# Characterizing the foaming process of polymers: Review of experimental methods

Vipin G Krishnan, Luca Fiorucci, Alexandru Sarbu, Wiebke

Drenckhan-Andreatta

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Vipin G Krishnan, Luca Fiorucci, Alexandru Sarbu, Wiebke Drenckhan-Andreatta. Characterizing the foaming process of polymers: Review of experimental methods. Advances in Colloid and Interface Science, 2025, 344, pp.103579. 10.1016/j.cis.2025.103579. hal-05391352

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# Characterizing the foaming process of polymers: Review of experimental methods

Vipin G. Krishnan<sup>a,*</sup>, Luca Fiorucci<sup>a</sup>, Alexandru Sarbu<sup>b</sup>, Wiebke Drenckhan-Andreatta<sup>a,*</sup>

## ARTICLE INFO

**Keywords:**

Foaming

In-situ characterization

Polymer foam

Bubbles

## ABSTRACT

Polymer foams have become increasingly significant in both scientific research and commercial applications due to their wide range of uses. Traditionally, the optimization of polymer foaming processes has relied on time-consuming trial-and-error methods, which has delayed scientific progress in this area. Recent studies suggest that achieving the desired foam properties requires the simultaneous optimization of both formulation and process. This approach moves beyond basic “before” and “after” investigations, advocating for a more thorough exploration of the entire foam expansion process, from the initial mixture to the final polymer foam. In this review article, we provide a detailed overview of the existing experimental techniques for in-situ characterization of the foaming process across various types of polymer foams, with a natural emphasis on polyurethane systems due to their prominent representation in the academic literature. We examine the strengths and weaknesses of these methods and provide recommendations for future advancements in this field. By carefully adopting these more advanced approaches, it is possible to better understand and optimize the foaming process, leading to improved control over final properties of polymer foams. This review aims to contribute to enhancing the academic and practical knowledge of polymer foaming, ensuring more efficient and innovative developments in the industry.

## 1. Introduction

The already outstandingly wide range of properties of polymeric solids can be extended via the integration of gas pores. For pore dimensions of the order of micrometers and larger, one commonly refers to “macro-porous polymers”. If these pores are “closely packed”, i.e., if they touch each other, one commonly refers to “polymer foams”. This close-packed configuration arises typically for a relative foam density below 0.36 (or porosity above 64 %) [1]. At the higher limit of this density, the pores resemble closely packed spheres (Fig. 1a,b), while in the limit of low densities, the pores have shapes of neatly packed polyhedra (Fig. 1c,d). Across the whole density range, either the pores can create an inter-connected network in an open-cell foam (Fig. 1b,d), or thin membranes can separate all the pores in a closed-cell foam (Fig. 1a,c) [2].

The presence of this aerated architecture dramatically modifies all of the physical properties of the polymeric material [4–8]: the overall density is reduced; high stiffness-to-weight ratios can be achieved; complex mechanical properties ensure unique shock absorption;

optimized morphologies lead to excellent thermal and sound absorption while electric loss remains minimal; high surface-to-volume ratios can be used for catalytic reactions; connected porosities are excellent for filtering and sponging applications; and matching of mechanical and structural properties turns polymer foams into excellent candidates for tissue engineering. Moreover, specific foam morphologies have the capacity to turn polymer foams into metamaterials, a classic example being auxetic foams [9].

Due to this wide range of useful properties, polymeric foams have entered a multitude of applications [10–15]: from food (bread, cakes, marshmallows, etc.); via seating applications, mattresses, packaging and shoe design, to thermal and acoustic insulation, and medical applications. As a result, global polymer foam market was worth about 140 billion USD in 2023 and is predicted to grow to about 240 billion USD by 2032 [16].

In many cases, the processes of generation of polymer foams have been optimized over several generations in tedious trial and error procedures. However, the increasing environmental pressures on replacement of certain components of the formulations, or the foaming of

<footnote><sup>a</sup> Institut Charles Sadron (CNRS-UPR22), University of Strasbourg, 67034, Cedex 2, Strasbourg, France</footnote>

<footnote><sup>b</sup> SOPREMA SAS, 67100 Strasbourg, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: vipin.gopalakrishnan@ics-cnrs.unistra.fr (V.G. Krishnan), wiebke.drenckhan@ics-cnrs.unistra.fr (W. Drenckhan-Andreatta).</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Electron microscopy images of different types of polymer foams. (a) and (b) are adapted from ref. [3].</figcaption></figure>

completely new polymers, require a much more efficient approach to innovation, building on the existing scientific know-how generated over the last 30 years. While our understanding of the structure-property relations of solid polymer foams has sufficiently advanced in allowing to predict what kind of foam morphology has to be combined with what kind of polymer properties for a given application [17–19], the greatest remaining hurdle is to establish the appropriate foaming process and formulation to obtain the desired foam morphology.

As sketched in Fig. 2, many foaming processes (and the ones of interest in the review) start with initially liquid(–like) mixtures of different components, within which gas bubbles are created by chemical or physical blowing processes, during which the liquid matrix solidifies via polymerization and/or crosslinking. The blowing process may be driven by gas-releasing chemical reactions (for example, CO₂-releasing water-isocyanate reaction during polyurethane foaming [20], H₂-release during silicone reactive foaming [21–24], etc.) or by physical creation of gas bubbles. The latter relies either on mechanical frothing,

or on liquid-gas phase transitions initiated through external influences such as heating or pressure release. Mostly, the chemical reactions are exothermal, providing the heat for physical blowing – hence coupling chemical and physical parameters. In all cases, foaming and solidification processes are interconnected, often in an antagonistic way, turning it into a real challenge to establish the optimal formulation for a desired foam property. Secondly, as sketched in Fig. 3, at constant formulations, it has been shown that the process itself has a major influence on the final foam properties [25–28], making it as important as the formulation. This includes (I) the integration of air bubbles in the mixing stage, which act as heterogeneous nucleation sites for the foaming process, or (II) the nature of the mixing of often highly reactive substances. And last but not least, since most of the foaming process takes place when the polymer matrix is still in a liquid-like state, the foam experiences a range of “ageing” mechanisms such as coalescence or gas exchange between neighboring bubbles, and gravity-driven drainage of liquid towards the bottom of foam – all leading to a decrease in foam quality. The presence of these ageing mechanisms often demands to find appropriate stabilizing agents and to ensure that the polymer network becomes solid enough once the stabilizing agents loose efficiency. Hence, as indicated in Fig. 3, to obtain a desired polymer foam, the formulation and the process must be optimized simultaneously, paying particular attention to the interdependence of foaming process, foam decay and solidification process, which tend to be directly coupled to the choice of formulation. A systematic approach to this subject therefore requires establishing how these different items are interlinked in the evolving foam and to determine the ideal combination for a desired foam morphology. Theoretical and computational modelling of the foaming process has advanced well in recent years [29,30] to allow for detailed comparison with experimental measurements at different size scales (molecular scale to macroscopic scale) throughout the entire process. It is only through a dynamic interplay between modelling and experiment that we will identify the key parameters and mechanisms of a successful foaming process. Until now, most experimental studies have focused on “before” & “after” investigations, neglecting the precious temporal evolution of the nascent foam and therefore, insight into the complex interplay of the acting mechanisms. We think that experimental techniques and our understanding of liquid and solid foams are well advanced to tackle the full foaming process.

