding to symmetric and $S > 0$ to asymmetric flames). The critical value of $m$ depends on several factors including Le, $a$, and heat losses. Generally, symmetric flame shapes are favored when the fresh gas flows in the same direction as the flame at high speed, whereas asymmetric shapes arise when the fresh gas flows opposite to the flame, or in the same direction but with low speed. Similar conclusions were obtained more recently by Kelly et al. [34, 35], who numerically studied symmetry breaking in narrow channels propagating in Poiseuille-type flows. It was observed that the flame is more likely to become asymmetric when the fresh gas flow is in the opposite direction to the flame and when $Le < 1$; whereas, when the flow favors the flame, it tends to remain symmetric.

In most experimental studies of flame propagation in Hele-Shaw cells, the fresh gas is initially quiescent prior to ignition. However, as the flame propagates, thermal expansion induces a fresh gas flow at velocity $m$, which interacts with the flame and may influence its shape and propagation behavior. Common experimental techniques used to measure flame propagation in Hele-Shaw cells, such as schlieren imaging or direct chemiluminescence, do not allow quantification of the fresh gas velocity upstream of the flame. Consequently, no experiments have been conducted to study the influence of $m$ on flame shapes. Addressing this gap, the objective of this paper is to demonstrate experimentally the effect of $m$ and $a$ on flame symmetry. To this end, particle image velocimetry (PIV) is employed to examine H$_2$/air mixtures with $\phi \in [0.5, 1]$ in Hele-Shaw cells with $h \in [2.6, 3.7]$ mm, where the flame propagates from the open to the closed end. This range of conditions ensures the presence of both symmetric and asymmetric flame shapes, consistent with the $\phi-h$ map proposed by Ballossier et al. [26]. Two gas injection configurations are tested to achieve $m < 0$ (fresh gas flowing in the same direction as the flame) and $m > 0$ (fresh gas flowing opposite to the flame). To our knowledge, PIV has not previously been applied to flame propagation in millimeter-scale gaps. These measurements enable the understanding of the role that $m$ and $a$ play on flame symmetry, and permit to validate the numerical predictions by Dejoan et al. [33] by testing the proposed critical boundary $m = f(a)$.

The paper is organized as follows: section 2

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<figure><img src="image_2.png" /><figcaption>Fig. 1. Experimental set-up for simultaneous OH\*-chemiluminescence and PIV visualization: (a) 3D view, and (b) top view</figcaption></figure>

describes the experimental methodology, section 3

presents the results and discussion, and section 4 summarizes the main conclusions.

## 2. Methodology

### 2.1. Experimental set-up

The experimental setup is illustrated schematically in Figure 1, where a) shows the 3D schematic and b) the top view. The Hele-Shaw cell has a width (W) of 20 mm and a height (H) of 150 mm. The width was chosen to limit the development of cell structures in the flame, thereby ensuring that the flame tip remains close to the center, where the lateral visualization (gap) is focused. Nevertheless, the dimensions are large enough to observe flame instabilities. Three gap thicknesses, i.e., *h* = 2, 2.6 and 3.7 mm, are examined to investigate both symmetric and asymmetric flames, based on the maps defined by Ballossier et al. [26]. The channel is oriented vertically and has an open (top) end and a closed (bottom) end. Ignition is achieved at the open end using tungsten electrodes of 2 mm diameter, separated by approximately 1 mm, with an energy discharge of around 36 mJ. For each test, the channel is filled with the desired H₂/air mixture through a small hole at the bottom. The H₂ and air flow rates are effected using mass flow controllers (Bronkhorst EL-Flow Select), which are calibrated to achieve the desired φ with an accuracy of ±4%.

Flame propagation is measured simultaneously on the cell face and within the gap (see Figure 1). Face visualization is performed to ensure that the PIV measurements within the gap are captured at the flame tip and not at a cusp formed by instabilities. For the

face visualization, spontaneous OH\* chemiluminescence (with a wavelength in the UV range, approximately 306–315nm) is recorded. A Photron Fast Cam MiniAX camera, offering a maximum resolution of 1 Mpx and a maximum frame rate of 170,000 FPS, is used for this purpose. Since the camera's spectral response is insufficient for UV detection, a Hamamatsu high-speed gated image intensifier unit (C10880-03F) is employed, coupled to a Cerco UV lens (100 mm F/2.8) equipped with a UV filter transmitting in the 240–410 nm range.

