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# A review and analysis of particle size parameters and their relationships to physical properties of growing media

Stan Durand, William Carl Fonteno, Jean-Charles Michel

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Stan Durand, William Carl Fonteno, Jean-Charles Michel. A review and analysis of particle size parameters and their relationships to physical properties of growing media. Soil Science Society of America Journal, 2024, 88 (3), pp.652 - 666. 10.1002/saj2.20661. hal-04748592

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ORIGINAL ARTICLE

Fundamental Soil Science

# A review and analysis of particle size parameters and their relationships to physical properties of growing media

Stan Durand<fnref n="1" />

<figure><img src="image_3.png" /></figure>

William Carl Fonteno<fnref n="2" />

Jean-Charles Michel<fnref n="1" />

**Correspondence**

Stan Durand, EPHOR Research Unit
L'Institut Agro, Angers, 49000, France.
Email: stan.durand@agrocampus-ouest.fr

Assigned to Associate Editor Jingyi Huang.

**Funding information**

EVADEA; Klasmann-Deilmann; Premier
Tech Horticulture; Angers Loire Métropole;
TurfTech Ltd; Floragard; Conseil Régional
des Pays de la Loire

**Abstract**

An expanded description of particle morphology and the analysis of its relationships with physical properties may help to optimize the selection of raw materials and particle size fractions used as growing media constituents. Previous works have described the outlines of these relations based mostly on sieving procedures to characterize particle size distribution. They have shown limited and sometimes contradictory results due to the different methods used, size fractions selected, and physical properties measured. Also, sieve analysis, which separates particles based on their width, is less accurate for non-spherical particles, which is the case for most growing media constituents. Recent works have promoted the use of dynamic image analysis (DIA) to precisely analyze both particle length and width. Five raw materials were chosen (white and black peats, coir, pine bark, and wood fiber) and sieved to obtain various particle size fractions. For each particle size fraction and the raw materials, the mean weight diameter (MWD), derived from sieving, was calculated, whereas mean particle length and width were determined using a DIA tool, the QicPic device. Also, physical properties were assessed from water retention curves established using Hyprop systems. The statement that the larger the particle size, the higher the air-filled porosity (AFP), the lower the water holding capacity (WHC) was more precisely redefined. Large variations in WHC and AFP mainly occurred for finest particle size fractions, whereas changes were conversely very small or non-existent for larger particle sizes. From data obtained for each particle size fractions, regression models were established to relate mean particle length and width (both determined using DIA) and MWD (determined from sieving) with WHC and AFP. Mean particle length was identified as the most relevant parameter for predicting WHC and AFP of the raw materials tested.

1 | INTRODUCTION

Growing media manufacturers engineer growing media to provide the plant root system with a physical environment conducive to rapid and robust growth. To that end, several industry processes are used to develop and define the quality of materials. These include (1) separation by sieving or

**Abbreviations:** AFP, air-filled porosity; AW, available water; Chord<sub>Min</sub>, minimum chord diameter; DIA, dynamic image analysis; EAW, easily available water; Feret<sub>Max</sub>, maximum Feret diameter; MWD, mean weight diameter; PSD, particle size distribution; TP, total porosity; WHC, water holding capacity.

<footnote n="1">¹EPHOR Research Unit L'Institut Agro,
Angers, France</footnote>

<footnote n="2">²Department of Horticultural Sciences,
North Carolina State University, Raleigh,
North Carolina, USA</footnote>
screening, (2) altering particle size by grinding or cutting, and (3) defibration or expansion of the raw components. These actions modify the shape and surface aspects of the particles and culminate in the manufacture of particles with predefined size ranges. With the considerable growth of soilless culture as well as the need to substitute peats (which are the main raw materials used as growing media components) for environmental issues (Bonn et al., 2016), manufacturers aim to promote current peat alternatives and to find new ones being more sustainable and more locally produced (Blok et al., 2021). They also seek to optimize the morphology of these raw materials in order to provide efficient growing media in terms of physical properties and water and air bioavailability for the root system.

Particle size distribution (PSD) analysis is a common procedure used to characterize physical properties as it affects particle arrangement and subsequently the water retention and flow properties of the growing media (Verdonck & Demeyer, 2004). Since the 1980s, many references have concluded that the larger the overall particle size, the higher the air-filled porosity (AFP) and the lower water holding capacity (WHC). However, their values vary widely depending on the materials tested. Table 1 summarizes the literature on the topic and shows a diversity of approaches. Indeed, the works were performed for different types of materials and different particle size ranges (raw materials, fractionated materials, blends) with respect to different physical properties, measured using various protocols with different parameters used to characterize the particle size. The latter are most commonly arithmetic or geometric mean weight diameter (MWD) (Kemper & Rosenau, 1986), coarseness index (Richards et al., 1986), or mass proportion of a given fraction.

This review reveals different observations due to the different approaches. Some authors noted that easily available water (EAW), available water (AW), WHC, or AFP seemed to be related to particle size, showing linear (Abad et al., 2005; Prasad & Ní Chualáin, 2004) or quadratic/power regressions (Durand et al., 2023c; Richards et al., 1986; Verdonck & Demeyer, 2004; Verhagen, 1997), whereas others did not (Caron et al., 2005; Handreck, 1983). Also, some suggested that some relationships apply to some blends (Naasz & Busière, 2011; Richards et al., 1986), while others did not (Prasad & Ní Chualáin, 2004). Finally, in this review (Table 1), it suggests that the effect of the particle size on the physical properties of growing media is confined to certain ranges in particle size (Durand et al., 2023c; Fields et al., 2015; Handreck, 1983; Nkongolo & Caron, 1999).

Although solid phase and pore phase organization, and consequently, physical properties, are influenced by PSD, other parameters affect water and air retention and flow properties (Boudreault et al., 2014; Caron & Michel, 2017). Mixing and potting operations can largely alter the bulk density by modifying the pore size distribution (Blok et al., 2019;

## Core Ideas

* Image analysis can be used to characterize particle size to understand relationships with physical properties.

* Changes in physical properties as a function of particle size occur within a limited size range.

* Particle length provides the best estimate of raw material properties based on those of individual fractions.

Gruda & Schnitzler, 2004) and affect the integrity of materials by changing their particle and pore size (Heiskanen, 1994; Heiskanen et al., 1996). Physical properties can be greatly affected by container geometry (i.e., container height) (Bilderback & Fonteno, 1987; Owens & Altland, 2008; Raviv et al., 2002). Changes in physical properties during cultivation occur due to drying/wetting cycles (with possible shrink/swell phenomena and decrease in wettability) related to the irrigation management and to root development in the growing media (Michel, 2019; Michel & Kerloch, 2017). Biodegradation of some growing media constituents has also been reported to decrease particle size and thus to change air and water retention for wood fiber and bark growing media (Jackson et al., 2009).

In the references cited in Table 1, PSD was generally determined by sieving methods, except that of Durand et al. (2023c), who used the dynamic image analysis (DIA) method. Sieving procedures are the most common methods used by manufacturers and researchers for PSD analysis of growing media. Various procedures are used, some of them being standardized (AFNOR, 2007; ISO, 1988). These cost-effective methods are easy and fast to implement. However, several authors have shown that this method is less descriptive, especially for elongated particles (Bartley et al., 2022; Gil et al., 2014). Recently, DIA tools have been introduced to describe particle morphology of materials used as growing media (Bartley, 2019; Durand et al., 2023a, 2023b, 2023c; Nguyen et al., 2022). This method consists of analyzing individual randomly oriented particles captured by a camera (Trubetskaya et al., 2017), allowing a multidimensional characterization of each particle size and shape (e.g., length, width, circularity, convexity, elongation, and roundness). From particle size descriptors measured by DIA on a large diversity of raw materials, Durand et al. (2023c) showed stronger correlation between WHC and mean particle length of raw materials than with mean particle width and MWD.