To help future studies pay attention to the full evolution of the foam,

<figure><img src="image_4.png" /><figcaption>Fig. 2. Temporal evolution of a classical expanding foam (here PU foam) on the macroscopic level (top) and the microscopic level (bottom).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 3. Schematic illustration of the fundamental building blocks towards obtaining a desired polymer foam.</figcaption></figure>

from initial mixture to final solid polymer foam, we provide here a
detailed summary of different appropriate measurement techniques. We
show how they can be used to extract precious information during the
foaming process. We discuss their advantages, but also their limitations.
While we made an effort to cover a wide range of polymeric systems, the
predominant use of polyurethane foams colors also this review. Most of
the introduced principles can, however, easily be transferred to other
polymeric systems, which is why we hope that this review (I) inspires a
more systematic approach to the characterization of the generation of
solid polymer foams, and (II) leads to the generation of a more profound
academic understanding of the underlying mechanisms so urgently
required for the efficient optimization of complex processes and for-
mulations towards the development of innovative polymer foams.

## 2. Tools for the characterization of the foaming process

Multiple characterization techniques exist in the current literature
for the in-situ follow-up of foaming process, each of them focusing on

specific foam features, as summarized in Fig. 4. For example, a good
foam for thermal insulation should have low density, small, homoge-
nous and closed cells, and a good mechanical resistance. Here we
introduce different characterization methods and explain what kind of
information can be extracted from these techniques. Our choice to
divide this section into four sub-sections allows not only to group
different techniques according to their measurement principles but also
allows us to discuss the main criteria required for an appropriate
foaming process and eventually, for a performant foam. Often, several
methods can be found in the same sub-section, since different techniques
can deliver the same information about the foaming system.

2.1. Analysis of foam density and morphology

The real-time or sequential observation of the foam growth process,
either through direct imaging or via reconstructed images, referred to
here as foam visualization, allows for a visual interpretation of the dy-
namic foaming behavior. Different techniques are available for this

<figure><img src="image_6.png" /><figcaption>Fig. 4. Graphical summary of the methods presented in this article which are used to characterize foaming processes at different scales.</figcaption></figure>
purpose, each having its advantages and drawbacks, which will be discussed in the following and which are summarized in Table 1.

The simplest technique is to capture the entire foaming process using an optical device (camera/microscope). A video or a sequence of images of the entire foaming process - combined with appropriate image analysis tools - not only provides a way for an in-depth visual analysis of the evolution of macroscopic foam properties (such as foam height, shape, etc.; see top row of Fig. 2 for an example), but can also deliver important information about bubble/cell nucleation and growth process at the bubble scale. A disadvantage of optical methods is, however, that visualization is possible only on the sample surface (see Fig. 5a).

An in-situ optical surveillance of bubble formation from the beginning of bubble growth until the end of the foaming process permits the determination of the evolution of key foaming parameters such as bubble size distribution or bubble density. The literature contains a series of reports on the visualization of free foaming of polypropylene (PP) [31,32], polystyrene [33,34] and polyurethane (PU) [20] using custom-built visualization devices. For example, Wu et al. [31] employed a hot-stage visualization apparatus with high-speed camera for the in-situ imaging of low-density polyethylene (LDPE) foaming (Fig. 5a) and were able to precisely measure the temporal evolution of number density and size of the cells (see Fig. 5b,c). Such measurements can quantitatively reflect the real-time evolution of cellular structure in the growing foams. By investigating cell density as a function of foaming time, Deng et al. [32] showed that it is possible to draw important conclusions on the influence of the foaming environment, namely, melt temperature, pressure or foaming agent content, on the PP injection molding foaming process. With their home-designed optical microscopy system, Leung et al. [35] observed that under different gas concentrations, there is a change in the critical nucleation radius. A simple set-up based on a high-speed optical camera allowed Brondi et al. [26] to confirm the fact that air bubble inclusion during the pre-mixing stage of reactive PU foaming plays a crucial role in directing the final morphology of foam.

Optical visualization at the bubble scale combined with image analysis also allows for spotting foam decay mechanisms acting in the evolving foam, especially bubble coalescence (merging of bubbles) and Ostwald ripening (gas exchange from smaller bubbles to larger bubbles), and thereby provide the right impetus to reduce these mechanisms to obtain high quality foams. To quote a few examples, organofluorine additives were shown to be efficient in the controlled inhibition of bubble coarsening in PU foams by Brondi et al. [36], thanks to the analysis of images obtained by an optical camera during the foaming process. The examination of nucleation and growth of silicone foams under an optical microscope by Jawhar et al. [37] showed that in these foams, cell coalescence has a significant influence on the cell growth. Beyond applications to synthetic polymer foams, in-situ visualization methods have also provided a lot of understanding about bubble nucleation and growth in food foams [38].

Unfortunately, the application of optical methods is limited to the surface of foam sample, providing no direct information on the inside of the sample. Extrapolation of these surface observations to the bulk behavior therefore requires specific experimental care, and ideally, additional proof that this extrapolation can be done. Since heterogeneous nucleation may arise preferentially at the container surface, specific care needs to be taken. In many cases, the foaming liquid is also opaque, prohibiting observations at the bubble scale. Even with transparent liquids, multiple light reflections occurring at the air-liquid interfaces render the foaming system opaque in presence of many bubbles, hence limiting access to important information from visual inspection. However, in this case, important information can still be obtained from a macroscopic image analysis [39,40]. For example, the measurement of foam height (related to foam volume and density) as a function of foaming time (see Fig. 2 and Fig. 6) has become a standard method to compare the evolution of different formulations. The height evolution is considered to be one of the fingerprints in quality assurance testing of foams. From the height vs time curve, other fundamental foam parameters such as rise velocity, rise time (defined as the time between initial mixing and the highest foam expansion), etc. are also obtained. The rise profile is the first pictographic indicator of foam stability/instability, and from Fig. 6a, an ideal foaming process is characterized by the perfect timing between foam blowing and solidification process, and the absence of foam decay mechanisms. Fig. 6b shows the experimental foam rise profiles of a thermoset foam at different catalyst concentrations [41] and provides a clear insight on the best formulation for the foaming process. Combining the final foam height (and hence the foam volume at known container cross-section) with the mass of the foam, the foam density is often calculated. The evolution of the relative density of the foam is then obtained by dividing this foam density by the density of the same polymer in its bulk form.