To study the fluid dynamics within the gap, the PIV technique is employed. An identical Fast Cam MiniAX camera is used, coupled with a Laowa 25 mm F/2.8 ultra-macro 5× lens to visualize the millimeter-scale gap. A PIV tracer, consisting of a 50%/50% glycerol/propylene glycol aerosol, is mixed with the H₂/air mixture prior to injection into the channel. The aerosol is generated by heating with an electric resistance, producing microscopic particles carried by the H₂/air flow. This tracer is appropriate for PIV applications as it creates small, stable particles that scatter light effectively. The light source is a Continu Opus 532 nm laser, which passes through a spherical lens (ThorLabs AC508-300-AB-ML) with focal length *f* = 300 mm, focusing the beam onto a cylindrical lens, which then generates a light sheet that passes through the channel. This sheet is positioned near the center of the cell face to measure velocity fields close to the flame tip relative to the channel face. As illustrated in Figure 1 b), the camera used for face visualization is slightly tilted to prevent the laser sheet from entering the UV light intensifier and camera, thereby avoiding potential damage.
One limitation of the PIV technique is the neces-
sity of using tracer particles, which dilute the reactive
mixture and may potentially alter its combustion be-
havior. Therefore, it is essential to assess the impact
of the tracer and determine whether it affects flame
propagation. This analysis is presented below.

2.2. Tracer effect on flame propagation

The tracer used is a 50% – 50% liquid mixture
of glycerol and propylene glycol, which is evapo-
rated by an electric resistance and then diluted within
the H₂/air mixture. After evaporation, the mixture
cools, generating an aerosol of microscopic particles
that serve as tracers to obtain the velocity fields. Al-
though aerosol tracers are commonly used in PIV ap-
plications, it is important to quantify their effect on
flame propagation in millimeter scales since these par-
ticles evaporate during combustion (absorbing heat)
and subsequently burn (releasing heat). One key pa-
rameter indicating the potential influence of the tracer
is the consumption speed, which is estimated from
two consecutive images as S_c = (1/W) (dA_b/dt), where A_b is the
area of burnt gases and W is the channel width. This
approach, commonly used in Hele-Shaw experiments
[26], accounts for the increase in flame front area due
to instabilities. Figure 2 compares flame propaga-
tion with and without tracer for h = 2.6 mm and
φ ∈ [0.5, 1]. Figure 2 a) Presents chronophotographs
of the flame front for φ = 1, showing that the tracer
does not significantly affect the flame shape during
propagation. Figure 2 b) Shows the corresponding
S_cons values with their respective standard deviations
(each test was repeated three times). It is observed
that for all φ, S_cons is slightly higher when the tracer
is added, indicating that the heat released during par-
ticle combustion outweighs the heat absorbed during
evaporation. However, the little S_cons difference sug-
gest that the particles do not have a significant effect
on the consumption speed.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Tracer effect on (a) flame front chronophotography in the Hele-Shaw face for $\phi = 1$ and $h = 2.6$ mm, and (b) consumption speed $S_{\text{cons}}$, for $\phi \in [0.5, 1]$ and $h = 2.6$ mm.</figcaption></figure>

On the other hand, due to the high temperatures
generated at the flame front, a heat diffusion zone

is expected to develop toward the fresh gas, where
aerosol particles may evaporate. For this reason, it is
important to determine the distance between the parti-
cles and the flame front. To this end, the experimental
setup depicted in Figure 1 is used, but with both cam-
eras focused on the gap. This arrangement enables si-
multaneous flame visualization via both the PIV tracer
and OH\* chemiluminescence, thereby revealing the
exact position of the front. Figure 3 shows the su-
perimposition of both images obtained for a mixture
with $\phi = 0.7$ and $h = 3.7$ mm. A small displacement
of only 4% of $h$ is observed, and, importantly, the
flame front obtained with the tracer closely matches
the shape obtained with the OH\* chemiluminescence.
This demonstrates that the methodology used is suit-
able not only for analyzing velocity fields upstream of
the flame but also for quantifying flame symmetry and
asymmetry.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Superimposition of the images of the chemiluminescence produced by the OH⁺ radical and the tracer scattered light for the PIV technique.</figcaption></figure>

