# Formation and stability of fibers obtained by cold gelation of pea protein isolate aggregates in a hydrodynamic spinning process

Alice Vilotte, Hugues Bodiguel, Deniz Gunes, Christophe Schmitt, Denis Roux, Emilie Guilbert, William Chèvremont, Clément de Loubens

<figure><img src="image_1.png" /></figure>

## ► To cite this version:

Alice Vilotte, Hugues Bodiguel, Deniz Gunes, Christophe Schmitt, Denis Roux, et al., Formation and stability of fibers obtained by cold gelation of pea protein isolate aggregates in a hydrodynamic spinning process. Food Hydrocolloids, 2023, 145, pp.108999. 10.1016/j.foodhyd.2023.108999. hal-04144969

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Submitted on 28 Jun 2023

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<figure><img src="image_2.png" /></figure>
# Formation and stability of fibers obtained by cold gelation of pea protein isolate aggregates in a hydrodynamic spinning process

Alice Vilotteª, Hugues Bodiguelª,*, Deniz Z. Gunesb,c, Christophe Schmittb, Denis Rouxª, Emilie Guilbertª, William Chèvremontd, Clément de Loubensª

## Abstract

Using plant protein sources in the formulation of food products is an important option to reduce the overall carbon footprint of the human diet. However, the ability to convert plant proteins into functional ingredients can hamper their use by the food industry. Our objective was to assemble pea protein isolate (PPI) aggregates into edible fibers. They were obtained by co-injection of a suspension of PPI aggregates with a solution of calcium chloride by means of physico-chemical bonds, i.e. in the absence of thermal treatment or chemical reaction. As soon as specific hydrodynamic conditions were met, homogeneous fibers of few hundreds µm diameter and few cm length were obtained. Small angle X-ray scattering showed that the building blocks of these fibers were dense aggregates of 400 nm radius. Calcium and PPI concentrations required for the processing of fibers were roughly given by the sol-gel state diagram of PPI aggregates. Compared to their dairy protein based equivalent, PPI fibers were obtained with a low mass fraction of protein (3% w/w) and were stable regardless of the concentration of calcium chloride used. We concluded that the robustness of the hydrodynamic spinning process was attributed to the strong reactivity of PPI aggregates with calcium ions and the low tendency of PPI gels to syneresis.

## Keywords:

plant protein, gelation, SAXS, calcium, microstructure

## 1. Introduction

A wider use of plant protein sources in our diet is crucial to improve and re-balance the sustainability of the current food system. Fortunately, recent advances in crop selection, agricultural efficiency as well as the development of mild protein extraction processes have enabled a variety of plant protein ingredients for food formulation (Sim et al., 2021). Besides their nutritional value, these plant proteins have been shown to have multiple uses and functionalities in food applications, provided that they are properly chosen and combined with the other food ingredients in complex matrices (Kumar et al., 2022). Hence, it has been shown that due to the various extraction processes, plant proteins do exist in various colloidal states. It is therefore important to apply appropriate treatment to standardize and maximize their functionality during food formulation by controlling their aggregation state (Amagliani & Schmitt, 2017; Schmitt et al., 2021).

An interesting type of protein aggregate is micro or nano fiber, which allows production of various types of edible structures and textures (Kouhi et al., 2020). Protein fibrils of about 100 nm persistence length can be obtained by self-assembly of partially hydrolyzed proteins upon prolonged heat treatment in

very acidic environment. It was initially applied to whey proteins, but was successfully tested on a variety of plant protein sources (Cao & Mezzenga, 2019; Li et al., 2023). The main limitation of this process is the time required for protein treatment as well as the harsh pH conditions, i.e. pH 2.0, which are difficult to scale up. Therefore, it is worthwile to look for alternative options to produce plant protein fibers.

Recently, long microscopic protein fibers (≈ 100 µm diameter) were obtained by a simple hydrodynamic method. The process consisted of co-injecting a suspension of whey protein isolate (WPI) fractal aggregates with a solution of calcium chloride (Vilotte et al., 2022). The sol-gel transition was triggered by the diffusion of calcium ions into the jet of aggregates. Gelation resulted from both screening of electrostatic interactions and specific binding of calcium ions with aggregated proteins (Alting et al., 2003; Kharlamova et al., 2018). Whereas fiber diameter was tuned by the hydrodynamic conditions, such conditions could also lead to hydrodynamic instabilities which limited the formation of the fibers. More importantly, strong non-monotonic effects of calcium concentration were reported due to a competition between micro-phase separation and osmotic phenomena which controlled the stability of the fibers.