In the present study, measurements of PSD determined by DIA and of some physical properties (WHC and AFP, in particular) were performed on raw materials commonly used
<table><caption>TABLE 1 State of the art: Relations between particle size and physical properties of growing media constituents.</caption><thead><tr><th>References</th><th>Materials studied</th><th>Variables used for describing particle size</th><th>Finding regarding physical properties</th></tr></thead><tbody><tr><td>Handreck (1983)</td><td>Pure and mixture of fractionated pine bark. Fractionated sand. Mixture of sand and pine bark.</td><td>Intervals of individual fractions. Proportion of particle in a given fraction.</td><td><ul><li>&lt;0.5 mm particles (%) have the greater effect on AFP and AW.</li><li>✓<sup>a</sup> 0.1–0.25 mm particles ⇌<sup>a</sup> ↗<sup>a</sup> AFP, ↗ AW to a greater extent than particle range 0.25–0.5 and &lt;0.1 mm.</li><li>✓ &lt;0.1 mm particles (%) ⇌ ↗<sup>a</sup> AFP, ↗<sup>a</sup> AW.</li><li>Particle ranging from 0.1 to 0.25 mm have twice the AW of 0.25–0.5 mm.</li><li>Pine bark particle &lt;0.25 mm have higher AW than sand of the same size range.</li></ul></td></tr><tr><td>Bunt (1984)</td><td>Raw peats. Minerals: perlite, vermiculite, clay, sand. Peat: Minerals blends.</td><td>Raw<sup>b</sup></td><td><ul><li>No correlation between TPS and BD with particle size of minerals.</li><li>Mixture of fine mineral with peat has lower AFP than individual mineral or peats.</li><li>Coarse grade of minerals reduces the EAW (&gt;25% by vol.) and the WHC; EAW not affected by fine grade of mineral.</li></ul></td></tr><tr><td>Richards (1986)</td><td>Mixtures of pine bark, sand, coal</td><td>&gt;1 mm particles (%)</td><td><ul><li>✓ &gt;2 mm particles (%) ⇌ ↗<sup>a</sup> WHC, ↗<sup>a</sup> AFP.</li><li>Linear correlation with physical properties.</li></ul></td></tr><tr><td>Limbers and Rehme (1997)</td><td>Screened (star) sod and milled peat at 10, 20, and 50 mm</td><td>&gt;5 mm and &lt;0.2 particles (%)</td><td><ul><li>AFP is related to particle content of &lt;0.2 and &gt;5 mm.</li><li>✓ &gt;5 mm particles increase the AFP, conversely for ✓ 0.2 mm particles.</li></ul></td></tr><tr><td>Verhagen (1997)</td><td>Raw and screened (&lt;16 mm) milled peat</td><td>&lt;1 mm particles (%)</td><td><ul><li>Power/quadratic relationship with AFP.</li><li>Separate components are not useful to predict the AFP of the mixture.</li></ul></td></tr><tr><td>Nkongolo and Caron (1999)</td><td>Mixture of peat (50%), gravel (10%), with various fraction of wood bark (40%)</td><td>Arithmetic MWD</td><td><ul><li>AFP constant for &gt;2 mm particles.</li><li>Pore tortuosity increases and gas diffusivity decreases with increasing size of bark fractions (gas diffusivity of 1–2 &amp; 2–4 mm &gt;8–16 &amp; 8–25 mm).</li></ul></td></tr><tr><td>Gruda et al. (2001)</td><td>Wood fiber</td><td>&lt;1 mm particles (%)</td><td><ul><li>Quadratic relation with WHC</li></ul></td></tr><tr><td>Prasad and Ni Chualain (2004)</td><td>Raw and mixed peat. Mixes of peat and coir, bark, composted green waste.</td><td>&lt;1 mm particles (%)</td><td><ul><li>Linear correlation ✓ &lt;1 mm particles (%) ⇌ ↗<sup>a</sup> AFP (determined at –5 kPa) for peat.</li><li>No correlation for mixes.</li></ul></td></tr><tr><td>Verdonck and Demeyer (2004)</td><td>Raw and fractionated peat, composted bark, perlite. Mixes of peats, composted bark peat/perlite.</td><td>Proportion of particle in a given fraction</td><td><ul><li> ↗<sup>a</sup> Particle size fraction ⇌ ↗<sup>a</sup> EAW, ↗<sup>a</sup> AFP</li></ul></td></tr><tr><td>Abad et al. (2005)</td><td>Peats coir</td><td>Geometric mean diameter &gt;1 mm particles (%)</td><td><ul><li>0.125–1 mm particles (%) have a high impact on WHC, EAW, and AFP conversely to smaller and greater particles.</li><li>✓ &gt;1 mm particles (%) ⇌ ↗<sup>a</sup> EAW, ↗<sup>a</sup> WHC, ↗<sup>a</sup> AFP.</li><li>✓ Particle size ⇌ ↗<sup>a</sup> hydraulic conductivity.</li></ul></td></tr><tr><td>Caron et al. (2005)</td><td>Mixes of bark, peat, perlite, coir, sand, wood finer with varying proportion of coarse particle</td><td>Arithmetic MWD</td><td><ul><li>✓ Coarse particles (%) ⇌ ↗<sup>a</sup> AFP; ✓ &lt;1 mm particles (%) ⇌ ↗<sup>a</sup> AFP.</li><li>Maximum gas diffusivity with particles from 2 to 4 mm except for fibrous materials.</li><li>Not correlated with AW and gas diffusivity.</li></ul></td></tr><tr><td>Naasz and Bussière (2011)</td><td>Mixtures of peat, peat-perlite and peat-sawdust</td><td>Arithmetic MWD &lt;0.3 mm and 0.8–2 mm fractions (%)</td><td><ul><li>✓ &lt;0.3 mm (%) ⇌ ↗<sup>a</sup> AFP, ↗<sup>a</sup> gas diffusivity, ↗<sup>a</sup> pore tortuosity, ↗<sup>a</sup> saturated hydraulic conductivity.</li><li>MWD not correlated to AFP and slightly to EAW.</li></ul></td></tr></tbody></table>

(Continues)
<table><caption>TABLE 1 (Continued)</caption><thead><tr><th>References</th><th>Materials studied</th><th>Variables used for describing particle size</th><th>Finding regarding physical properties</th></tr></thead><tbody><tr><td>Cannavo and Michel (2013)</td><td>Fine peat (0–10 mm). Coarse peat (20–40 mm).</td><td>Raw</td><td><ul><li>\ Particle size ⇔ \ AFP, ↗ unsaturated hydraulic conductivity</li></ul></td></tr><tr><td>Fields et al. (2015)</td><td>Screened pine bark</td><td>Raw</td><td><ul><li>✓ Particle size ⇔ \ container capacity (curvilinear correlation), ↗ air space.</li><li>No difference between material screen at 6.3 and 4 mm regarding all physical properties studied.</li><li>Coarse fraction sieved from 2 to 12.7 mm has an equivalent TP, while the fraction <2 mm has a lower TP.</li><li>\ Particle size ⇔ ↗ hydraulic conductivity.</li></ul></td></tr><tr><td>Durand et al. (2023c)</td><td>White and black peats, wood fiber, coir, pine bark, perlite, green waste compost</td><td>Mean particle length</td><td><ul><li>\ Mean particle length, ↗ WHC (quadratic relation)</li></ul></td></tr></tbody></table>

Abbreviations: AFP, air-filled porosity; AW, available water; BD, bulk density; EAW, easily available water; MWD, mean weight diameter; TP, total porosity; TPS, total pore space; WHC, water holding capacity.