2.3. Mixtures

The mixtures evaluated correspond to H₂/air with
$\phi \in [0.5, 1]$, where the fundamental properties re-
quired for the analysis are presented in Table 1. These
values were obtained using Cantera [36] with the
Mevel mechanisms [37], designed for the H₂/O₂/N₂
combustion. The flame thickness, $\delta_f$, is defined
based on the maximum temperature gradient across
the flame front, i.e., $\delta_f = (T_b - T_u)/(dT/dx)_{\text{max}}$, where
$T_b$ and $T_u$ are the burned and unburned gas temper-
ature, respectively. For the Le calculation, the ef-
fective Lewis number $Le_{\text{eff}}$ proposed in [38] is used
in this work, i.e., $Le_{\text{eff}} = Le_D$ for $\phi < 0.6$, and
$Le_{\text{eff}} = (Le_D + ALe_E)/(1+A)$ for $0.6 < \phi < 1$, where
$Le_E$ and $Le_D$ are the Le for the excess and deficient
reactant, respectively, $A = 1 + \beta(1/\phi - 1)$, and $\beta$ is
the Zel'dovich number, which is calculated from the
explosion theory [39].

2.4. Gas injection configurations

Two gas injection configurations are tested, as il-
lustrated in Figure 4. Configuration 1 corresponds

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<caption>Table 1.</caption>

Mixtures studied with the corresponding laminar flame speed, $s_L$, flame thickness, $\delta_f$, and Lewis number, $Le$. The properties are calculated using the Mevel mechanisms [37].

<table><thead><tr><th>φ</th><th>s<sub>L</sub> [m/s]</th><th>δ<sub>f</sub> [mm]</th><th>Le<sub>eff</sub></th></tr></thead><tbody><tr><td>0.5</td><td>0.52</td><td>0.44</td><td>0.31</td></tr><tr><td>0.6</td><td>0.93</td><td>0.38</td><td>0.40</td></tr><tr><td>0.7</td><td>1.35</td><td>0.36</td><td>0.55</td></tr><tr><td>0.8</td><td>1.74</td><td>0.36</td><td>0.61</td></tr><tr><td>0.9</td><td>2.09</td><td>0.37</td><td>0.67</td></tr><tr><td>1.0</td><td>2.38</td><td>0.37</td><td>0.80</td></tr></tbody></table>

to the setup already used in most Hele-Shaw studies [7, 14, 16, 25, 26], where a valve at the gas inlet is closed prior to ignition to ensure that the fresh gas is initially quiescent. In this case, a solenoid valve (PARKER LEGRIS, ref. 4202152120) is used to shut off the reactant flow inlet 35 ms before ignition. This delay introduces some uncertainty in the mixture composition near the open end due to buoyancy-driven gas stratification. However, it is necessary to maintain an initially quiescent mixture and to prevent interaction between the flame and the incoming reactants. Since, in this configuration, the flame propagates from the open end toward the closed end of the channel, the net flow of fresh gases is expected to be zero in order to satisfy the boundary conditions. Consequently, depending on the axial position $x$ at which the laser sheet intersects the flow, either positive or negative fresh-gas velocities may be measured. To ensure that $m < 0$ is consistently obtained—i.e., that the fresh gases flow in the same direction as the flame propagation—the laser sheet is positioned near the mid-point of the channel in the $x$-direction, where the flame tip is located. Despite this, both symmetric and asymmetric flame shapes can be observed under this configuration, depending on $\phi$ and $h$, as reported in [26].