Interestingly, pea protein isolate (PPI) was shown to have the ability to form aggregates upon heat treatment in order to produce nanoparticles or larger micrometer scale dense aggre-

<footnote>ªUniv. Grenoble Alpes, CNRS, Grenoble INP, LRP, 38000 Grenoble, France</footnote>

<footnote>ᵇNestlé Research, Nestlé Institute of Food Sciences, Vers-Chez-Les-Blanc, Lausanne 26, CH-1000, Switzerland</footnote>

<footnote>ᶜCurrent adress: Department of Chemical Engineering and Center for Food and Microbial Technology, KU Leuven, 3001 Leuven, Belgium</footnote>

<footnote>ᵈESRF, The European Synchrotron, CS 40220, Grenoble F-38043, France</footnote>

<footnote>*hugues.bodiguel@univ-grenoble-alpes.fr</footnote>
gates (Tanger et al., 2021), while being sensitive to the presence
of calcium ions (Fan et al., 2020; Amagliani et al., 2023).

The objective of this paper was to extend the process of
hydrodynamic spinning of edible protein aggregates to PPI ag-
gregates. They were obtained by heat-induced aggregation and
co-injected with a solution of calcium chloride in a core-annular
flow. The structure of PPI aggregates was investigated by small
angle X-ray scattering (SAXS). Then, we studied the stability
of these fibers, their microstructure and the range of hydrody-
namic conditions leading to the formation of stable fibres. In
this paper, we compare the results obtained with WPI (Vilotte
et al., 2022) to new results obtained with PPI. As PPI aggregates
have a higher reactivity to calcium ions than WPI aggregates
(Silva et al., 2018), we expected to reveal some remarkable fea-
tures of PPI based fibers.

**2. Materials and methods**

2.1. *Suspensions of PPI aggregates*

Pea protein isolate (PPI) Pisane C9 (batch 873053) was man-
ufactured by Cosucra (Warcoing, Belgium). The proximal com-
position of the PPI was (in g/100g powder wet basis): protein
80.72, ash 5.37, moisture 4.15, fat 8.76. Protein composition
was about 70% salt-soluble globulins and 5% water-soluble al-
bumins (Moll et al., 2022).

A PPI solution of 5 % w/w was dissolved in demineralized water, 0.02 % w/w sodium azide was added to the solution to prevent bacterial growth. The solution was gently stirred for 3 h at ambient temperature until complete dissolution of PPI powder and then homogenized at 250 bars with a two-stage high pressure homogenizer PandaPLUS 2000 (GEA) to ensure maximum solubility of the pea protein (Moll et al., 2021; Amagliani et al., 2023). The pH was adjusted at 7.0 with 1M HCl.

Solutions of calcium chloride were prepared by dissolv-
ing CaCl2·2H2O powder purchased from Sigma-Aldrich (CAS
number 10035-04-8) into demineralized water. The concentra-
tion of calcium chloride C<sub>Ca2+</sub> ranged from 35 mM and 5.9 M.

PPI aggregates were produced by heating the solution of
5% w/w PPI for 15 min at 95°C in 10 mL Pyrex tubes. The
suspension of aggregates was then cooled down in an ice bath
and kept at 4°C during one night. The hydrodynamic radius
R<sub>h</sub> of the aggregate was measured by Dynamic Light Scatter-
ing (VASCO Particle size Analyzer, Cordouan Tech.) and was
about 400 nm. Figure 1-b shows the sol-gel state diagram of
PPI aggregates. We also reported results obtained with WPI
aggregates, see Vilotte et al. (2022) for details. Briefly, the sus-
pension of fractal WPI aggregates was obtained by heating a
solution of 8 % w/w WPI at 10 mM NaCl and pH 7.0 at 92°C
for 30 min. The aggregates had a 70 nm R<sub>h</sub> and fractal dimen-
sion of 2 (Vilotte et al., 2021). The sol-gel state diagram of WPI
aggregates has been studied by Kharlamova et al. (2018).