<sup>a</sup>The following symbols: ↗, \, ⇔, respectively mean increase, decrease, leads to.

<sup>b</sup>Distribution into size interval or cumulative distribution is presented, and the materials are distinguished by the global PSD curve.

as growing media components, as well as on particle size fractions derived from these raw materials, with the following objectives:

1. Analyze and model the changes in physical properties as a function of particle size;

2. Assess the degree of relevance of different particle size descriptors (mean length, mean width, and MWD) to predict WHC and AFP of raw materials from values measured and estimated by the model from particle size fractions.

## 2 | MATERIALS AND METHODS

### 2.1 | General approach

To meet these objectives, the approach chosen was to sieve materials into several particle size fractions, and then, for each raw material and fraction generated, to measure the physical properties as well as morphological characteristics of particles by DIA.

### 2.2 | Rationale

The methods used in this work are novel compared to traditional methods to characterize the size of particles and their physical properties.

First, sieving measures as much as possible (Bartley et al., 2019) the second smallest particle dimension (generally referred to as the width), whereas DIA provides length, width, and several other parameters (e.g., particle perimeter, projected area, and shapes). DIA was successfully used in the

works of Bartley (2019), Nguyen et al. (2022), and Durand et al. (2023a, 2023b, 2023c), where the pros and cons of DIA versus sieving were discussed. Among them, DIA is an expensive tool, without standardized protocol and few scientific references for soils and growing media, but offers continuous and precise particle size and shape distributions, expressed in terms of modeled volume, projected area, size, or number of particles. In contrast, sieving procedures are low-cost methods, and standard procedure exists (EN 15428, 2007 for growing media). However, they only describe particles by their width, which is less appropriate for non-spherical particles (such as most of growing media components). Their accuracy is also limited by the discrete PSD obtained, which is expressed by mass.

Second, these data were combined with water retention measurements made using Hyprop systems, providing a more detailed water retention curve than standardized methods used for growing media, for example, EN 13041 (AFNOR, 2000). This tool has had limited use to measure the physical properties of growing media so far (Fields et al., 2016; Schindler et al., 2015).

### 2.3 | Particle size analysis

Particle size analysis of raw and fractionated materials was conducted using the QicPic dynamic image analyzer (Sympatec GmbH), allowing detection of particle sizes ranging from 17 µm to 33.8 mm. Length and width of each particle were assessed from the maximum Feret diameter (Feret<sub>Max</sub>) and minimum chord diameter (Chord<sub>Min</sub>), respectively (Bartley, 2019; Durand et al., 2023a, 2023c; Nguyen et al., 2022),
<figure><img src="image_4.png" /><figcaption>**FIGURE 1** Diameters assessed by dynamic image analysis (DIA), maximum Feret diameter (Feret<sub>Max</sub>), and minimum chord diameter (Chord<sub>Min</sub>), referring, respectively, to particle length and width.</figcaption></figure>

as depicted in Figure 1. Feret<sub>Max</sub> is the maximal distance between two parallel tangents of the particle contour. A chord is the maximum straight distance between two points of the particle contour, measured horizontally; the device measures 20 chords by rotating the particle. Chord<sub>Min</sub> is the smallest chord among all measured chords.

Measurement procedure was detailed by Durand et al. (2023a) and is summarized here. DIA is implemented on wet materials previously dispersed in water. Approximately 2–3 g of material was stirred with ~10–15 L water in a tank for 10 min, then passed through the QicPic in a constant flow through a flow cell placed in front of a high-resolution camera for continuous image recording. The frame rate was 80 frames/s; 2 min of measurement were conducted per repetition. Three repetitions were carried out, representing 10⁷ particles per replicate. The weighting of particles is done according to the projected area of the particles. Raw statistics from the data measured by DIA are provided by the software Paqxos (version 5.0) dedicated to the QicPic device.

Particle size analysis was also conducted on raw materials using the wet sieving procedure detailed in Durand et al. (2023a) and inspired by the standard EN 15428 (AFNOR, 2007). However, in contrast with this latter, materials were sieved at the water content as conditioned in bags for use in culture (67%, 70%, 63%, 49%, and 30% mass moisture content for white peat, black peat, coir, pine bark, and wood fiber, respectively), instead of a mass moisture content below 15%. The material retained on each sieve was washed with a shower sprayer (~1 L) above the sieve column to facilitate the particle segregation (ISO, 1988; Robertson et al., 1984), then oven-dried at 105°C for 48 h and dry-weighed. Three replicates were carried out. The sieve apertures of the set were as follows: 0.2, 0.5, 1, 2, 4, 5, 8, 10, and 16 mm.

## 2.4 | Measurement of physical properties

The water and air retention properties of the materials were determined using Hyprop devices (Meter), which continuously measures the water potential with two tensiometers and the mass moisture content with a scale of the material during a free evaporation cycle (Schindler et al., 2015). The materials were prepared as described in the standard NF EN 13041 (AFNOR, 2000). A PVC (polyvinylchloride) cylinder (20 cm height and 11 cm diameter) was manually filled without packing with the material, slowly wetted (30 min) from the bottom, saturated for 24 h, and then allowed to equilibrate for 48 h to a water potential of –5 kPa. The cylinder was then emptied, the material homogenized, and a column of two superimposed cylinders (5 cm height and 8 cm diameter each, i.e., 10 cm height for the column) was filled with the material, without packing, and slowly rewetted from the bottom and saturated for 24 h. The double cylinder was then removed from the saturation tray (after water drainage); the upper cylinder and the material contained in it were removed, leaving only the measuring cylinder (i.e., 5 cm height and 8 cm diameter) used for the measurements with the Hyprop devices. Data obtained were used to calculate the total porosity (TP), AFP, WHC, AW, and EAW as defined by De Boodt and Verdonck (1972). All these values are expressed in volumetric content (%). Total porosity was assessed considering a particle density of 1.55 g/cm³ (AFNOR, 2000; Lemaire et al., 1989). WHC and AFP, respectively, correspond to the volume occupied by water and air at –1 kPa, AW corresponds to the volume of water released between –1 and –10 kPa, and EAW corresponds to the volume of water released between –1 and –5 kPa. At least two replicates were carried out per sample (with a maximum of four replicates).

## 2.5 | Growing media components and particle size fractions studied

This study was carried out from five raw materials representative of the main growing media constituents in the worldwide market (Schmilewski, 2017): white milled *Sphagnum* peat, black *Sphagnum* peat, coir (*Cocos nucifera*), fresh pine bark (*Pinus maritima*), and wood fiber (*Picea* and/or *Abies*). Information about materials are reported in Table 2.