In configuration 2, the solenoid valve remains open throughout the entire flame propagation process, generating a fresh gas flow in the opposite direction to the flame movement, i.e., $m > 0$. It is expected that this condition favor the formation of asymmetric flame shapes. The main limitation of this configuration is that the fresh gas velocity must remain lower than the flame speed to avoid blow-off; otherwise, the flame fails to propagate from the open to the closed end. The fresh gas velocity is changed by adjusting the total flow rate of the reactants for each mixture, while maintaining the corresponding $\phi$. As a result, slower mixtures—such as lean mixtures—require lower flow rates to avoid flame blow-off. Since in this configuration there are two opposing flows, i.e., the flow induced by the flame and the flow of fresh gases in the opposite direction, it is possible to obtain net fresh gas velocities close to zero ($m \approx 0$), or even going in the same direction of flame propagation ($m < 0$) if the

<figure><img src="image_5.png" /><figcaption>Fig. 4. Fresh gas injection configurations.</figcaption></figure>

flow induced by the flame is faster than the fresh gas flow.

## 2.5. *S*, *m*, and *v*<sub>f</sub> calculation

Some of the key parameters considered to analyze symmetry breaking are the dimensionless fresh gas velocity $m$, the dimensionless flame speed $v_f$, and the symmetry factor $S$. Figure 5 illustrates an example of a symmetric ($\phi = 1$) and an asymmetric ($\phi = 0.5$) flame for a channel gap of $h = 2.6$ mm, which are used to define these parameters from the experimental observations. Figure 5 a) shows the flame propagation along the face of the Hele-Shaw cell, where the position of the laser sheet used for PIV measurements is indicated in green. As seen, the laser is positioned near the center of the channel to capture the velocity field at the flame tip. The laser plane is located far enough from the ignition point in the $y$-direction to avoid transient effects. Notably, for the lean mixture ($\phi = 0.5$), flame instabilities generate cusps in which the local fresh gas flow direction is opposite to that of the main flame propagation. For this reason, tests in which such cusps are captured within the PIV field of view are excluded from the analysis to ensure accurate characterization of the flow at the flame tip.

Figure 5 b) shows the flame propagation within the gap, where the raw PIV images are presented, which are also used to estimate the asymmetry factor $S$. For this purpose, the definition used in [26] is adopted, namely $S = 2|A_1 - A_2|/(hr_f)$, where $A_1$ and $A_2$ are the surface area of the flame on each side of the half-gap distance, $h/2$ is the half gap, and $r_f$ is the flame extension (see Figure 5 b) upper). This definition yields an asymmetry factor ranging from 0, indicating a perfectly symmetric flame, to 1, corresponding to a fully asymmetric flame. In this work, the criterion established in [26] is used, where flames with $S \le 0.1$
<figure><img src="image_6.png" /><figcaption>Fig. 5. Examples of flame propagation in Hele-Shaw of $h = 2.6$ mm for a symmetric ($\phi = 1$) and asymmetric ($\phi = 0.5$) shapes. a) Propagation in the face, b) raw PIV images in the gap, c) PIV velocity fields in the gap, and d) velocity profiles. The green line in a) corresponds to the position of the laser plane.</figcaption></figure>

are considered symmetric, and those with $S > 0.1$ are classified as asymmetric. This classification is illustrated by the two examples in Figure 5, where for $\phi = 1$, $S = 0.04$, indicating symmetry, while for $\phi = 0.5$, $S = 0.3$, indicating asymmetry. Although this definition is analogous to the one used by Dejoan et al. [33], they did not normalize $S$ by geometric flame parameters, resulting in values outside the [0, 1] range. Therefore, in this study, normalization by $h$ is applied to their numerical results to enable direct comparison within the same range.

The next parameter to estimate is $m$. In the simulations conducted by [33], $m$ is an input parameter, where the hydrodynamic part of the governing equations is simplified by assuming a parabolic Poiseuille velocity profile that is unaffected by the flame. They defined $m < 0$ for flows moving in the same direction as the flame propagation, and $m > 0$ for flows moving in the opposite direction. It is important to note that, numerically, by prescribing $m$ as an input, uniform velocity profiles are obtained in front of the flame along the y-axis of the channel.