In order to keep the size of the aggregates constant over
the whole study, the concentration of the suspensions of PPI
and WPI aggregates, C<sub>agg</sub>, was varied by dilution or by gentle
evaporation at 30°C for several hours under stirring.

<figure><img src="image_3.png" /><figcaption>Figure 1: **a:** Fibers were obtained by co-injecting a suspension of PPI aggregates with a suspension of calcium chloride. The residence time was fixed at 6 s, whatever the flow rates used. Fibers were then stored in a calcium bath for 20 min (maturation step) to complete their gelation. **b:** State diagram of PPI gelation and syneresis. PPI aggregates were obtained by heating 5 % w/w PPI, pH 7.0 at 95°C for 15 min.</figcaption></figure>

2.2. Small-Angle X-Ray Scattering

The structure of PPI and WPI aggregates was characterized
by SAXS experiments (Echaniz et al., 2025) on beamline ID02,
ESRF (Grenoble) which offered an energy of 8.0 - 20.0 keV
and a sample-detector distance from 1.5 *m* to 31 *m* (Narayanan
et al., 2018). We perform measurements at 10 *m* and 31 *m* at
fixed energy of 12.230 *keV*, which correspond to a range of
scattering vector (*q*) from 2 × 10<sup>-3</sup> to 0.3 nm<sup>-1</sup>. Samples were
analyzed under static conditions in a flow through quartz cap-
illary of 2 mm inner diameter. This made it possible to mea-
sure the background and the sample at the same specific point,
which ensured a good background subtraction. The exposition
time was set to 0.5 s. This value has been determined to get
enough statistics for each spectrum, without any sample radi-
ation damages seen on the scattering curves. In addition, the
sample has been pushed forward into the capillary, so that a
fresh sample is measured for each acquisition. For each sam-
ple, the background of the cell containing water and 10 spectra
were acquired. Spectra of aggregates were obtained by averag-
ing the 10 data sets and subtracting the background. For both
suspensions of protein aggregates (i.e. 8 % w/w WPI, 10 mM
NaCl, pH 7.0 at 92°C during 30 min and 5 % w/w PPI, pH 7.0
at 95°C during 15 min), the spectrum could be assimilated to
the form factor of the aggregates, as the scattered intensity was
linear with respect to the aggregate concentration, in the whole
range of scattering vector (data not shown).

The radius of gyration R_g of the WPI and PPI aggregates
was measured in the low q range (q ≪ 1/R_g) of the scattered
intensity *I* using the Guinier analysis,

$$I(q) = I_0 \exp(-q^2 R_g^2/3) \quad (1)$$

where $I_0$ is the scattered intensity when *q* tens to 0. $R_g$ was obtained by a least-square fitting.

## 2.3. Hydrodynamic spinning

Fibers were obtained by co-injecting the suspension of PPI aggregates with a solution of CaCl₂ in a coaxial needle (Ramé-Hart Instruments), with inner and outer radii $r_i = 178$ µm and $r_o = 356$ µm, respectively (Fig. 1). The needle was embedded into a fluorinated ethylene-propylene flexible tube (Fluigent) immersed in a water-bath (27°C). Core and annular flow rates, $Q_{agg}$ and $Q_{Ca^{2+}}$, were controlled by a syringe pump (Nemesys, Cetoni). The residence time $\tau_r$ was kept fixed at 6 s by varying the tube length *L* from 11 to 225 cm. We defined the mean velocity by $v = (Q_{agg} + Q_{Ca^{2+}})/\pi r_0^2$ and $\tau_r$ by the ratio $v/L$. The diameter of the jet *D* of aggregates can be calculated by solving momentum balance and mass conservation equations in laminar flow conditions (Bonhomme et al., 2011). In the limit of low viscosity ratio $m = \eta_{Ca^{2+}}/\eta_{agg}$, it reads $D = 2r_0/\sqrt{1+2\alpha}$, where $\alpha = Q_{agg}/Q_{Ca^{2+}}$ is the ratio of flow rates, $\eta_{Ca^{2+}}$ and $\eta_{agg}$ the viscosities of the solution of CaCl₂ and aggregates, respectively. In our study, $v$ ranged from $10^{-2}$ to 0.8 m/s and *q* from 1 to 100. In these conditions, the Reynolds number $Re= \rho vr_0/\eta_{Ca^{2+}}$ ranged from 4 to 200. We showed in our previous paper the need to finely control hydrodynamic parameters in order to obtain long WPI fibers (Vilotte et al., 2022). Further in this paper, we show that the same hydrodynamic considerations apply for the hydrodynamic spinning of long PPI fibers.