Each raw material was sieved to obtain specific particle size fractions (Table 2) using the same procedure previously described for particle size analysis by wet sieving. The materials were collected wet (and not dried) in order to avoid risks of particle shrinkage and/or increased intensity of hydrophobicity, likely damaging their physical properties (Michel, 2015). Choice of size intervals was based on literature review (Handreck, 1983; Verdonck & Demeyer, 2004) and the abundance of each fraction size within the raw
<table><caption>TABLE 2 Main information about raw materials and particle size fractions studied.</caption><thead><tr><th>Materials</th><th>Origin (supplier)</th><th>Extraction process</th><th>PSD raw material <sup>a</sup></th><th colspan="6">Particle size fractions studied <sup>b</sup> (mm)</th></tr></thead><tbody><tr><td>Black peat, H6–H8<sup>c</sup></td><td>DE (FL)</td><td>Frozen</td><td>0–7</td><td>0–0.2</td><td>0.2–0.5</td><td>0.5–1</td><td>1–2</td><td>2–8</td></tr><tr><td>Coir</td><td>CI (PT)</td><td>Grounded</td><td>0–25</td><td>0–0.2</td><td>0.2–0.5</td><td>0.5–1</td><td>1–2</td><td>2–5</td><td>5–16</td></tr><tr><td>Fresh pine bark</td><td>FR (PT)</td><td>Screened</td><td>0–10</td><td>0–0.2</td><td>0.2–0.5</td><td>0.5–1</td><td>1–2</td><td>2–5</td><td>5–10</td></tr><tr><td>White peat, H3–H6<sup>c</sup></td><td>LT (KD)</td><td>Milled</td><td>0–25</td><td>0–0.2</td><td>0.2–0.5</td><td>0.5–1</td><td>1–2</td><td>2–5</td><td>5–8</td></tr><tr><td>Wood fiber</td><td>DE (KD)</td><td>Defibrated</td><td>2–4</td><td>0–0.5</td><td>0.5–1</td><td>1–2</td><td>2–5</td><td>5–10</td></tr></tbody></table>

Abbreviations: CI, Ivory Coast; DE, Germany; FL, Floragard Vertiebs-GmbH; FR, France; KD, Klasmann-Deilmann; LT, Lithuania; PSD, particle size distribution; PT, Premier Tech Horticulture France.

<sup>a</sup>Particle size distribution given by the suppliers.

<sup>b</sup>Particle size fractions generated by wet sieving.

<sup>c</sup>Von Post degree of humification of *Sphagnum* peat. H3–H6: little to fairly humified, H6–H8: fairly to well humified (Bridgham & Lamberti, 2009).

materials. The resulting cumulative particle width $Chord_{Min}$ and length $Feret_{Max}$ distributions of each fraction and raw material measured by DIA are presented in Figure 2. Note that the cumulative width distribution curves obtained by DIA using $Chord_{Min}$ (Figure 2) are not strictly restricted to sizes defined by sieve openings, due to the limitations previously mentioned for sieving procedures (incomplete segregation of particle aggregates and non-spherical particle shapes), and also because the DIA is preceded by particle agitation in water, enabling better particle individualization.

## 2.6 | Parameters and modeling approach used for analyzing relationships between particle size and physical properties (WHC and AFP)

Mean particle length and width were used as indicators of PSD determined by DIA, as suggested by Durand et al. (2023a). The arithmetic MWD (Caron et al., 2005; Kemper & Rosenau, 1986), derived from the sieving procedure used for fractioning raw materials, was also calculated for each raw material and size fraction.

According to the previous literature focused on relationships between PSD and physical properties, WHC and AFP were selected as indicators describing physical properties measured using the Hyprop systems.

For a given material, relationships between particle size parameters (i.e., mean particle length, mean particle width, MWD) and both WHC and AFP measured on all particle size fractions were then fitted using similar equation as that used in the Van Genuchten's (1980) model to describe water potential versus water content relationships. These equations were expressed as follows:

$$WHC_{MPL,MPW, MWD} = WHC_{min} + \frac{WHC_{max} - WHC_{min}}{(1 + |\alpha.MPL, MPW, MWD^n|)^m} \quad (1)$$

$$AFP_{MPL, MPW, MWD} = AFP_{min} + \frac{AFP_{max} - AFP_{min}}{(1 + |\alpha.MPL, MPW, MWD^n|)^m} \quad (2)$$

where $WHC_{MPL}$, $WHC_{MPW}$, $WHC_{MWD}$ and $AFP_{MPL}$, $AFP_{MPL}$, $AFP_{MPW}$, $AFP_{MWD}$ are the WHC and the AFP for a mean particle length MPL, mean particle width MPW, and mean weight diameter MWD, respectively; $WHC_{min}$ and $AFP_{min}$ are the minimum WHC and the minimum AFP, $WHC_{max}$ and $AFP_{max}$ are the maximum WHC and the maximum AFP for a given material, determined by model fitting. $\alpha$, $n$, and $m$ are empirical parameters, with $m$ fixed as $m = 1 - 1/n$.

From the fitted curves established for each particle size parameters, root mean square error (RMSE), $r^2$, and absolute and relative errors between measured and predicted WHC and AFP for the raw material were calculated as indicators of the ability of each particle size parameter. A one-way analysis of variance (linear model with fraction as a factor and AFP, AW, EAW, TP, or WHC as single continuous variable) followed by a Tukey's honestly significant difference (with confidence level of 95%) was used to distinguish the physical properties of the different size fractions for a given material and has been carried out using RStudio software (version 4.1.1).

# 3 | RESULTS

## 3.1 | Physical properties of raw materials

The raw materials showed varying water and air retention properties (Table 3). Total porosity was very high for all samples (varying between 89% and 95% vol.), as commonly observed for most of organic growing media constituents. Black and white peats showed high WHC (77% and 75% vol., respectively), high EAW (32% and 30% vol.), and low AFP (12% and 17% vol.), whereas wood fiber and coir exhibited high AFP (69% and 65% vol., respectively), low WHC (26%
<figure><img src="image_5.png" /><figcaption>FIGURE 2 Cumulative particle width (minimum chord diameter [Chord<sub>Min</sub>]) and length (maximum Feret diameter [Feret<sub>Max</sub>]) distributions of the various particle size fraction (in mm) generated by sieving.</figcaption></figure>

and 31% vol.), and low EAW (12% and 16% vol.), with pine
bark presenting intermediate retention properties (Table 3).
These results agree with the abundant literature reported on
that topic (Caron & Michel, 2021; De Boodt & Verdonck,
1972; Michel, 2010).