To experimentally calculate $m$, the velocity field is extracted from the raw PIV images (Figure 5 b)) using the Matlab software DPIV-soft [40]. This software analyzes pairs of images containing reflective particles by cross-correlating them to determine particle displacement, which reveals the velocity field. The results show the velocity around the flame in the fresh gas region. The PIV results are shown in Figure 5 c), where the velocity field around the flame in the fresh

gas region is visualized. Note that the field within the burned gas is not observed because the tracer evaporates in that region. However, for the objectives of this study, measuring the velocity field in the fresh gas is sufficient. These fields are normalized by the respective laminar flame speed, $s_L$, of each mixture. Unlike the uniform velocity profiles obtained numerically in [33], experimental profiles may exhibit some variation along the y-direction. Therefore, the distance $d$ depicted in Figure 5 b), which corresponds to the gapwise distance between the flame tip and the point where the velocity profile is measured, is considered in the analysis.

Figure 5 d) above shows the fresh gas velocity ($v_{fg}$) profiles obtained for $d = 1/4h$, $1/2h$, and $h$. A notable difference is observed between the two mixtures, with the fresh gas velocity significantly slower for the leaner mixture ($\phi = 0.5$). However, within each mixture, the velocity profiles at the different distances $d$ show no substantial variation. The same profiles are shown normalized by the respective laminar flame speed, $s_L$, in Figure 5 d) (bottom). Normalizing reduces the apparent difference between the $\phi = 1$ and $\phi = 0.5$ profiles, reflecting the lower $s_L$ value for the lean mixture. The velocity profile at $d = 1/2h$ represents an average profile between the flame tip and $d = h$, and thus only this profile is used for subsequent analyses. Following the definition in [33], the dimensionless fresh gas velocity $m$ is taken as the average normalized velocity, indicated by the dashed horizontal lines in Figure 5 d) (bottom) for each mixture. No-

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tably, all measured velocity profiles closely follow a Poiseuille flow pattern, which is confirmed by fitting a parabola with $R^2 > 0.9$. Finally, to calculate the dimensionless flame speed $v_f = V_f/s_L$, the flame tip position is tracked over time (not shown here), yielding a linear $y = f(t)$ profile with $R^2 > 0.98$, being $V_f$ the slope of this linear fit. The $v_f$ values are shown for each mixture in Figure 5 b), presenting a higher value for $\phi = 1$ ($v_f = 3.04$) than for $\phi = 0.5$ ($v_f = 1.64$).

### 3. Results and discussion

This section discusses the results obtained, where the effect of $m$ and $a$ on flame symmetry are analyzed individually. Finally, the combined influence of both parameters is examined, and an analysis of the Péclet (Pe) and Damköhler (Da) numbers is carried out, which are parameters that fundamentally govern flame behaviour in Hele-Shaw configurations [34].

#### 3.1. *m* effect

Figure 6 shows the relationship between $v_f$ and $m$ for all the tests conducted. A clear trend is observed: as $m$ becomes more negative-i.e., when the fresh gas flows faster in the same direction as the flame—the flame propagation speed increases.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Normalized flame speed, $v_f$, as a function of normalized fresh gas flow velocity, $m$, together with a linear trend (dashed line).</figcaption></figure>

When compared to the linear trend (dashed line) shown in Figure 6, it is evident that, for most cases, the flame propagates faster than the fresh gas flow. Furthermore, within the range $m \in [-2, 2]$—corresponding to $v_f \in [0, 4]$—a noticeable dispersion in the data is observed. To better understand this dispersion, Figure 7 presents the $v_f = f(m)$ profiles focused on this specific range, alongside the numerical predictions by Dejoan et al. [33] for $Le = 1$ and $Le = 0.8$, for a fixed gap-to-flame-thickness ratio $a = 6$. In this figure, solid lines represent symmetric flame solutions, while dashed lines correspond to asymmetric solutions. The experimental data points

<figure><img src="image_8.png" /><figcaption>Fig. 7. *Le* effect on the relation between the normalized flame speed, $v_f$, and the normalized fresh gas flow velocity, $m$. The solid lines represent the function for symmetric flames and the dashed lines for asymmetric flames proposed by Dejoan et al. [33] for a fixed $a = 6$.</figcaption></figure>

are colored according to their effective Lewis number, $Le_{eff}$.