As the time scale of calcium diffusion through the jet of aggregates $\tau_d \approx r_i^2/D_{Ca^{2+}}$ is of the order of 300-500 s, the residence time of 6 s was not sufficient to induce a full gelation of the jet. So, we collected the pre-formed fiber into a calcium bath (at the same concentration as the flux), in which they were stored for 20 min. Our previous experiments with dairy proteins showed that this step was very critical for the stability of the WPI fibers (Vilotte et al., 2022). In this paper, we investigate the stability conditions for the production of PPI fibers so to compare them with the WPI fibers

Lastly, parameters which were varied in this paper were $C_{agg}$, $C_{Ca^{2+}}$, *L*, *v* and $\alpha$. The residence time in the tube and in the calcium bath was set to 6 s and 20 min, respectively.

## 2.4. Microscopy

Fibers were observed by bright field microscopy (Olympus IX-72) with a ×4 objective just after the production, and all along the maturation step.

The inner structure of the fibers was observed by scanning electron microscopy (SEM). First, fibers were washed with distilled water, freeze-dried and pasted on a stub covered with double-sided carbon tape. Then, the specimens were coated with Au/Pd and secondary electron images were recorded with an FEI Quanta 250 scanning electron microscope equipped with a field emission gun and operating at 2.5 kV.

<figure><img src="image_4.png" /><figcaption>Figure 2: Normalized scattered intensity $I/I_0$ as a function of the scattering vector *q* for suspensions of PPI (green line, 5% w/w PPI, pH 7.0 at 95°C for 15 min) and WPI (blue line, 8% w/w WPI, 10 mM NaCl, pH 7.0 at 92°C for 30 min) aggregates used to produce the fibers. Red and black lines are Guinier fits (Eq. 1) for PPI and WPI aggregates, respectively. The dashed black line is $I \sim q^{-2.7}$.</figcaption></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>Figure 3: a: State diagram of PPI fiber formation and maturation. Green circles stand for stable PPI fibers within 20 min of maturation step. Green crosses are for cases where no PPI fibers were formed. The state diagram of PPI fiber formation is compared with that of the WPI obtained by Vilotte et al. (2022) for the same hydrodynamic conditions. $v=7.4 \times 10^{-2}$ m/s and $\alpha=10$. b: Fiber diameter after 20 min maturation as a function of calcium concentration for 5% w/w PPI fibers (circles) and 10% w/w WPI fibers (diamonds).</figcaption></figure>
# 3. Results and discussion

## 3.1. Structure of PPI aggregates

In this section, we analyse the structure of the PPI aggregates used to produce the fibers by co-injection of a suspension of PPI aggregates with a solution of calcium chloride at 27°C, Figure 1-a. Two steps were required to obtain the PPI aggregates. First, a dispersion of PPI was microfluidified to increase their solubility and decrease the particle size from 100 µm radius to 100 nm radius, see Moll et al. (2021) for details. Then, a 5% w/w PPI suspension at neutral pH was heated at 95°C for 15 min. Guinier analysis of static X-ray scattering intensity of the heated suspensions of PPI shows that the radius of gyration $R_g$ of the aggregates was 460 nm, green line in Fig. 2. This value is in line with the hydrodynamic radius obtained by DLS ($R_h$ = 400 nm), and laser diffraction analysis carried out by Amagliani et al. (2023). So, the heat treatment increased the size of the aggregates by a factor of 4.