Unlike optical devices which require post image processing and analysis for the determination of height evolution of foams, devices based on the flight time measurements of ultrasound can provide real-time curves of foam height as a function of time [42]. The best example for such an instrument is FOAMAT, which is a proprietary measurement system working with cup-foams [29,43–45]. A series of additional measurement modules, including a thermocouple, a pressure sensor, or a dielectric polarization sensor, make the setup versatile in a way that along with foam height, reaction temperature, rise pressure, viscosity, curing state, etc. can be measured simultaneously during the foaming process [46,47]. Because of the multitude of information it delivers, FOAMAT is now a popular tool among researchers in academia and industry, especially those working on PU foams. Since no comparable commercial alternatives currently exist, the term “FOAMAT” has become a standard reference in the literature. By exploiting FOAMAT measurements, Eceiza et al. [48] proposed to split the foam generation process of flexible PU foam into four different steps, as shown in Fig. 7: (1) bubble growth, (2) bubble packing, (3) cell opening, and (4) final

<table><caption>**Table 1**
Summary of the different visualization techniques.</caption><thead><tr><td>Technique</td><td>Advantages</td><td>Disadvantages</td><td>Highest Spatial Resolution</td><td>Temporal Resolution</td><td>Cost</td></tr></thead><tbody><tr><td>Optical Imaging</td><td>- Simple<br/>- High speed imaging possible</td><td>- Poor penetration<br/>- Limited to surface analysis</td><td>> 1 µm</td><td>High (down to ms)</td><td>Low</td></tr><tr><td>Cryo-SEM</td><td>- High resolution<br/>- Possibility to freeze a liquid system undergoing reactions</td><td>- Not real-time<br/>- Sample freezing may alter structure<br/>- Requires vacuum</td><td>> 1 nm</td><td>Very low (static only)</td><td>High</td></tr><tr><td>Micro-CT (X-ray Tomography)</td><td>- Access to 3D internal structure<br/>- Non-destructive</td><td>- Slow scan times for lab-based machines<br/>- Radiation effects<br/>- Beamtime required for synchrotron</td><td>> 0.5 µm (laboratory);<br/>> 100 nm (synchrotron)</td><td>Low for lab-based machines (min/h)<br/>High for synchrotron (> 1 s)</td><td>Lab-based: medium to high<br/>Synchrotron: Very high</td></tr><tr><td>X-ray Radioscopy</td><td>- Real-time imaging<br/>- Good for dynamic processes</td><td>- 2D projection only<br/>- Radiation damage possible</td><td>~ 10–100 µm</td><td>Very high (ms)</td><td>Medium to high</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>Fig. 5. (a) Bubble nucleation and growth in low-density polyethylene foam monitored using a high-speed optical camera, and the corresponding (b) cell density and (c) average cell size at different times of the foaming process. Adapted from ref. [31].</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. (a) A schematic diagram of foam height H as a function of time showing various scenarios. (b) Experimental curves showing foam height H vs time of a thermoset foam with different catalyst contents (Legends indicate the concentrations of catalyst). The higher the catalyst content, higher is the reactivity. (b) is adapted from ref. [41].</figcaption></figure>

curing. They put in evidence the effect of catalyst concentration on different stages of the foaming process. In a similar study on Michael addition foams, the optimal catalyst concentration required for a successful foaming process was obtained from FOAMAT measurements by Mikelis and co-workers [41]. Kurańska et al. [49,50] performed a comparative study on the influence of different polyols on final foam properties of rigid PU, where they observed significant changes in foam height, rise rate and dielectric polarization of the foam upon changing the polyol. To put it briefly, a wide range of information about the foaming process and the subsequent modification can be deduced from the careful monitoring of different foam features.

Though optical devices can deliver some morphological information about the foams, their spatial resolution is limited and does not permit the probing of sub-micron structural information like cell wall thickness, strut thickness, or even cell sizes below a few microns. If such information is sought for, scanning electron microscopy (SEM) has become one of the most widely used tools for the precise microstructural

characterization of foams. SEM is most frequently used for in-depth investigations of the final foam [25,51,52]. For example, Coste et al. [51] used SEM for the quantification of cell sizes of Aza-Michael foams, which were found to depend on the choice of acrylate and blowing agent concentration.

SEM can also be used after cryogenically quenching the reacting systems at different stages of the foaming process. In this regard, cryogenic SEM (cryo-SEM), as demonstrated by Reignier et al. [53], provides a decent approach for the microstructural follow-up of rising foams. The sample requires no additional chemical treatments but involves freezing and cutting/fracturing before visualization. Samples are withdrawn at regular intervals from the reaction mixture, subjected to flash freezing in liquid nitrogen and stored there for subsequent SEM imaging. The temperature inside the SEM chamber is maintained in such a way that the sample remains frozen during the imaging and thus, preserves the original morphology at the time of withdrawal. Using this approach, Reignier et al. [53] visualized the highly heterogeneous nature of the
<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Monitoring PU foaming process using the FOAMAT instrument. Based on various measurements obtained from the FOAMAT device, the foam generation process is divided into four stages: bubble growth, bubble packing, cell opening and final curing. Adapted from ref. [48].</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 8.** (a) Cryo-SEM micrographs showing the heterogeneous nature of initial PU reactant mixture at different magnifications together with the corresponding schematic illustration. (b) MRM images of bread dough at different times during the fermentation process. (c) X-ray radiographs of flexible polyurethane during foaming. (a), (b) and (c) are adapted from ref. [53], ref. [57] and ref. [59], respectively.</figcaption></figure>
initial reactive mixture of PU (see Fig. 8a), which was composed of sub-micron sized droplets of physical blowing agent, micron sized nodules of dispersed phase and large bubbles of air, all dispersed in a continuous phase, as illustrated in the scheme in Fig. 8a. They revealed a non-classical nucleation mechanism in the PU foaming process, where blowing agent droplets are dissolved entirely into the continuous matrix before diffusing through it into the pre-existing air bubbles, rather than creating their own bubbles by vaporization (classical homogeneous nucleation). To further prove this, they showed that the number of cells in the final foam is equivalent to the number of air bubbles in the initial mixture. A similar study was performed by Hamann et al. [54] to show the additional impact of perfluorocarbons. Both studies are perfect examples to prove the key role played by air entrapment (during mixing) on the final foam morphology. Despite the important potential of cryo-SEM, its use in foaming process follow-up is limited due to challenges in sample preparation. Rapid freezing often introduces artifacts such as ice crystal formation, shrinkage, or structural fractures, potentially distorting the actual structure and leading to misinterpretation of the observed features. The need to work under vacuum may also evaporate certain volatile compounds. Moreover, cryo-SEM is technically demanding, time-consuming and expensive, making it less popular in the industrial setup [55].