## 3.2 | Physical properties as a function of particle size fractions

For each material, no significant correlation between TP and
particle size fractions was observed (Table 3). However, the
finer particle size fractions showed lower TP, except for bark,
<table><caption>TABLE 3 Particle size (mean length, maximum Feret diameter [Feret<sub>Max</sub>]; mean width, minimum chord diameter (Chord<sub>Min</sub>); mean weight diameter) and physical properties of raw materials and derived particle size fractions.</caption><thead><tr><th rowspan="2">Materials</th><th rowspan="2">Particle size fractions (mm)</th><th rowspan="2">Proportion of fractiona (% mass)</th><th rowspan="2">Mean particle length (mm)</th><th rowspan="2">Mean particle width (mm)</th><th rowspan="2">Mean weight diameter</th><th rowspan="2">TP</th><th colspan="4">Volumetric content (%)</th></tr><tr><th>AFP<sup>b</sup></th><th>WHC<sup>b</sup></th><th>AW<sup>b</sup></th><th>EAW<sup>b</sup></th></tr></thead><tbody><tr><td rowspan="7">Black peat</td><td>Raw<br>n = 2<sup>c</sup></td><td></td><td>0.64</td><td>0.33</td><td>1.09</td><td>89c</td><td>12c</td><td>77ab</td><td>38b</td><td>32c</td></tr><tr><td>0–0.2<br>n = 2</td><td>22</td><td>0.17</td><td>0.08</td><td>0.10</td><td>90b</td><td>10c</td><td>80a</td><td>27c</td><td>19d</td></tr><tr><td>0.2–0.5<br>n = 2</td><td>23</td><td>0.51</td><td>0.23</td><td>0.35</td><td>92a</td><td>18b</td><td>74bc</td><td>46a</td><td>40a</td></tr><tr><td>0.5–1<br>n = 2</td><td>22</td><td>0.85</td><td>0.35</td><td>0.75</td><td>92a</td><td>23b</td><td>69c</td><td>40b</td><td>36b</td></tr><tr><td>1–2<br>n = 2</td><td>16</td><td>1.42</td><td>0.64</td><td>1.50</td><td>91a</td><td>55a</td><td>36d</td><td>11d</td><td>9e</td></tr><tr><td>2–8<br>n = 2</td><td>17</td><td>3.70</td><td>1.69</td><td>5.0</td><td>90b</td><td>56a</td><td>34d</td><td>11d</td><td>7e</td></tr><tr><td>Raw<br>n = 2</td><td></td><td>1.81</td><td>0.28</td><td>3.77</td><td>96b</td><td>65d</td><td>31c</td><td>22c</td><td>16b</td></tr><tr><td rowspan="10">Coir</td><td>0–0.2<br>n = 2</td><td>20</td><td>0.22</td><td>0.13</td><td>0.10</td><td>92e</td><td>7g</td><td>85a</td><td>40b</td><td>16b</td></tr><tr><td>0.2–0.5<br>n = 2</td><td>15</td><td>0.54</td><td>0.27</td><td>0.35</td><td>93d</td><td>11f</td><td>82a</td><td>54a</td><td>47a</td></tr><tr><td>0.5–1<br>n = 2</td><td>12</td><td>1.71</td><td>0.52</td><td>0.75</td><td>94c</td><td>56e</td><td>38b</td><td>16d</td><td>13b</td></tr><tr><td>1–2<br>n = 2</td><td>10</td><td>3.02</td><td>0.68</td><td>1.50</td><td>95b</td><td>72c</td><td>23d</td><td>9e</td><td>5c</td></tr><tr><td>2–5<br>n = 2</td><td>13</td><td>6.01</td><td>0.94</td><td>3.50</td><td>96b</td><td>79b</td><td>17e</td><td>8e</td><td>5c</td></tr><tr><td>5–16<br>n = 2</td><td>30</td><td>8.14</td><td>1.26</td><td>10.5</td><td>97a</td><td>88a</td><td>9f</td><td>3f</td><td>2c</td></tr><tr><td>Raw<br>n = 2</td><td></td><td>1.00</td><td>0.47</td><td>1.63</td><td>86c</td><td>37c</td><td>49b</td><td>28c</td><td>19bc</td></tr><tr><td>0–0.2<br>n = 2</td><td>9</td><td>0.21</td><td>0.12</td><td>0.10</td><td>87c</td><td>9d</td><td>78a</td><td>45b</td><td>19b</td></tr><tr><td>0.2–0.5<br>n = 2</td><td>16</td><td>0.51</td><td>0.25</td><td>0.35</td><td>84d</td><td>6d</td><td>78a</td><td>65a</td><td>55a</td></tr><tr><td>0.5–1<br>n = 2</td><td>20</td><td>1.16</td><td>0.49</td><td>0.75</td><td>87c</td><td>54b</td><td>33c</td><td>20d</td><td>14cd</td></tr><tr><td>1–2<br>n = 2</td><td>26</td><td>2.15</td><td>0.81</td><td>1.50</td><td>89b</td><td>63ab</td><td>26cd</td><td>15e</td><td>12de</td></tr><tr><td>2–5<br>n = 2</td><td>27</td><td>4.14</td><td>1.63</td><td>3.50</td><td>90ab</td><td>68a</td><td>22d</td><td>12e</td><td>8ef</td></tr><tr><td>5–10<br>n = 2</td><td>2</td><td>14.70</td><td>6.27</td><td>7.50</td><td>92a</td><td>72a</td><td>20d</td><td>10e</td><td>7f</td></tr><tr><td rowspan="4">Fresh pine bark</td><td>Raw<br>n = 3</td><td></td><td>0.56</td><td>0.23</td><td>1.89</td><td>92d</td><td>17cd</td><td>75a</td><td>40ab</td><td>30b</td></tr><tr><td>0–0.2<br>n = 3</td><td>17</td><td>0.21</td><td>0.10</td><td>0.10</td><td>90e</td><td>10d</td><td>80a</td><td>26cd</td><td>14cd</td></tr><tr><td>0.2–0.5<br>n = 3</td><td>24</td><td>0.54</td><td>0.22</td><td>0.35</td><td>94ab</td><td>15cd</td><td>79a</td><td>46a</td><td>30b</td></tr><tr><td>0–0.2<br>n = 3</td><td>17</td><td>0.21</td><td>0.10</td><td>0.10</td><td>90e</td><td>10d</td><td>80a</td><td>26cd</td><td>14cd</td></tr></tbody></table>

(Continues)
<table><caption>TABLE 3 (Continued)</caption><thead><tr><th>Materials</th><th>Particle size fractions (mm)</th><th>Proportion of fractiona (% mass)</th><th>Mean particle length (mm)</th><th>Mean particle width (mm)</th><th>Mean weight diameter</th><th>TP</th><th>AFP<sup>b</sup></th><th>WHC<sup>b</sup></th><th>AW<sup>b</sup></th><th>EAW<sup>b</sup></th></tr></thead><tbody><tr><td rowspan="5">Wood fiber</td><td>0.5–1<br>n = 3</td><td>18</td><td>0.79</td><td>0.31</td><td>0.75</td><td>95a</td><td>19c</td><td>76a</td><td>48a</td><td>41a</td></tr><tr><td>1–2<br>n = 4</td><td>11</td><td>1.14</td><td>0.40</td><td>1.50</td><td>95a</td><td>32b</td><td>63b</td><td>32bc</td><td>26b</td></tr><tr><td>2–5<br>n = 3</td><td>15</td><td>2.93</td><td>1.27</td><td>3.50</td><td>94bc</td><td>37ab</td><td>57b</td><td>25cd</td><td>19c</td></tr><tr><td>5–8<br>n = 3</td><td>15</td><td>4.09</td><td>1.56</td><td>6.50</td><td>94c</td><td>45a</td><td>49c</td><td>18d</td><td>12d</td></tr><tr><td>Raw<br>n = 3</td><td></td><td>1.86</td><td>0.47</td><td>1.87</td><td>95a</td><td>69bc</td><td>26e</td><td>16cd</td><td>12cd</td></tr><tr><td rowspan="5">Wood fiber</td><td>0–0.5<br>n = 3</td><td>22</td><td>0.78</td><td>0.14</td><td>0.25</td><td>95a</td><td>37e</td><td>58a</td><td>45a</td><td>38a</td></tr><tr><td>0.5–1<br>n = 4</td><td>15</td><td>1.31</td><td>0.30</td><td>0.75</td><td>96a</td><td>55d</td><td>41b</td><td>30b</td><td>26b</td></tr><tr><td>1–2<br>n = 3</td><td>29</td><td>2.36</td><td>0.58</td><td>1.50</td><td>96a</td><td>64c</td><td>32c</td><td>20c</td><td>16c</td></tr><tr><td>2–5<br>n = 3</td><td>29</td><td>4.52</td><td>1.29</td><td>3.50</td><td>96a</td><td>74ab</td><td>22d</td><td>14cd</td><td>10cd</td></tr><tr><td>5–10<br>n = 3</td><td>5</td><td>11.33</td><td>3.23</td><td>6.50</td><td>95a</td><td>76a</td><td>19de</td><td>11d</td><td>8d</td></tr></tbody></table>