Fitting $I(q)$ by a power law in the range $5 \cdot 10^{-3} - 3 \cdot 10^{-3} \text{ nm}^{-1}$ shows that the fractal dimension $d_f$ of PPI aggregates was about 2.7, which corresponds to a compact object and is significantly higher than the 2.0 reported for heated soy globulin (Chen et al., 2016). At high $q$ (>0.09 $\text{nm}^{-1}$), an inflection is visible on the spectra. The Porod plot ($Iq^4$ as a function of $q$, data not shown) presents an oscillation in the high $q$ range. This oscillation is characteristic of the scattering of a sphere. By fitting the scattering intensity of a suspension of (monodisperse) spheres on the data, a radius of about 10 nm was estimated.

All these results lead us to the conclusion that there are three important scales in the $q$ range $10^{-3} - 0.2 \text{ nm}^{-1}$. The 400 nm aggregates obtained after the heating process were the result of the aggregation of some compact soluble aggregates obtained by microfluidization. These compact aggregates were themselves composed of 10 nm entities.

Contrary to PPI aggregates, it is well established that WPI aggregates obtained by heat-induced aggregation at pH 7.0 are characterized by a fractal dimension of about 2 and that their size can be tuned by the ionic strength (Gimel et al., 1994; Mehalebi et al., 2008; de Guibert et al., 2020; Vilotte et al., 2021). More specifically, WPI aggregates used to produce fibers in our previous publication (Vilotte et al., 2022) were 10 times smaller than PPI aggregates, $R_g$ = 40 nm, blue line in Fig. 2. The hydrodynamic radius of WPI aggregates obtained by DLS was larger than $R_g$ obtained by DLS, $R_h$ = 70 nm. The polydispersity, the porous structure and the weak scale separation between WPI aggregates and the oligomers could explain this difference.

## 3.2. Fiber stability during the maturation step

The role of physicochemical parameters on the formation and stability of PPI fibers was first studied by varying the PPI concentration $C_{agg}$ and calcium concentration $C_{Ca^{2+}}$ during the hydrodynamic process and the maturation step. The hydrodynamic parameters were chosen far from the stability limits of the jet, i.e. $v = 7.4 \cdot 10^{-2} \text{ m/s}$ and $q = 10$, see below.

<figure><img src="image_7.png" /><figcaption>Figure 4: Scanning electron microscopy images of 5% w/w PPI fibers obtained with (a) 35 mM and (b) 4 M calcium chloride. (c) Scanning electron microscopy images of 8% w/w WPI fibers obtained with 2.9 M calcium chloride, adapted from Vilotte et al. (2022).</figcaption></figure>

The state diagram of the formation of PPI fibers shows two regions: either PPI fibres were formed and remained stable during the maturation step, or no fibres were formed, green areas in Fig. 3-a. PPI fibers could not be obtained if $C_{agg}$ was lower than 2.5 % w/w and $C_{Ca^{2+}}$ was lower than 0.01 M. These limits corresponded roughly to the limits of sol-gel transition as shown in the state diagram in Fig. 1-b. The sol-gel phase diagram shows a small domain at high $C_{Ca^{2+}}$ and low $C_{agg}$ characterized by syneresis (black squares), which did not seem to limit the formation of fibers.
This state diagram was surprisingly simple in comparison with that of WPI fibers (Vilotte et al., 2022), which is summed up in blue in Fig. 3-a. As for PPI fibers, WPI fibers were obtained only if $C_{agg}$ was larger than a threshold of 6% w/w instead of 2.5% w/w for PPI aggregates. This difference highlights that PPI aggregates can be more easily cross-linked by calcium ions than WPI aggregates, which is explained by a higher affinity between PPI and calcium ions (Silva et al., 2018). Moreover, WPI fibers produced between 0.2 and ≈2 M $CaCl_2$ swelled and dispersed during the maturation step. Above ≈2 M $CaCl_2$, stable fibers were again obtained. Dispersion of WPI fibers was concurrent with the emergence of syneresis in the sol-gel state diagram of WPI aggregates which starts for $C_{Ca^{2+}}$ as small as .01 M; see Kharlamova et al. (2018) for details. This limit was ten times higher for PPI aggregates, which explains why the dispersion of PPI fibers was not observed. But a closer look of the evolution of the diameter $D$ of the fibers with $C_{Ca^{2+}}$ showed that PPI fibers also swelled up to 3 M $CaCl_2$, Fig. 3-b. In contrast to WPI fibers, the increase in diameter was limited and did not lead to dispersion of the fibers. This is fully consistent with the difference in the syneresis limit value between the two systems. Above 3 M, the diameter of PPI fibers decreased. We observed the same phenomenon for WPI fibers. This shrinking was interpreted as the consequence of an osmotic phenomenon triggered by the high difference of chemical potential between the suspensions of aggregates and the solution of $CaCl_2$ at high concentration (Vilotte et al., 2022). This osmotic pressure difference creates a flux of water from the fiber towards the calcium which concentrates the aggregate in the fiber and promotes a sol-gel transition.