Another powerful technique to follow in-situ the foaming process is magnetic resonance microscopy (MRM) which is based on spatial encoding of NMR signals, enabling images of opaque objects with micron-sized spatial resolution [56]. This non-invasive technique can provide real-time images of different stages of cell development (see Fig. 8b). For example, Bonny et al. [57] introduced a protocol for dynamic MRM imaging of bread dough fermentation to understand how the fermentation process directs the final bread foam texture, allowing them to compare three different dough compositions. MRM is particularly useful for bread analysis since cell sizes and cell wall thicknesses are of the order of 10–1000 µm. When it comes to fast foaming processes, its low temporal resolution makes it difficult to capture rapid bubble nucleation, growth, and coalescence events in real time.

X-ray radioscopy is yet another non-standard technique for the dynamic visualization of cell morphology during the foaming process. Creating a two-dimensional map of projected X-ray absorption of the foaming sample, as shown in Fig. 8c, X-ray radioscopy exploits the strong difference between X-ray absorption of polymers and gases. In combination with image analysis, it therefore allows a quantitative study of the evolution of foam density and also gives some idea of cell sizes, cell density, etc. [58,59]. For example, Pardo-Alonso et al. [60] applied this technique to follow-up a reactive foaming process, helping them to develop insights into the heterogeneous nucleation effect of nanoparticles in PU foaming systems, which was not clearly understood by the ex-situ measurements. It also strengthened the idea that nucleation dominates over coalescence during the initial stages of foaming in nanocomposites.

The above-mentioned techniques can only furnish two-dimensional data of the foaming systems, whereas X-ray tomography or tomoscopy (time-resolved tomography) is capable of constructing finest quality 3D images of foams [61–63] via the point-by-point reconstruction of local X-ray absorption capacity of the sample obtained after taking X-ray radioscopies at different angles of the sample. Such 3D reconstructions require heavy data acquisition and processing, demanding the need for powerful computing resources. The new generations of lab-based X-ray tomographs have a sub-micron spatial resolution, appropriate to record full foam structure of the final solid foams [64]. However, due to long imaging times (several hours per 3D image at maximum resolution), these lab scale tomographic set-ups can only be used for foams with very slow expansion, as shown in the example of a foaming PMMA block at 150 °C in Fig. 9.

For in-situ visualization of faster foaming processes, synchrotron X-ray sources with very high intensities (10⁶ times higher than lab systems) must be used [65], pushing full 3D imaging at micrometric resolution down to a second of imaging time. Apart from the high intensities, synchrotron radiation allows for the use of phase contrast X-ray imaging that can easily distinguish between different materials of similar characteristics [66]. Time-resolved experiments carried out on PU [65], metal [62,67] and bread [61] foams demonstrated that X-ray tomography provides a better understanding of the nucleation and growth process. For example, Pérez-Tamarit et al. [65] performed tomoscopy experiments on PU foams without and with silica nanoparticles. The resulting reconstructed 2D and 3D images of both systems at advancing times of the foaming process are shown in Fig. 10a. Already from simple visual inspection, it was clear that silica nanoparticles enhanced the nucleation in PU foams. Using image analysis, nucleation density, relative density and cell size were obtained (Fig. 10b), according to which the process was classified into three regimes: (1) nucleation, (2) growth and (3) wet-dry transition. Silica nanoparticles were found to influence the dynamics of all the above-mentioned processes in PU foaming system. Later, this was explained by the presence of gas pockets entrapped on the silica particles [27]. Overall, detailed 3D monitoring of the real-time evolution of foams allows to experimentally evaluate the involved mechanisms and test the existing theoretical models, yet the experiments remain heavy to conduct, depend on access to beamtime, and they generally require sophisticated computational image analysis of large data sets. Despite its power and necessity, it is therefore likely that synchrotron-based tomoscopy imaging will remain for another while a rather academic undertaking conducted by specialists on a small selection of model systems.

To summarize, foaming characteristics obtained using optical imaging methods or instruments like FOAMAT deliver first important information about the foaming process and final foam properties. These observations allow us to draw first conclusions on the efficiency of foaming processes via the investigation of bubble nucleation and growth mechanisms at the bubble scale, or the evolution of relative density at

<figure><img src="image_11.png" /><figcaption>**Fig. 9.** Foam formation over 50 min in an initially solid PMMA block heated to 150 °C imaged by a lab-tomograph (RX Solutions). Top row: 2D reconstruction. Bottom row: 3D reconstruction (Image courtesy of Damien Favier).</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Fig. 10.** (a) 2D and 3D reconstructed X-ray tomography images at different times of PU foaming process (with and without silica nanoparticles), and (b) the corresponding evolution of cell nucleation density, relative foam density and cell sizes, obtained by image analysis. Adapted from ref. [65].</figcaption></figure>

the foam scale, etc. These techniques are comparatively simple, less expensive and easy to set up, but provide only the details of the foam surface. To probe inside the foaming system visually, more sophisticated instruments such as SEM, MRM, X-ray radioscope, etc. are required, the most sought-after technique so far being SEM due to its high resolution. However, SEM still lacks popularity to follow up the foaming process because of the technical complexity associated with the cryogenic process and the necessity to cut/break the samples. In all these techniques, resultant images are two-dimensional; whereas in X-ray tomography, 3D visualization of the system is possible. Therefore, the ideal technique for the visualization of foaming process would be 3D computer tomography, which currently has limitations such as restricted temporal and spatial resolution, incompatibility with high temperatures and reactive environments characteristic of polymer foaming, need for large and heavy instrumentation, and substantial computational effort required for image processing and analysis. Given their significant value in offering non-destructive and complete three-dimensional imaging, the scientific community may want to consider developing advanced computer tomographic techniques featuring faster scanning systems, improved detector sensitivity, and integration with in-situ heating or reaction chambers to enable dynamic monitoring under realistic processing conditions of faster foaming processes, thereby making such techniques

available to a wider community. In order to help the reader in choosing the appropriate technique, Table 1 summarizes the presented techniques with respect to their advantages, disadvantages, spatial resolution, temporal resolution and cost.

It is also important to add that for each visualization technique, we should consider how the resulting images can be used effectively. This may range from simple visual inspection to a detailed quantitative analysis of the evolution of pore size distributions, pore shapes, strut dimensions, spatial distributions, etc. The latter may require heavy numerical efforts, accompanied by ongoing research on efficient treatment of complex 2D, 3D or 4D (spatial and temporal information) data [68]. These efforts are being boosted by increasing computing power and advanced algorithms which are either integrated into commercial software or freely available [40,69]. More importantly, a real leap forward in the image analysis is currently underway due to the rapid evolution of Machine Learning methods [68,70,71]. Unfortunately, it goes beyond the scope of this article to present these different tools in detail, but the reader should be aware that this is a rapidly developing field, offering a fast-growing number of powerful solutions to a variety of analysis problems.
## 2.2. Characterization of thermal evolution