The numerical results indicate that in this $m$ range, data dispersion is expected due to the onset of thermodiffusive instabilities, which are particularly prominent in lean H₂-air mixtures. Consistent with this, the majority of the experimental points fall within the numerical bounds set by the symmetric $Le = 1$ and asymmetric $Le = 0.8$ solutions. Notably, most of the mixtures tested in this study exhibit $Le_{eff} < 0.8$, further increasing their susceptibility to thermodiffusive effects. The results from Dejoan et al. [33] also suggest that, even for symmetric flames, low Lewis numbers can result in a nonlinear $v_f = f(m)$ relationship, contributing to the observed dispersion. Additionally, part of the dispersion arises from the different $a$ values tested, as $v_f = f(m)$ is also expected to vary with $a$ for a fixed $Le$ [33].

Beyond its influence on $v_f$, it is expected that $m$ plays a key role in determining flame symmetry. As shown in Figure 6, all tests with $m < -2$ resulted in symmetric flame shapes. However, for $m > -2$, both symmetric and asymmetric flames were observed, depending on the values of $m$ and $a$. The influence of $a$ is examined in more detail in subsection 3.2.

To illustrate the *m* effect, Figure 8 a) presents PIV results for $\phi = 0.6$ and $h = 2.6$ mm, using the two gas injection configurations described in subsection 2.4. Since the mixture composition and channel gap remain unchanged, key parameters such as $a$ and $Le$ are held constant across both tests. In configuration 1, the flame induces a fresh gas flow in the same direction as its propagation, while in configuration 2, the fresh gas flows in the opposite direction. As expected, $m$ significantly influences the flame symmetry, with the symmetry factor increasing from $S = 0.03$ in configuration 1 to $S = 0.39$ in configuration 2. Note that, in configuration 2, the fresh gases are clearly deflected
to the left side as they approach the flame. This is also evident in the velocity profiles shown in Figure 8 b), where the maximum velocity is shifted toward the left, which is the longer side of the flame front. Finally, the corresponding values of *m* are shown for both cases, consistently indicating *m* < 0 for configuration 1 and *m* > 0 for configuration 2.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Flame propagation for $h = 2.6$ mm and $\phi = 0.6$ under the fresh gas injection configurations described in Figure 4. a) PIV fields, and b) velocity profiles.</figcaption></figure>

Despite the significant influence of the fresh gas flow direction on flame symmetry, it is important to note from Figure 6 that most tests exhibiting asymmetric flame shapes correspond to cases with $m < 0$. This indicates that the flow direction alone is not a sufficient condition to determine flame symmetry or asymmetry. Instead, there exists a critical value of *m* that depends on other parameters such as *Le*, and *a* [33]. This is illustrated in Figure 9, which shows the asymmetry factor *S* as a function of *m*. The numerical results from [33] are included as dashed lines for different values of *a*. For each *a*, there exists a critical *m* above which asymmetric flame shapes emerge, with symmetric solutions expected to the left of each curve. Overall, the experimental data align well with the numerical predictions.

For $m < -2$, all experimental data show $S < 0.1$, indicating symmetric flame structures. Most of the experimental points with $a \in [7.1, 10.9]$ lie close to the numerical curve corresponding to $a = 8$. Additionally,

three experimental data points with $a = 5.8$ and $m \approx 1$ are found near the $a = 6$ curve. Finally, for $a \in [4.2, 5.6]$, only symmetric flame shapes were observed experimentally. According to the $a = 5.5$ numerical curve, this is consistent, as asymmetries in this regime would require $m > 1$.

<figure><img src="image_10.png" /><figcaption>Fig. 9. Asymmetry factor *S* as a function of *m* for different values of *a*. The dashed lines correspond to the numerical results proposed by Dejoan et al. [33] for different *a* values.</figcaption></figure>

### 3.2. *a* effect

In the previous section, the influence of the dimensionless fresh gas velocity *m* on flame speed and symmetry was analyzed. However, the results revealed varying trends depending on the gap-to-flame-thickness ratio *a*, whose effect is explored in this section. Figure 10 shows the variation of *a* as a function of *φ* for the three gaps (*h*) evaluated. As expected, *a* increases with both *h* and *φ*, following the behavior of $\delta_f$ as presented in Table 1.