To summarize, PPI aggregates present several remarkable features of the process of their shaping into fibers. Compared to WPI aggregates, their greater reactivity with calcium ions allowed us to produce fibres with a smaller concentration of PPI than of WPI. In addition, syneresis phenomena were strongly delayed during the ionic gelation of PPI aggregates, which allowed PPI fibers to remain stable, regardless of the calcium chloride concentration used.

### 3.3. Fiber structure

For PPI fiber as wall, the decrease in diameter at high calcium concentration was attributed to the existence of an osmotic flux that shrunk the fibers. This phenomenon is due to a small selectivity of the gels to calcium chloride and will be described in detail in a forthcoming paper. The first consequence of this phenomenon is the shrinkage of the object, as reported in Fig. 3-b for WPI and PPI fibers at high calcium concentration. In the case of WPI fibers, a second consequence was observed: the spontaneous formation of a core-shell structure due to the transport of aggregates by the osmotic flux and their concentration in the shell. SEM images of PPI fibers at low and high calcium concentration (Fig. 4-a, b) do not show any evidence of a denser shell, conversely to WPI fibers (Fig. 4-c). Note that the apparent porosity seen in the SEM images was due to the freeze-drying process applied prior to performing SEM examination. The formation of a core-shell structure is influenced by various parameters, including the permeability of the gel, its

selectivity towards calcium ions, and the reaction rate. In the case of PPI aggregates, based on our observations, we can only speculate that the necessary combination of physicochemical conditions required for the formation of core-shell fibers was not achieved.

### 3.4. Hydrodynamic conditions for the spinning of aggregates

Lastly, the influence of hydrodynamic parameters on the formation of PPI was briefly studied and compared with our extensive study on WPI fibers (Vilotte et al., 2022). Fig. 5-a shows the state diagram of PPI fiber formation (green) in the $v-\alpha$ plane. Blue dashed lines are the two limits of stability as observed for WPI fibers, noted $v_1(\alpha)$ and $v_2(\alpha)$. The state-diagram is also illustrated by pictures of WPI and PPI fibers at fixed outlet velocity $v = 7.4 \ 10^{-2} \ \text{m/s}$ and various flow rate ratios $\alpha$, Fig. 5-c. As for WPI fibers, long PPI fibers were obtained in a well-defined window of hydrodynamic parameters. At high outlet velocity $v > v_2$, no or cut fibers were obtained. This limit was explained by inertia-driven instabilities in core-annular flow of miscible fluids Cubaud & Notaro (2014), see Vilotte et al. (2022) for details on WPI fibers. In short, the destabilization of the flow can be triggered either by diffusion or inertia, depending on the values of the Péclet (Pe) and Reynolds (Re) numbers (Cubaud & Notaro, 2014). In our experiments, the flow conditions were stable concerning diffusive instabilities as $Pe = vr_o/D_{Ca^{2+}}$ was larger than the threshold value of $0.5 \times 10^4$ reported by Cubaud & Notaro (2014). Inertia destabilizes also miscible core-annular flow if the Reynolds number is larger than 900/$\alpha$ for a viscosity ratio of 10 (Cubaud & Notaro, 2014). This order of magnitude was roughly in line with the $v_2$ limit obtained for WPI fibers. Note that the limit was slightly larger for PPI than for WPI fibers, which could be due to differences in the kinetics of gelation. At low $v$ and high $\alpha$ ($< v_1$), pieces of gel were obtained instead of long fibers. We observed that a clog was formed at the outlet of the inner nozzle and regularly evacuated. This limit is reached when the characteristic time of PPI gelation $\tau_g$ is equivalent to the residence time of the aggregates in the entrance region of the core-annular flow ($\approx r_0$), i.e. $v_1(\alpha) = r_0(\alpha + 1)/\tau_g$. Consequently, we estimated a characteristic time of gelation for PPI aggregates of about 0.8 s.