Temperature is one of the critical parameters in the foaming process, especially if the foaming reaction is exothermic in nature. The choice and efficiency of physical blowing agents depend a lot on the thermal evolution of the reaction, which is often correlated with the solidification process. It is therefore important to conduct in-situ temperature measurements during the foaming process. This can be done either with thermocouples [72] or using infrared (IR) cameras. Foam expansion measurement techniques like FOAMAT integrate thermocouples into the system for recording temperature evolution during foaming along with other sensors to simultaneously measure foam height, dielectric polarization, etc. For example, Santiago-Medina et al. [73] observed simultaneous appearance of peaks in dielectric polarization and temperature in tannin foams and concluded that this was a good indication of a perfectly balanced formulation (see Section 2.4 for a more detailed description of dielectric polarization measurements). However, one of the disadvantages of thermocouples is that they provide only local temperature measurements, which can be misleading with respect to the complete thermal profile of overall foaming system. For example, the temperature in the center of an exothermic foam during the foaming reaction would be much higher than that towards the surface of the foam, moreover, the cooling rate will be much higher at the foam surface than towards the center of the foam. One way of tackling this irregularity is to employ a series of thermocouples at different positions within the foam; a temperature logger with multiple thermocouple slots can be used for the real-time temperature monitoring in multiple spots of the foaming systems. An example of such a measurement is given in Fig. 11a, which shows different temperature evolutions for different radial positions during the exothermic foaming process of an Aza-Michael reaction (unpublished work by the authors). However, one needs to keep in mind that these thermocouples are intrusive and may interfere with the expansion process, leading to inhomogeneities in foam structure. Currently, there are no alternatives that provide accurate internal temperature measurements without some degree of intrusion. By using a fine-gauge thermocouple and optimizing its placement inside the foam, the degree of intrusion can be minimized.

Unlike thermocouples, IR thermal imaging is a non-invasive visual detection technique for real-time temperature monitoring, and therefore, does not interfere with the foaming process. In this method, spatially resolved thermal (IR) radiation from the foaming system is captured using a dedicated infrared camera and converted into colored images, where different colors represent different temperatures. For

example, as shown in Fig. 11b, Santiago-Calvo et al. [74] used a PU foaming system for demonstrating the utility of IR cameras. The authors named this methodology "infrared expandometry" since they were able to characterize the expansion kinetics of the foam along with its temperature evolution by combining image analysis with IR camera measurements. Apart from providing the temperature of the whole sample surface without interfering with the foaming process, this method also furnished precise information regarding the volume expansion of the foam and helped in detecting heterogeneities like thermal hot spots (Fig. 11c), which might have occurred due to poor mixing of reactive components. By taking the radial average of the temperature (in the green rectangular boxes shown on the top of Fig. 11d) of the foam along the foam height, the authors were able to condense the whole foaming process into one single image (time-temperature map), as shown at the bottom of Fig. 11d. They validated the accuracy of their temperature measurements with the aid of a thermocouple. Despite all these positive features, IR cameras can only measure the surface temperature of foams. Therefore, to have the best approximation of the evolution of the temperature distribution within the foam system, the best approach is to couple minimally intrusive thermocouples for internal readings and IR cameras for surface temperatures.

## 2.3. Analysis of viscoelastic foam properties

Mechanical strength is one of the most critical properties for any material when it comes to practical applications. Mechanical properties of final foams are usually measured by compression test, which establish key parameters like Young's modulus or elastic and plastic deformation regions [41,51,75]. However, in-situ measurements of the evolution of mechanical properties during the foaming process are more complex since the same technique needs to characterize an initially liquid mixture until the final solid foam. This is commonly achieved using shear rheology which relates the torque required to shear the sample between two axially symmetric plates allowing to obtain the viscoelastic shear moduli for a given shear amplitude and frequency $\omega$. The elastic shear modulus $G'$ provides information on the solid nature of sample, while the loss modulus $G''$ is related to the sample's effective viscosity $\eta = G''/\omega$. In-situ monitoring of the evolution of foam mechanics by rheology has proven to be a successful method in this respect, allowing to a certain degree to decouple the mechanical contribution of the polymer matrix from the overall foam mechanics [76–80].

The complexity of a fast reactive foaming process involving temperature rise, volume change, viscosity build-up, phase separation, etc.

<figure><img src="image_13.png" /><figcaption>Fig. 11. (a) An example of temperature measurements obtained using thermocouples placed at different radial positions inside a growing foam undergoing an exothermic Aza-Michael reaction (unpublished work by the authors). (b) Schematic illustration of infrared expandometry. (c) Sequence of infrared images obtained during the PU foaming process, exhibiting thermal hotspots generated due to poor mixing of reactants. (d) Evolution of the vertical temperature profile or the 2D temperature map of PU foam. (b), (c) and (d) are adapted from ref. [74].</figcaption></figure>
makes it challenging for a conventional rheometer to follow the asso-
ciated rheological changes. To counter this, Mora et al. [76] designed
what they call a “flooded parallel plate geometry” (where the lower
plate of the rheometer is attached to the inside of the bottom of a
disposable paper cup and the second plate is lowered into the cup such
that the foam flows within and around the geometry), and were suc-
cessful in following the evolution of visco-elastic shear moduli during
the foaming of PU systems. Fig. 12a shows an example of the obtained
storage (G') and loss (G") moduli as a function of foaming time, allowing
the authors to identify four independent regions in the PU foaming
process. Region 1 was associated with the bubble nucleation stage.
Because of the delay in sample loading, stage 1 was already surpassed
before the start of measurement, and hence, no data was collected. To-
wards the end of region 1, G' crosses G" to exhibit a solid-like behavior,
which is characteristic of liquid foams whose solid-like behavior results
from the tightly packed bubbles [4]. Region 2, therefore, was identified
with bubble network formation and growth. Region 3 was characterized
by another rapid increase in the elastic modulus, which corresponded to
urea phase separation and stiffening of polymer matrix. This is also the
phase when cell opening takes place because of the continued chemical
reaction and gas pressure build-up, leading to termination of volume
expansion. Region 4 was identified with the foamed elastomer: the foam
reached its maximum elastic modulus, dominated by the polymer
modulus. While this evolution is qualitatively correct, quantitative
interpretation should be done with care since a major drawback of the
used geometry was the difficulty to attain adiabatic foaming conditions,
which are crucial for the realistic analysis of foaming processes since
foams are excellent thermal insulators [81,82]. Under non-adiabatic
conditions, heat exchange between the rheometer geometry and reac-
tive foaming system can significantly alter the thermal environment. If
the temperature of rheometer plates is not identical to that of foaming
system, the plates can act as heat sink to reduce exothermic reaction
temperature, and lead to delayed reaction kinetics. As a result, while the

qualitative trends of foam evolution may still be observed, quantitative
rheological measurements such as modulus development and viscosity
change can be misrepresented. M. J. Elwell [80], with the aid of a
modified temperature-controlled rheometer plate, experimentally
proved the necessity of forcing an adiabatic environment during rheo-
logical sampling of PU foaming systems. As shown in Fig. 12b, the
author put in evidence a difference in the development of the elastic
shear modulus under isothermal (dashed line) and forced-adiabatic
(solid line) conditions. Later, Elwell et al. [83] employed such forced-
adiabatic rheological measurements for systematic in-situ monitoring
of the structural development in flexible PU foams.

