## 2 Materials and Methods
### Characterization of Grain Physical Properties  
The moisture content \(X\) (kg\(\cdot\)kg\({}^{-1}\) d.b.) of wheat kernels was determined by the standard thermogravimetric analysis in a convective oven (UM 700, Memmert GmbH & CO. KG, Schwabach, Germany) at 105 \(\pm\) 1 \({}^{\circ}\)C for 24 h and natural air circulation according to AOAC [39], where moisture of 0.123 \(\pm\) 0.001 kg\(\cdot\)kg\({}^{-1}\) d.b. was observed (dry matter of 89.01 \(\pm\) 0.01%).  
The principal geometrical characteristics of kernels, length \(L\) (mm), width \(W\) (mm) and thickness \(T\) (mm) were measured via a digital Vernier caliper (Digi-Met IP 67, Helios-Preisser GmbH, Gammertingen, Germany) with a measuring resolution of \(\pm\)0.01 mm. Measurements were carried out for a total of 100 randomly selected kernels. Shape-dependent geometric properties such as arithmetic diameter \(d_{a}\) (mm), geometric diameter \(d_{g}\) (mm), sphericity \(\vartheta\) (%), aspect ratio \(R_{a}\) (-) and unit volume \(V\) (mm\({}^{3}\)) were estimated from the basic geometrical characteristics, as described by [PERSON] and [PERSON] [40]. The equivalent diameter \(d_{e}\) (mm) of kernels was calculated as:  
\[d_{e}=\sqrt[3]{\frac{6\;V}{\pi}} \tag{1}\]  
From [PERSON] et al. [41], the surface area \(A\) (mm\({}^{2}\)) of kernels was estimated as:  
\[A=\frac{\pi\;W}{2}\bigg{(}W+\frac{L}{c}\text{arcsinc}\bigg{)}\text{ with }c=\sqrt{1-\bigg{(}\frac{W}{L}\bigg{)}^{2}} \tag{2}\]  
In addition, the gravimetric properties were assessed. Unit mass \(m\) (g) of kernels was measured by means of an analytical high-precision balance with an accuracy of \(\pm\)0.10 mg (Sartorius BP221S, Sartorius AG, Gottingen, Germany). Solid density \(\rho_{s}\) (kg\(\cdot\)m\({}^{-3}\)) was defined based on the toluene displacement method in a 25 mL pycnometer (Blaubrand, Wertheim, Germany) as described by [PERSON] [42]. Toluene was utilized as a water-insoluble liquid. The solid density \(\rho_{s}\) was determined as:  
\[\rho_{s}=\frac{m_{gr}\;\rho_{tol}}{m_{gr}+m_{fl,\;tot}-m_{gr,\;fl,\;tol}} \tag{3}\]  
where \(m_{gr}\) (g) is the mass of kernel, \(m_{fl,tol}\) (g) is the mass of pycnometer flask filled with toluene, \(m_{gr,fl,tol}\) (g) is the mass of kernels soaked in toluene solution together with the flask and \(\rho_{tol}\) (kg\(\cdot\)m\({}^{-3}\)) is the toluene density. The default bulk density \(\rho_{l0}\) (kg\(\cdot\)m\({}^{-3}\)) was measured by freely pouring kernels into a cylindrical container (150 mm diameter, 100 mm height) by maintaining a natural flow rate until overflowing. Afterwards, the surplus mass was gently swiped off using a wooden striker from the brim of the container and weighted. Hence, the bulk density \(\rho_{b0}\) was calculated as:  
\[\rho_{b0}=\frac{m_{c}}{V_{c}} \tag{4}\]  
where \(m_{c}\) (kg) is amassed mass in the container and \(V_{c}\) (m\({}^{3}\)) is the occupied volume. The default (uncompacted) pore volume \(\varepsilon_{0}\) (-) was defined as the fraction of the volume of intergranular voids in the bulk and was calculated as a function of the solid density and bulk density:  
\[\varepsilon_{0}=1-\frac{\rho_{b0}}{\rho_{s}} \tag{5}\]