Note: Means with the same letter are not statistically different. Statistics using Tukey's honestly significant difference with $\alpha = 0.05$ were performed to test the differences observed between the fractions themselves and the raw material for a given material and a given physical property (TP, AFP, WHC, AW, and EAW), independently.

Abbreviations: AFP, air-filled porosity; AW, available water; EAW, easily available water; TP, total porosity; WHC, water holding capacity.

<sup>a</sup>Proportion by mass of the fraction composing the raw material, measured from the sieving procedure.

<sup>b</sup>AFP and WHC determined at -1 kPa; AW determined between -1 and -10 kPa; and EAW determined between -1 and -5 kPa, as defined by De Boodt and Verdonck (1972).

<sup>c</sup>n: number of replicas performed for physical properties assessment using Hyprop.

where the lowest value was noted for the 0.2–0.5 mm fraction due to the high content of sand present in this specific particle size fraction. For coir and bark, higher TP was reported for the coarser fractions, and conversely for intermediate particle size fractions for peats and wood fiber. These observations have been detailed by Durand, Boivin et al. (2023), describing in depth the shrinkage curves and the particle arrangement of these particle size fractions.

For peats, bark, and coir, no clear relationship was observed for EAW and AW with particle size fractions (Table 3). The highest EAW and AW were observed in the 0.2–0.5 mm particle size fractions for coir, pine bark, and black peat, and in the 0.5–1 mm particle size fraction for white peat, suggesting that water is strongly retained in the finest fractions and thus slightly less available. In contrast, for coarser particle size fractions than those previously reported, EAW and AW decreased with the increasing particle size fractions and reached a plateau or a minimum value for coarsest particle size fraction (see Tukey tests, Table 3). These changes in EAW and AW observed for peats, bark, and coir can be extended to wood fiber, although this latter showed, in contrast with the others, a general decrease in EAW and AW with an increase

in particle size (see Tukey tests, Table 3). However, due to the very low content in the 0.2–0.5 mm particles, this size fraction could not be collected, and the finest fraction for wood fiber was represented by the <0.5 mm size fraction, perhaps explaining its higher EAW and AW and the progressive decrease in EAW and AW as a function of increasing particle size fractions.

WHC and AFP values (Table 3) partly corroborate observations usually reported in the literature (Table 1), indicating that the smaller the particle size, the higher the WHC, and conversely, the lower the AFP for all materials tested (Table 3); WHC and AFP are strongly and inversely correlated ($r = 0.99$; $p < 0.0001$). However, relationships between particle size and both WHC and AFP are not linear, as suggested by Equations (1) and (2) that allowed to highly fit relationships between WHC and AFP with mean particle length and width, and to a lesser degree with MWD, as suggested by $r^2$ and RMSE values (Table 4).

Based on previous works indicating that the mean particle length is the most significant size descriptor (Igathinathane et al., 2009) and also the most discriminating parameter for describing particle morphology (i.e., size and shape) of
<table><caption>TABLE 4 Root mean square error (RMSE) and determination coefficient (r²) of model fitting to physical properties (water holding capacity [WHC] and air-filled porosity [AFP]) as a function of particle size (length, width, and mean weight diameter).</caption><thead><tr><th rowspan="3">Size descriptor<br>Physical<br>properties</th><th colspan="4">Mean particle length (Feret<sub>Maw</sub>)</th><th colspan="4">Mean particle width (Chord<sub>Min</sub>)</th><th colspan="4">Mean weight diameter</th></tr><tr><th colspan="2">WHC</th><th colspan="2">AFP</th><th colspan="2">WHC</th><th colspan="2">AFP</th><th colspan="2">WHC</th><th colspan="2">AFP</th></tr><tr><th>r<sup>2</sup></th><th>RMSE</th><th>r<sup>2</sup></th><th>RMSE</th><th>r<sup>2</sup></th><th>RMSE</th><th>r<sup>2</sup></th><th>RMSE</th><th>r<sup>2</sup></th><th>RMSE</th><th>r<sup>2</sup></th><th>RMSE</th></tr></thead><tbody><tr><td>Black peat</td><td>0.99</td><td>1.48</td><td>0.99</td><td>2.70</td><td>0.99</td><td>1.36</td><td>0.99</td><td>2.39</td><td>0.99</td><td>2.96</td><td>0.99</td><td>2.70</td></tr><tr><td>Coir</td><td>0.99</td><td>2.93</td><td>0.99</td><td>2.97</td><td>0.99</td><td>1.84</td><td>0.99</td><td>2.10</td><td>0.99</td><td>6.73</td><td>0.99</td><td>7.32</td></tr><tr><td>Pine bark</td><td>0.99</td><td>1.73</td><td>0.99</td><td>3.94</td><td>0.99</td><td>1.68</td><td>0.99</td><td>4.27</td><td>0.99</td><td>1.82</td><td>0.99</td><td>4.27</td></tr><tr><td>White peat</td><td>0.97</td><td>2.86</td><td>0.97</td><td>3.08</td><td>0.97</td><td>2.94</td><td>0.96</td><td>3.49</td><td>0.98</td><td>1.49</td><td>0.98</td><td>1.52</td></tr><tr><td>Wood fiber</td><td>0.99</td><td>0.73</td><td>0.99</td><td>0.79</td><td>0.99</td><td>0.42</td><td>0.99</td><td>0.43</td><td>0.99</td><td>0.30</td><td>0.99</td><td>0.27</td></tr><tr><td>Mean RMSE</td><td>—</td><td>1.95</td><td>—</td><td>2.70</td><td>—</td><td>1.65</td><td>—</td><td>2.54</td><td>—</td><td>2.66</td><td>—</td><td>3.22</td></tr></tbody></table>

Abbreviations: Chord<sub>Min</sub>, minimum chord diameter; Feret<sub>Maw</sub>, maximum Feret diameter.