While the priority of shear rheometers is the measurement of shear
forces, Neff and Macosko [77] demonstrated the usefulness of analysing
the normal force evolution (the force exerted on the rheometer plates by
the foam during expansion) for the foam expansion and accurate spot-
ting of cell opening during the foaming of PU. Fig. 12c shows the normal
force profile of one of the PU formulations along with the evolution of its
elastic shear modulus, G'. The authors divided it into three regions,
namely, bubble growth and packing, foam expansion, and phase sepa-
ration/cell opening. The steep rise in normal force in the first region was
assigned to the initial foam rise and modulus build-up resulting from
bubble network formation. G' remained constant in the second region,
but the normal force kept increasing because of foam expansion.
Another rapid increase in normal force was observed in the third region,
which was predominantly due to polymer stiffening. The microphase
separation was followed by cell opening and therefore, the end of foam
expansion, which was detected from the sudden dip in normal force.

The above descriptions prove the power of rheology measurements
to follow in-situ the evolution of viscoelastic foam properties, allowing
to identify and separate the evolution of key features such as the foaming
process, solidification of the continuous phase or film opening. Despite
of this, rheology of foam rise lacks popularity among researchers
because of the associated technical complexities and difficulty to retain

<figure><img src="image_14.png" /><figcaption>**Fig. 12.** (a) Rheological curve (G' and G" as a function of time) demonstrating the four regions of a reactive PU foaming process. (b) Rheological curves showing the difference in the evolution of modulus under forced-adiabatic (solid lines) and isothermal (dashed lines) conditions. The second curve in each set is a repetition of the experiment. (c) Normal force profile of a typical PU foaming formulation under the rheometer; the sudden drop in normal force around 80 s corresponds to the cell opening. (d) Results obtained during a typical in-situ DMA experiment. (a), (b), (c) and (d) are adapted from ref. [76], ref. [80], ref. [77] and ref. [90], respectively.</figcaption></figure>
the rising foam between the parallel plate geometries, which restricts the thickness of sample to be tested to a few layers of cells [84,85]. However, most modern rheometers are equipped with high-speed, motorized heads combined with sensitive measurements of the normal force, which can rapidly adjust in response to foam expansion, enabling better tracking of foam rise without disrupting the system. The latest modules allow for convenient temperature control and much larger gap sizes which can be adapted during the measurement via normal force control. Modern rheometers also benefit from a particularly wide range of torque sensitivities and in-situ adaptation of oscillation amplitudes, providing reliable measurements all along the evolution of the foam from a liquid to a solid material. Last but not least, standardized modules now provide in-situ tracking of bubble formation via optical observation through transparent plate geometries. We therefore expect this technique to gain popularity in the near future.

To avoid the technical issues of plate-plate geometries, Zhang et al. [86] showed that a paddle (or vane) geometry can be an excellent alternative. They employed the vane geometry to measure the modulus build-up during PU foaming and found results very similar to those obtained using temperature-controlled parallel plate geometries developed by Neff and Macosko [77]. Apart from the accuracy, other advantages of vane-based methods include the elimination of temperature control, larger gap for foam rise and easiness of experimentation. In another report, Singh et al. [78] employed normal force profiles obtained using the vane geometry to understand cell opening phenomena in PU foams. Testouri et al. [87] used paddle rheometer for the determination of gelation kinetics of bulk PU and to quantitatively study the effect of catalytic concentration on the crosslinking process. However, downsides of the vane geometry are the impossibility to analyze reliably the first instances of foam formation (the foam needs to grow first around the vane) and the difficulty of normal-force measurements. Moreover, removing the solid foam from the complex geometry is challenging, requiring often to work with disposable vane geometries.

Dynamic mechanical analysis (DMA) is another popular technique for the characterization of viscoelastic properties of solid foams. It measures the response of the sample to oscillatory, uni-axial compression as a function of time, temperature or frequency [88,89]. Due to similar reasons as rheology, the application of DMA for the in-situ follow-up of mechanical properties of rising foams had never been explored until Cimavilla-Roman et al. [90] devised a customized

measurement set-up for DMA which was comprised of a cup with a piston, both made of Teflon, in addition to the parallel plate fixture. The piston was designed in such a way that it can glide with low friction inside the cup either by compression force or by force of the expanding foam. With this new set-up, they were able to conduct the DMA of initially fluid PU foaming systems and simultaneously follow the foam expansion and modulus build-up. As shown in Fig. 12d, the foaming system exhibited a small increase at the beginning in the viscoelastic moduli due to the expansion of foam. This was followed by a rapid increase in G' and G'' due to the polymer stiffening. The maximum of G'' was ascribed to the vitrification point, where the morphology was frozen and chain mobility was hindered [59]. Once this point was reached, the rate of polymerization was diminished, and the modulus rise almost flattened out. Thus, Cimavilla-Roman et al. demonstrated the efficiency of time-resolved DMA for the faultless monitoring of the evolution of viscoelastic moduli of reactive foams.

Acoustic techniques are yet another non-standard method for the in-line and non-invasive monitoring of foam growth due to the high sensitivity of speed and attenuation of sound with respect to the number and size of gas cells in foams [91]. For example, low-frequency ultra-sound was used for in-situ monitoring of the fermentation process during bread making [92,93], and important information regarding the cell expansion and mechanical properties of the matrix were obtained. The first report on the use of ultra-sonic sound velocity as a reliable technique for in-situ characterization of a reactive foaming process (PU foams) was published by Holt et al. [94], as exemplified in Fig. 13. The authors demonstrated the suitability of acoustic techniques to monitor different stages of PU foaming, especially the curing phase, and to extract the mechanical stiffness of the cured foam.

As seen in this section, follow up of foam mechanics during foam formation provides a lot of important information about the key foaming stages. Especially, rheology was shown to be an efficient method for in-situ mechanical characterization of the foaming process and to obtain sufficient degree of decoupling between the mechanics of the polymer matrix and the overall foam. Even though our understanding of the rheology of liquid and solid foams (and their coupling) has advanced significantly over the last 15 years [4,95], allowing for much finer interpretation of the rheology curves of reactive foams, rheo-foaming studies have not gained much popularity over time due to the associated technical challenges. We believe that with further innovations in

<figure><img src="image_15.png" /><figcaption>Fig. 13. Measurement of speed of sound in a reacting polyurethane foam, together with resistivity and density measurements. Adapted from ref. [94].</figcaption></figure>
geometry design, thermal control, and real-time adaptability, rheo-
foaming will become more routine and broadly accessible in future,
allowing for more realistic simulation of real foaming conditions.