These results highlight the direct influence of *a* on flame symmetry. For $h = 2$ mm, all tests yielded symmetric flame shapes, including cases under gas injection configuration 2. This explains why symmetric flames are still observed for $m > 0$, as previously shown in Figure 6. In contrast, all experiments conducted with $h = 3.7$ mm resulted in asymmetric flame shapes, regardless the *m* value. Finally, for the intermediate gap of $h = 2.6$ mm, both symmetric and asymmetric flame shapes were observed, depending on *m*. This behavior aligns with the numerical predictions by Dejoan et al. [33], which indicate that the critical value of *m* separating symmetric from asymmetric regimes increases with decreasing *a*.

To illustrate the influence of *a*, Figure 11 presents two tests conducted with the same mixture ($\phi = 0.6$) and similar values of *m*, but in channels with different gaps: $h = 2$ mm and $h = 2.6$ mm. In this comparison, the only varying parameter is *a*, which changes as a function of *h*, since $Le$, $\delta_f$, and $s_L$ remain constant for a fixed mixture.

For the test with $h = 2$ mm, the velocity profile corresponds to gas injection configuration 1, where
<figure><img src="image_11.png" /><figcaption>Fig. 10. Dependence of *a* on *φ*, with *S* values in different colors.</figcaption></figure>

the flow is induced solely by the thermal expansion
of the flame. In this case, the measured dimension-
less velocity is *m* = -0.1. In contrast, the test with
*h* = 2.6 mm uses configuration 2 to achieve a sim-
ilar value of *m* = -0.09, where the incoming fresh
gas flow partially cancels out the flame-induced flow
near the flame front, resulting in net velocities close
to zero.

Despite having nearly identical *m* values and
identical mixture properties, the two tests exhibit
markedly different behaviors. The flame in the *h* =
2 mm channel remains symmetric and propagates
more slowly (v<sub>f</sub> = 1.77), whereas the flame in the
h = 2.6 mm channel becomes asymmetric and prop-
agates faster (v<sub>f</sub> = 2.48). This clearly demonstrates
the significant role of *a* in controlling both flame sym-
metry and propagation characteristics in narrow chan-
nels.

The combined $m = f(a)$ effect on flame symmetries is presented below, in which the boundary proposed by Dejoan et al. [33] are tested.

3.3. $m = f(a)$ boundary testing

The results presented above demonstrate that flame
symmetry is governed by the combined influence of
*m* and *a*. Figure 12 shows the experimental *m* = *f*(*a*)
data, along with the critical boundary proposed by De-
joan et al. [33], plotted as a solid line. As observed,
this boundary effectively separates the symmetric and
asymmetric flame shapes. All experimental points are
correctly classified, with the exception of one sym-
metric data point at *a* = 5.8 and *m* ≈ 1, which lies
close to the critical boundary but is predicted as asym-
metric. This minor discrepancy aside, the results con-
firm the predictive capability of the numerical model
proposed in [33], and further validate the key role of
both *m* and *a* in governing flame shape asymmetry in
narrow channels.

<figure><img src="image_12.png" /><figcaption>Fig. 11. Flame propagation for $\phi = 0.5$ for $h = 2$ and 2.6 mm. a) PIV fields, and b) velocity profiles. Test with $h = 2$ mm is performed using the configuration 1, and test with $h = 2.6$ mm using the configuration 2 described in Figure 4.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. 12. Testing of the symmetric/asymmetric $m = f(a)$ boundary obtained numerically by Dejoan et al. [33].</figcaption></figure>

To further analyse the physics underlying symme-
try breaking, we now examine the roles of the Péclet
(*Pe*) and Damköhler (*Da*) numbers, which fundamen-
tally govern flame behaviour in Hele–Shaw configu-
rations. The definitions used by Kelly et al. [34] are
used in this work, i.e., *Da* = (h²/D<sub>T</sub>)/(δ²<sub>T</sub>/D<sub>T</sub>) and
*Pe* = v<sub>fg</sub>h/D<sub>T</sub>, where D<sub>T</sub> is the thermal diffusivity.