<table><caption>TABLE 5 Parameters of Equations 1 and 2 for the model fitting physical properties (water holding capacity [WHC] and air-filled porosity [AFP]) as a function of mean particle length.</caption><thead><tr><th rowspan="2">Materials</th><th colspan="3">WHC</th><th colspan="3">AFP</th></tr><tr><th>WHC<sub>max</sub><br>(% Vol.)</th><th>WHC<sub>min</sub><br>(% Vol.)</th><th>α</th><th>n</th><th>M</th><th>α</th><th>AFP<sub>max</sub><br>(% Vol.)</th><th>AFP<sub>min</sub><br>(% Vol.)</th><th>M</th></tr></thead><tbody><tr><td>Black peat</td><td>77</td><td>34</td><td>0.0010</td><td>9.81</td><td>0.90</td><td>56</td><td>14</td><td>0.0011</td><td>11.44</td><td>0.91</td></tr><tr><td>Coir</td><td>85</td><td>12</td><td>0.0009</td><td>3.05</td><td>0.67</td><td>86</td><td>6</td><td>0.0009</td><td>2.75</td><td>0.64</td></tr><tr><td>Pine bark</td><td>78</td><td>23</td><td>0.0011</td><td>7.03</td><td>0.86</td><td>68</td><td>7</td><td>0.0010</td><td>9.44</td><td>0.90</td></tr><tr><td>White peat</td><td>80</td><td>53</td><td>0.0010</td><td>6.14</td><td>0.84</td><td>42</td><td>11</td><td>0.0011</td><td>4.36</td><td>0.77</td></tr><tr><td>Wood fiber</td><td>90</td><td>18</td><td>0.0017</td><td>2.32</td><td>0.57</td><td>77</td><td>5</td><td>0.0017</td><td>2.34</td><td>0.57</td></tr></tbody></table>

growing media constituents (Durand et al., 2023b), Figure 3 represents the changes in WHC and AFP (%) as function of this single size parameter for particle size fractions and raw materials, as well as the fitting model (Equations 1 and 2) based on particle size fractions data.

As shown in Figure 3 describing the changes in both WHC and AFP as a function of mean particle length (Feret<sub>Max</sub>), the models used (Equations 1 and 2; Table 5) provided some insights into the relationships between WHC, AFP, and mean particle length. Models drew curvilinear curves (Figure 3), showing strong decreases in WHC and, conversely, strong increases in AFP, in the range of finest particles (i.e., mean particle length lower than 1.25 mm for peats, 1.5 mm for bark and wood fiber, and 2.5 mm for coir). For greater mean particle length, the curves showed lower decreases in WHC and lower increases in AFP (coir and wood fiber) or reached a plateau (bark and peats). Thus, WHC of 60% vol. was approximately reached for mean length particles not exceeding 0.75 mm for wood fiber, 0.85 mm for bark, 0.95 mm for black peat, and 1.15 mm for coir and white peat, whereas a minimum of 20% vol. for AFP was found for mean length particles higher than 0.45 mm for wood fiber, and in the range of 0.75–0.85 mm for the other raw materials (WHC = 60% vol. and AFP = 20% vol. corresponding to the minimum thresholds usually recommended; Morel et al., 2000).

## 3.3 | Predicting water holding capacity and air-filled porosity of raw materials from particle size fractions

From these fitting models established for each of the three size parameters and obtained from particle size fractions, comparisons between measured and estimated WHC and AFP values for the raw materials were performed (Table 6). Except for wood fiber, mean particle length consistently gave the best estimation, with mean absolute errors of 5.1% and 4.1% for WHC and AFP, respectively. In contrast, mean absolute errors calculated for WHC and AFP reached 15.9% and 16.0% for mean particle width, and 18.5% and 20.8% for MWD.

# 4 | DISCUSSION

## 4.1 | Particle length as the most relevant parameter of the relationships between particle size and physical properties

Among all the size descriptors tested, mean particle length (estimated via Feret<sub>Max</sub>) provided a better prediction for WHC and AFP of raw materials, derived from particle size fractions data. These results are in line with conclusions reported
<figure><img src="image_6.png" /><figcaption>Mean particle length, Feret<sub>Max</sub> (mm)</figcaption></figure>

<caption>FIGURE 3 Water holding capacity (WHC) and air-filled porosity (AFP) (%) as function of mean particle length for particle size fractions and raw materials; and fitting model (Equations 1 and 2) based on particle size fractions data.</caption>

by Durand et al. (2023c), showing mean particle length as a reliable parameter for describing the relationship between particle morphology and WHC of raw materials. Igathinathane et al. (2009) and Durand et al. (2023b) reported that mean particle width (assessed via $Chord_{Min}$) seemed less reliable and less discriminating than mean particle length (assessed via $Feret_{Max}$) to better characterize particle size. Moreover, the discrete PSD obtained from sieving as well as the sieving methodological limitations could explain the lower accuracy of MWD, and then the higher mean error values (Table 6) for estimating physical properties. Indeed, sieving is less capable to accurately separate particles the more non-spherical they become (Bartley et al., 2022; Durand et al., 2023a; Gil et al., 2014; Igathinathane et al., 2009), precisely the con-

dition found in many growing media components (Bartley, 2019; Durand et al., 2023b). This was confirmed in Figure 2, showing that the particle width distribution (i.e., the theoretical dimension for separating particles by sieving; Ulusoy and Igathinathane, 2016) for each particle size fraction was larger than the size range strictly defining each fraction. Although weighing the distribution by projected area results in less weight being given to coarse particles than when weighted by volume (Bartley, 2019; Durand et al., 2023a), the mean particle size often being below the lower limit defining the fraction. This may be due to the systemic presence of particles finer than the lower limit of the interval. As a consequence, the MWD usually overestimates the mean particle size.
<table><caption>TABLE 6 Measured and estimated water holding capacity and air-filled porosity (% vol.) of raw material from their mean size (mm), calculated from Equations 1 and 2, with relative error (as an absolute value) and relative error (%).</caption><thead><tr><th>Size descriptor</th><th>Units</th><th>Black peat</th><th>Coir</th><th>Pine bark</th><th>White peat</th><th>Wood fiber</th><th>Mean errors values</th></tr></thead><tbody><tr><td>Measured WHC</td><td>% vol.</td><td>77.5</td><td>31.2</td><td>49.4</td><td>75.2</td><td>26.0</td><td></td></tr><tr><td>Measured AFP</td><td></td><td>11.9</td><td>64.5</td><td>37.1</td><td>17.0</td><td>69.3</td><td></td></tr><tr><td rowspan="6">Mean particle length (Feret<sub>Max</sub>)</td><td>Mean size</td><td>mm</td><td>0.64</td><td>1.81</td><td>1.00</td><td>0.56</td><td>1.86</td><td></td></tr><tr><td>Estimated WHC</td><td>% vol.</td><td>76.3</td><td>37.0</td><td>43.3</td><td>79.7</td><td>33.7</td><td></td></tr><tr><td>Relative error (WHC)</td><td>%</td><td>1.5</td><td>18.6</td><td>12.3</td><td>5.9</td><td>29.6</td><td>13.5</td></tr><tr><td>Absolute error (WHC)</td><td>lxl</td><td>1.2</td><td>5.8</td><td>6.1</td><td>4.5</td><td>7.7</td><td>5.1</td></tr><tr><td>Estimated AFP</td><td>% vol.</td><td>14.5</td><td>57.4</td><td>37.2</td><td>13.6</td><td>61.9</td><td></td></tr><tr><td>Relative error (AFP)</td><td>%</td><td>21.8</td><td>11.0</td><td>0.3</td><td>20.0</td><td>10.7</td><td>12.8</td></tr><tr><td rowspan="6">Mean particle width (Chord<sub>Min</sub>)</td><td>Mean size</td><td>mm</td><td>0.33</td><td>0.28</td><td>0.47</td><td>0.23</td><td>0.47</td><td></td></tr><tr><td>Estimated WHC</td><td>% vol.</td><td>72.1</td><td>79.6</td><td>35.7</td><td>80.1</td><td>32.9</td><td></td></tr><tr><td>Relative error (WHC)</td><td>%</td><td>7.0</td><td>155.1</td><td>27.7</td><td>6.5</td><td>26.5</td><td>44.6</td></tr><tr><td>Absolute error (WHC)</td><td>lxl</td><td>5.4</td><td>48.4</td><td>13.7</td><td>4.9</td><td>6.9</td><td>15.9</td></tr><tr><td>Estimated AFP</td><td>% vol.</td><td>19.5</td><td>14.2</td><td>48.5</td><td>13.0</td><td>62.6</td><td></td></tr><tr><td>Relative error (AFP)</td><td>%</td><td>63.9</td><td>78.0</td><td>30.7</td><td>23.5</td><td>9.7</td><td>41.2</td></tr><tr><td rowspan="6">Mean weight diameter</td><td>Mean size</td><td>mm</td><td>1.09</td><td>3.78</td><td>1.63</td><td>1.89</td><td>1.87</td><td></td></tr><tr><td>Estimated WHC</td><td>% vol.</td><td>44.4</td><td>15.6</td><td>22.8</td><td>60.8</td><td>29.0</td><td></td></tr><tr><td>Relative error (WHC)</td><td>%</td><td>42.7</td><td>50.0</td><td>53.8</td><td>19.1</td><td>11.5</td><td>35.4</td></tr><tr><td>Absolute error (WHC)</td><td>lxl</td><td>33.1</td><td>15.6</td><td>26.6</td><td>14.4</td><td>3.0</td><td>18.5</td></tr><tr><td>Estimated AFP</td><td>% vol.</td><td>50.4</td><td>81.0</td><td>67.6</td><td>32.9</td><td>66.7</td><td></td></tr><tr><td>Relative error (AFP)</td><td>%</td><td>323.5</td><td>25.6</td><td>82.2</td><td>93.5</td><td>3.8</td><td>105.7</td></tr><tr><td></td><td>Absolute error (AFP)</td><td>lxl</td><td>38.5</td><td>16.5</td><td>30.5</td><td>15.9</td><td>2.6</td><td>20.8</td></tr></tbody></table>