2.4. Monitoring of the atomistic foam properties

As discussed in the introduction, reactive foaming processes involve
the fast conversion of an initially liquid reactive mixture of low molec-
ular weight into a highly crosslinked solid network enclosing numerous
close-packed gas cells. Therefore, it is fundamentally imperative to study
the reaction kinetics in order to understand the evolution of the polymer
structure during the foaming process. Dielectric polarization curves
obtained from FOAMAT measurements are good indicators of the
crosslinking reaction during the foaming process. Dielectric polarization
results from the orientation of dipole moments of polar molecules under
the influence of an external electric field [46]. In a foaming system, as
shown in Fig. 7, with the progress in crosslinking reaction, dielectric
polarization decreases progressively due to the formation of less mobile
and more rigid network structures, which hinders the orientation of
dipoles. Dielectric polarization reaches a minimum and becomes con-
stant when the foam attains its final polymer structure (complete curing)
[46,48].

Spectroscopic techniques are often used for the deduction of the
chemical structure of any material. Infrared (IR) spectroscopy has been
widely employed for in-situ monitoring of the reaction kinetics and
polymer morphology development, particularly in PU foaming systems
[83,96–100]. In addition, these measurements are helpful in spotting
unwanted side reactions. With the help of specific features in the IR
spectra, rates of polymerization/cross-linking, phase separation, solidi-
fication, etc. can be quantitatively studied in the evolving foams. IR

investigations of the final foam samples have shown, for example, that
PU foams exhibit microphase separated morphology [99,101]. As the
polymerization reaction proceeds, the chain length and viscosity of the
products increase, leading to changes in interaction parameters and
eventually, microphase separation. Thus, the system becomes heterog-
enous both chemically and spatially. The final polymer morphology is
decided by the kinetic competition between polymerization and
microphase separation [99,102]. Elwell et al. [83,99] employed forced-
adiabatic conditions during Fourier Transform-IR (FT-IR) measurements
of a model PU foaming system. From the decaying in-situ FT-IR peaks
corresponding to the isocyanate functionality, they were able to monitor
the isocyanate conversion during the reaction. The onset of microphase
separation was detected by comparing the normalized absorbance bands
of soluble and hydrogen-bonded urea (Fig. 14a), the separation being
marked by the amplification of hydrogen-bonded urea and depletion of
soluble urea. Haseth et al. [96] demonstrated the successful application
of an IR transmitting fiber for the in-situ monitoring of PU foam curing
process. Such a fiber probe allowed sampling to be done outside the
spectrometer (here, the probe passed through the foam center), causing
no restrictions on the sampling environment. In a similar study using a
mid-IR fiber probe, Bhat et al. [97] investigated the effect of different
silicone surfactants on the relative rates of urethane and urea formation
during PU foaming, which are known to affect the final foam properties.

Bernal et al. [103] studied the effect of functionalized and non-
functionalized nanomaterials on the PU foaming process using in-situ
FT-IR measurements and found that isocyanate conversion during the
initial stages of reaction was delayed by the presence of nanomaterials.
However, the functionalized nanomaterials accelerated the onset of
microphase separation. Thus, it was proven again that real-time chem-
ical structure monitoring can provide the right impetus for the

<figure><img src="image_16.png" /><figcaption>**Fig. 14.** (a) Normalized IR absorbance peaks of soluble urea (hollow circles) and hydrogen-bonded urea (solid circles) at different times during the foaming of two different PU formulations. (b) Chemical image of PU foam obtained using near-IR hyper-spectral imaging (HSI). (a) and (b) are adapted from ref. [83] and ref. [104], respectively. (c) Synchrotron SAXS plot of scattered intensity as a function of scattering vector during PU foaming and (d) the corresponding log I(q<sub>max</sub>) vs time plot. (c) and (d) are adapted from ref. [105].</figcaption></figure>
manipulation of polymer morphology during the reactive foaming process. Recently, Chen et al. [104] proposed a non-contact IR technique based on near-IR hyper-spectral imaging (HSI) for the in-situ monitoring of PU foaming reactions. Apart from the non-contact nature, other advantages of this method over conventional FT-IR spectroscopy are faster acquisition times and enhanced spatial resolutions. The authors also demonstrated the capability of this imaging technique to obtain chemical images and map heterogeneities of foams, as shown in Fig. 14b. These kinds of chemical maps are based on the height ratio of two different IR peaks. For example, Fig. 14b is based on the height ratio of 1432 nm and 1500 nm peaks which corresponded to various NH and OH containing species, respectively, within the PU formulation.

Small-angle X-ray scattering (SAXS) can also give concrete and reliable information on the polymerization of fast reactive foams [80,83,105]. Ryan et al. [106] employed synchrotron SAXS experiments to follow the polymer structure development during bulk copolyurthane formation with the aid of a custom-built SAXS sampling cell. However, the adaptation of this technique for real-time monitoring of PU foaming processes was difficult due to the sample size constraints and isothermal sampling conditions. Like in in-situ rheology and IR measurements, adiabatic sampling conditions were crucial for the SAXS measurements to deliver reliable results. With this aim, Elwell et al. [105] designed a temperature-controlled SAXS cell that could hold larger samples which allowed them to successfully follow the kinetics of microphase separation during polymer structure development in the reactive PU foaming process. Fig. 14c shows plots of scattered intensity ($I(q)$) as a function of scattering vector for one of their formulations at different times during the foaming process. During the early stage of reaction, SAXS did not show any peak due to the homogeneous liquid nature of the reactants. Upon microphase separation, the first SAXS peak appeared, which continued to intensify until the vitrification arrested the microphase separation. The authors were able to identify three regions of polymerization: (I) homogeneous phase, (II) microphase separation and (III) vitrification, using the corresponding plot of logarithmic peak intensity ($I(q_{max})$) vs time, as shown in Fig. 14d. Further, they showed that the microphase separation occurred at critical isocyanate conversion (or critical degree of polymerization), as shown before using FT-IR [99], and that it followed the kinetics of spinodal decomposition. Later, the same group conducted an extensive in-situ study on the polymer structure development of PU foams, combining SAXS, FT-IR and rheology, and the obtained results were in good agreement with each other [83].

In summary, FTIR and SAXS are the two major techniques for probing the atomistic properties of reactive foams in real time. Among them, the former is a more easily accessible technique, especially after the introduction of fiber type IR probes, which allow the researchers to conduct experiments outside the spectrometer cells. Similar advances are not yet available for the SAXS sampling, making these experiments more difficult to be carried out, especially if synchrotron radiation is required. FTIR and SAXS provide complementary insights into the structural evolution of polymer foams at different length scales. FTIR provides atomistic information allowing analysis of chemical composition, functional groups and conformational changes during the foaming process. In contrast, SAXS captures nanoscale structural features such as domain sizes, phase separation and internal morphology, allowing the study of spatial organization within the foam matrix. Combined, both techniques provide a powerful multi-scale characterization approach. SAXS presents nevertheless specific challenges, including the need for a uniform preparation of the sample and the complexity of data interpretation due to overlapping scattering from multiple structural components. In addition, time-resolved SAXS often requires high-intensity synchrotron radiation to capture the rapid kinetics of foam formation. While effective, such high-intensity beams can induce radiation damage in polymer samples, potentially leading to structural changes such as chain scission, cross-linking or localized heating. These effects can affect the accuracy of measurements.