One important feature of the spinning hydrodynamic process is the possibility of tuning the diameter of the fiber thanks to the flow rate ratio $\alpha$. In fact, the diameter of the jet in core-annular flow is simply given by $D = 2r_o/\sqrt{1 + 2\alpha}$, in the limit of low viscosity ratio $m = \eta_{Ca^{2+}}/\eta_{agg}$. Consequently, the diameter of the fiber $D$ could be tuned by $\alpha$ and roughly followed to this hydrodynamic law, Fig. 5-b,c. However, $D$ was smaller for fibers obtained with high calcium concentration, which was consistent with the above-mentioned osmotic phenomena. It was also possible to obtain fibers on a larger range of $\alpha$ when the calcium concentration was increased.

## 4. Conclusion

In conclusion, we generalized the process of hydrodynamic spinning of protein aggregates to a plant protein, namely pea
<figure><img src="image_8.png" /><figcaption>Figure 5: **a:** State diagram of PPI fiber production in the *v* − *α* plane for 5% w/w PPI and 4.2 M CaCl₂. Circles correspond to the formation of long PPI fibers, whereas crosses show the formation of pieces of gel or cut fibers. Blue dashed lines show the limit of stability for WPI fibers (8% w/w WPI and 1.5 M CaCl₂ from Vilotte et al., 2022). **b:** Fiber diameter measured just after the production, for *v* = 7.4 × 10⁻² m/s as a function of the flow rate ratio *α*. Green and blue symbols correspond to 5% w/w PPI and 8% w/w WPI fibers for different CaCl₂ concentration. The solid line is the model prediction, *D* = 2r₀(1 + 2q)⁻¹/². **c:** Images of fibers formed with PPI and WPI aggregates for different CaCl₂ concentration, *v*=7.4×10⁻² m/s, *t*<sub>flow</sub>=6 s.</figcaption></figure>

protein isolate. Using this process, we produced long PPI pro-
tein fibers of few hundreds micrometer diameter. Static X-ray
scattering showed that the basic bricks of these fibers were PPI
aggregates of 400 nm radius and possess a characteristic dense
structure at least above a 10 nm scale. The strong affinity of
these aggregates to calcium ions allowed us to form fibers with
a small mass fraction of PPI (3% w/w). Furthermore, while
dairy protein gels were rapidly subject to syneresis, PPI gel
was not, making PPI fibres very stable regardless of calcium
concentration. Hence, we can infer that the hydrodynamic pro-
cess was robust, provided that the hydrodynamic conditions are

carefully selected to ensure stable formation of fibres. Finally,
we concluded that the hydrodynamic spinning of PPI aggre-
gates demonstrates the possibility of exploiting the colloidal in-
teractions of plant proteins in food processes in order to develop
new sustainable ingredients.

**Declaration of competing interest**

The authors declare that they have no known competing fi-
nancial interests or personal relationships that could have ap-
peared to influence the work reported in this paper.
CRedit authorship contribution statement

Alice Vilotte: Conceptualization, Investigation, Writing - original draft. Hugues Bodiguel: Conceptualization, Investigation, Supervision, Writing - original draft. Deniz Z. Gunes: Conceptualization, Supervision, Writing - review & editing. Christophe Schmitt: Conceptualization, Supervision, Writing - review & editing. Denis Roux: Investigation, Supervision, Writing - review & editing. Emilie Guilbert: Investigation, Writing - review & editing. William Chèvremont: Investigation, Writing - review & editing. Clément de Loubens: Conceptualization, Investigation, Supervision, Writing - original draft.

Acknowledgements

LRP is part of the LabEx Tec21 (ANR-11-LABX-0030) and of the PolyNat Carnot Institute (ANR-11-CARN-007-01). The authors thank Christine Lancelon-Pin (CERMAV-CNRS, Grenoble, France) for her assistance with scanning-electron microscopy. The authors acknowledge the NanoBio-ICMG chemistry platform (UAR 2607, Grenoble) for granting access to the electron microscopy facilities. We acknowledge the European Synchrotron Radiation Facility (ESRF) for providing beamtime.

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