## 4.2 | Compliance of results with the state of the art and new advances

The regression models showed largest variations in WHC and AFP for smaller particle size ranges, and conversely, much lower changes or a plateau in WHC and AFP for larger particle sizes. Models are described with high-confidence relationships between particle size and WHC and AFP, considering the whole PSD of each material, not a specific particle size range as usually previously considered in the literature. In this way, the proposed models differ with the linear correlation reported by Prasad and Ní Chualáin (2004) and Abad et al. (2005) and with the quadratic/power regression proposed by Verhagen (1997), both restricted to <1 mm particles. In contrast, the observations are in accordance with previous relationships observed between particle length and WHC on numerous raw growing media constituents using a similar regression model (Durand et al., 2023c). They also agree with those reporting changes in AFP and WHC depending on particle size when <3 mm particles were only considered (Handreck, 1983; Verdonck & Demeyer, 2004), and also with those showing that physical properties do not change (or very

little) beyond a certain particle size (Fields et al., 2015; Handreck, 1983; Nkongolo & Caron, 1999). In this current study, very low or no changes in WHC and AFP were observed for mean particle lengths higher than 1.5 mm for peats and bark, and 3 mm for coir and wood fiber. Consequently, the results qualified the simple conclusion usually reported that the longer the particle length, the higher the AFP and the lower the WHC.

In contrast, no clear correlation between particle size and both EAW and AW was observed, except for wood fiber. However, the inverse correlation observed between particle size and both EAW and AW for wood fiber should be differently interpreted because the finest particle size fraction considered was <0.5 mm and not <0.2 mm due to the small amount of both <0.2 mm and 0.2–0.5 mm particle size fractions. For the other materials, highest EAW and AW values were reported for the 0.2–0.5 mm (black peat, coir, and bark) and 0.5–1 mm (white peat) particle size fractions, and not for the finest fractions (<0.2 mm). These observations are, however, in accordance with those of the literature (Table 1), depending on particle sizes considered in these studies. Durand et al. (2023) reported much finer pores and much higher
shrinkage phenomena measured during the drying process for the <0.2 mm particle size fractions in comparison with the other particle size fractions to explain lower EAW and AW values for the <0.2 mm particle size fractions compared with the maximum values reported.

5 | CONCLUSION

This work detailed an approach in investigating relationships between PSD and physical properties of growing media constituents. This approach is based on PSD analysis using DIA of raw materials and the derived particle size fractions, and also on their physical properties measured using Hyprop systems.

The statement that the larger the particle size, the higher the AFP, the lower the WHC was redefined (i.e., specifying its limits). Relationships between particle size and both WHC and AFP were indeed successfully fitted using regression model, whatever the particle size descriptor used (mean length, mean width, and MWD). Large variations in WHC and AFP mainly occurred for finest particle size fractions (<1 mm for peats and bark and <2 mm for coir and wood fiber), whereas changes were conversely very small or non-existent for larger particle sizes. In contrast, no clear correlation was found between particle size and water availability.

Based on regression models between particle size descriptors and both WHC and AFP established from particle size fractions of a same raw material, comparisons between measured and estimated WHC and AFP on raw materials showed that only mean particle length is able to predict WHC and AFP for raw materials with good accuracy. No other particle size descriptors tested (mean particle width and MWD) provided any usable measure of prediction. With a similar approach, future research should further examine the relationships between particle size descriptors and other physical properties such as hydraulic conductivity and shrinkage. Investigations with blends of constituents should also be developed to determine whether mean particle length can also predict the physical properties of the growing media.

Compared to sieving procedures, DIA provided much more detailed information on particle morphology, enabling prediction of certain physical properties of materials. Its wider use by the growing media industry should help to select raw materials and specific particle size fractions for designing the next generation of growing media.

AUTHOR CONTRIBUTIONS

**Stan Durand:** Conceptualization; data curation; formal analysis; investigation; methodology; software; visualization; writing—original draft; writing—review and editing.

**William Carl Fonteno:** Supervision; validation; writing—review and editing.
**Jean-Charles Michel:** Conceptualiza-

tion; data curation; funding acquisition; project administration; resources; software; supervision; validation; visualization; writing—review and editing.

ACKNOWLEDGMENTS

The authors would like to thank the company partners, EVADEA, Floragard, Klasmann-Deilmann, Premier Tech Horticulture, and TurfTech Ltd., for providing the materials and/or funding for this work. We thank the technicians from the EPHor research unit who helped prepare the materials and set up the measuring tools: Yvette Barraud-Roussel, Céline Levon, and Dominique Lemesle. This research was also conducted in the framework of the regional program “Objectif Végétal, Research, Education and Innovation in Pays de la Loire,” supported by the French Region Pays de la Loire. We also thank the France-USA Fulbright program to support this work and the collaboration between the Horticultural Substrate Lab of the North Carolina State University (USA) and the EPHOR research unit of L’Institut Agro Rennes-Angers (France).

CONFLICT OF INTEREST STATEMENT

The authors report no conflicts of interest.

ORCID

Stan Durand https://orcid.org/0000-0002-3283-3870

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**How to cite this article:** Durand, S., Fonteno, W. C., & Michel, J.-C. (2024). A review and analysis of particle size parameters and their relationships to physical properties of growing media. *Soil Science Society of America Journal*, 88, 652–666. https://doi.org/10.1002/saj2.20661