Therefore, future efforts should focus on simplifying the experimental protocols so as to widen the application of these techniques and to explore new foaming chemistries.

### 3. Conclusions and outlook

As can be seen in this review, we avail of a wide range of experimental techniques to characterize the foaming process of reactive polymer foams. These techniques have already allowed to establish a reasonably good understanding of the overall temporal evolution of the observed features. For most systems (and generally for successful foaming), these can be grouped into four successive regimes characterized by the simultaneous evolution of the bubbles/cells and surrounding matrix (see Fig. 15):

1. Nucleation and growth of bubbles driven by gas release from chemical reactions and/or evaporation of physical blowing agents until bubbles are about to touch each other. In this regime, the sample is a "viscous bubbly liquid", characterized by $G'' > G'$ and the temperature rise is exponential (for exothermic reactions). The evolution of the bubble size distribution is the key experimental observation in this regime, being set by the coupling of bubble blowing and ageing effects (dissolution, Oswald ripening, coalescence, etc.).

2. Bubbles continue to grow. They start to touch and deform against each other (significant increase of foam height = decrease of foam density), creating a liquid foam having a finite shear elasticity due to the gas/liquid interfaces. The liquid foam formation is characterized by the intersection of $G'$ and $G''$ (leading to $G' > G''$). Since the matrix between the bubbles remains liquid at first, the foam is sensitive to different ageing effects (Oswald ripening, coalescence), as the bubbles are strongly pressed against each other. However, the viscosity increases rapidly and starts to diverge until reaching the gel point (roughly when $G' = G''$ of the matrix), i.e., the matrix becomes a soft solid and stops flowing between the bubbles. The maximum temperature of the system is reached in this regime, and towards the end of it, foam decay mechanisms are much less relevant.

3. The cells continue to grow a little, but their growth is hindered by the elasticity of the matrix. The matrix continues to rigidify, leading to a second important increase in the overall elastic shear modulus $G'$ of foam. Cell-opening has to arise towards the beginning of this regime (witnessed by a drop in normal force) so that the membranes can still rupture, while the elasticity of the matrix prohibits foam collapse. Maximum foam height (lowest density) is reached in this regime and foam temperature remains high due to its self-insulating nature. Also, this is when the final morphology of foam is attained.

4. The foam has stopped expanding since the matrix elasticity has increased drastically (and/or the cells are open). Without further changes in foam morphology, the overall mechanical response of the foam continues to stiffen due to the final stages of crosslinking of the foam matrix. Polymer shrinkage and cooling of the foam in this regime may eventually lead to measurable shrinkage of the foam. The final mechanical properties of the foam are almost entirely dependent on the foam density and strength of the matrix.

While this is globally the ideal scenario whose general features are now well captured by the complex theoretical/computational modelling efforts [29,30], our current academic understanding of the *optimal interplay* of these different features remains too limited to design efficiently new foaming formulations without having to go through extensive, experimental trial-and-error procedures. While modelling efforts have been made to describe the observations, it seems to us that they are not exploited enough yet to extract a fundamental understanding of the ideal combination of the different mechanisms to provide reliable guidelines in the search for optimal formulations (and processes). We think that this has four main reasons:
<figure><img src="image_17.png" /><figcaption>Fig. 15. Schematic illustration of different regimes of the foaming process and hypothetical curves showing the evolution of various properties with time.</figcaption></figure>

(I) In the past, this field has been essentially driven by industrial R&D (sometimes in collaborations with academics), creating a solid experimental know-how in industrial R&D departments - yet without a sufficiently profound interest by academics to generate a true fundamental understanding of the underlying mechanisms and their interplay.

(II) For a long time, academic efforts have focused on either liquid or solid foams in two separate academic communities, while this field requires to follow the evolution of an initial liquid foam into a solid foam, with much of its key science arising when the system is at an intermediate state.

(III) The modelling of reactive foaming processes is highly complex, linking chemistry, physical chemistry, physics and mechanics. While we already have a good academic understanding of most of the isolated mechanisms, their precise interplay (considering the large number of correlated parameters) is analytically impossible to predict fully. Computer simulations are therefore the tool of choice – and they are only starting to be realistic and powerful enough to reproduce experimental observations.

(IV) Modelling has to be accompanied by reliable experiments. Since most foaming methods are very rapid, many experimental tools have difficulties to follow the evolution in a manner which can be quantitatively compared with models. With recent technical evolutions (faster and better-resolved X-ray tomography, rheology, etc.), this gap is, fortunately, getting smaller. Moreover, researchers may take strong inspiration from techniques currently developed for either liquid or solid foams. To cite a few examples, acoustic techniques have been shown to obtain important structural information of either liquid or solid foams beyond simple flight time measurements [91,107]. Light scattering techniques have also been exploited in liquid foams to obtain information on bubble size and foam density [108]. They have also been adapted to solid foams [109] in recent times, promising interesting applications for evolving foams. Last but not at all the least, as far as we know, neutron scattering has not yet been exploited in this field, even though recent work on liquid

foams shows its power to access small scale information with the possibility to focus on specific items in the mixture after contrast matching [110].

Given the ongoing developments in the four areas mentioned above, we are optimistic that the future will see significant improvements in our ability to efficiently design formulations and processes that produce foams with desired properties. While growing academic understanding will be one of the important tools in this effort, the community is likely to be able to benefit from the increasing power of artificial intelligence (AI), if ways can be found to create large enough databases that unify experimental observations of a very wide range of systems, allowing AI to extract underlying correlations that can be used to make predictions for new formulations/processes.

### CRediT authorship contribution statement

**Vipin G. Krishnan:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Luca Fiorucci:** Writing – review & editing, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Alexandru Sarbu:** Writing – review & editing, Project administration. **Wiebke Drenc-khan-Andreatta:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

### Declaration of Competing Interest

None.

### Acknowledgements

The authors acknowledge fruitful discussions with Aurélie Hourlier-Targette, Leandro Jacomine, and Damien Favier. This work was
financed by (1) SOPREMA through the Foundation of the University of Strasbourg and Foundation Jean-Marie Lehn; and (2) via an ERC Consolidator Grant (agreement 819511 METAFOAM). It was conducted in the framework of the Interdisciplinary Institute Hi-FunMat, as part of the ITI 2021–2028 program of the University of Strasbourg, CNRS and Inserm, and was supported by IdEx Unistra (ANR-10-IDEX-0002) and SFRI (STRATUS project, ANR-20-SFRI-0012) under the framework of the French Investments for the Future Program.

## Data availability

Data will be made available on request.

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