38

39

40

41

42

43

44
Figure 13 presents the Da = f(Pe) diagram for the symmetric (o) and asymmetric (x) flames obtained in this work. This diagram reveals three flame regimes. For low Da < 40, reactions are slow relative to diffusion, gradients are homogenised, and flames remain symmetric regardless of Pe. For high Da > 60, reactions dominate over diffusion, so local perturbations are amplified; combined with Le < 1, thermodynamic effects enforce asymmetric flames independent of Pe. In the intermediate range 40 < Da < 60, reaction and transport compete: flame symmetry becomes Pe-dependent, with asymmetries near Pe ≈ 0 and symmetric flames at strongly negative Pe, where advection dominates and suppresses lateral instabilities.

<figure><img src="image_14.png" /><figcaption>Fig. 13. Damköhler number Da as a function of Péclet number Pe.</figcaption></figure>

## 4. Conclusions

This work presents an experimental investigation of the effect of the dimensionless fresh gas velocity (m), and the channel gap-to-flame thickness ratio (a) on flame symmetry in narrow Hele-Shaw channels. The Particle Image Velocimetry (PIV) technique is used to characterize the velocity field upstream of the flame. The experiments were performed for H₂/air mixtures with equivalence ratios $\phi \in [0.5, 1]$, and channel gaps $h = 2, 2.6$, and 3.7 mm, covering a wide range of flame thicknesses and Lewis numbers.

The experimental methodology used was successful for obtaining the fresh gas velocity fields in millimeter channels. The glycerol/propylene glycol aerosol used as a tracer does not significantly alter flame propagation or shape, as shown by comparisons of consumption speed ($S_{cons}$) and flame fronts with and without tracer. The tracer also reliably reproduces the flame front geometry, confirming the suitability of this method for analyzing flame symmetry in narrow channels. The velocity profiles upstream of the flame were found to follow a Poiseuille distribution, with high agreement ($R^2 > 0.9$) with parabolic fits. The dimensionless velocity $m$ was extracted by averaging the normalized velocity profile close to the flame.

A linear trend between the dimensionless flame speed $v_l$ and $m$ was observed, in agreement with numerical predictions. However, significant dispersion was found in the range $m \in [-2, 2]$, consistent with the presence of thermodiffusive instabilities for $Le < 1$ mixtures. The experimental data were well bounded by the numerical results for $Le = 1$ and $Le = 0.8$ presented in [33].

Regarding flame shape, although the direction of the fresh gas flow (i.e., sign of $m$) influences flame symmetry, it is not a sufficient condition to determine it. Asymmetric flame shapes were observed even for $m < 0$ under certain conditions, highlighting the need to consider the combined effect of $m$ and $a$. The latter was found to play a critical role in determining flame symmetry. For $a < 5.6$, all observed flames were symmetric, while for $a > 7.5$, all flames were asymmetric regardless of $m$. Intermediate values of $a$ resulted in both flame types depending on $m$. Additionally, the experimental data closely follow the critical symmetric/asymmetric boundaries proposed by Dejoan et al. [33] in the $m = f(a)$ and in the $S = f(m)$ space. Only one outlier was found, and even this point lies near the predicted boundary, supporting the robustness of the numerical results.

Finally, flame symmetry in Hele-Shaw cells results from the combined effects of Da and Pe. Low Da yields diffusion-dominated, symmetric flames, high Da leads to universally asymmetric flames due to rapid reactions, and at intermediate Da symmetry depends on Pe, with strongly negative Pe stabilizing symmetry and positive Pe promoting asymmetry. These results confirm the trends recently obtained numerically in [34].

This work provide an experimental study of the critical conditions for symmetry breaking in confined premixed flames, bridging the gap between numerical predictions and experimental observations. The findings demonstrate the importance of accurately quantifying fresh gas velocity to predict flame behavior in confined burners. This work opens new avenues for the experimental study of thermo-diffusive effects and flame-structure interactions in millimeter and sub-millimeter channels using PIV technique.

### CrediT authorship contribution statement

**C. Mejía-Botero:** Investigation, Formal analysis, Writing - Original Draft, Writing - Review & Editing.

**C. Almarcha:** Conceptualization, Investigation, Formal analysis, Writing - Review & Editing, Funding acquisition.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments

This research was supported by the ECOSAFE

ANR project ANR-21-CE05-0028.

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