## 3 Results and Discussion
### Water Absorption  
The phenomenon of swelling of the gel beads was tested for 210 min. Obtained results are presented in a graph (Figure 3). In all cases, swelling to the maximum value was observed, while in the case of the lowest concentration of apple pectin gel (1.5%) and pectin gels obtained from black and red currants, after reaching the maximum value of Wi, they decreased rapidly over time. The highest increase in absorbed water was found for the 4.5% apple pectin gel. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Pectin**} & \(\mathbf{M_{w}}\) & \(\mathbf{M_{n}}\) & \multirow{2}{*}{**Dp**} & \multirow{2}{*}{**R1**} & \multirow{2}{*}{**R3**} & \(\mathbf{c^{*}}\) \\  & \(\mathbf{kg\cdot mol^{-1}}\) & & & & & \(\mathbf{g\cdot dL^{-1}}\) \\ \hline Red & \multirow{2}{*}{1020} & \multirow{2}{*}{53} & \multirow{2}{*}{273} & \multirow{2}{*}{2.27} & \multirow{2}{*}{1.03} & \multirow{2}{*}{0.78} \\ current & & & & & & \\ Black & & & & & & \\ currant & 115.78 & 24 & 124 & 1.50 & 8.77 & 0.43 \\ Apple & 1576 & 81 & 5730 & 1.44 & 1.58 & 1.5 \\ \hline \end{tabular}  
* \(\mathrm{Dp}\)—degree of polymerization, R1—chain linearity, R3—chain branching.  
\end{table} 
Table 1: Molar masses and chain properties of pectin from different sources [18; 19; 22]. The rate constant \(k_{1}\) reached the value of 0.028 g\({}_{\rm H2O}\cdot(\)g\({}_{\rm gel}\cdot\)min\()^{-1}\) and it can be understood as the increase in the mass of absorbed water in each minute of the experiment (Table 2). The lower value of this coefficient describes the swelling rate of 3.0% gel of the same pectin, which obviously corresponds to the lower water absorption intensity (Figure 3). The values of the inhibition constant are low, which indicates a constant diffusion resistance in the gel over this time interval. The \(K\) value for the 3% gel is lower in comparison to 4.5%, which reflects the difference in the gel structure, probably resulting from the concentration of the pectin solution. In both cases, the concentration of the external gelling solution is above the first critical concentration (c*), which means that the external gelation solutions are classified as semi-dilute. Moreover, the changes in \(W(t)\) are characteristic for water-absorbing gels until the equilibrium value is obtained [13; 16; 17]. In the case of a gel obtained from a 1.5% solution, which corresponds to the first critical concentration, the dynamics of the water absorption phenomenon changes: in the tested time period, a maximum appears on the \(W(t)\) curve. For this reason, the kinetic model describing the swelling phenomenon is also changing: the resistance constant \(K\) changes as a function of time. Due to the low initial rate of water absorption, the rate constant \(k_{1}=0.0080\) g\({}_{\rm H2O}\cdot(\)g\({}_{\rm gel}\cdot\)min\()^{-1}\), while \(K\) has a high value of 0.1260 min\({}^{-1}\). Figure 3: Swelling of gel beads in distilled water. A similar pattern of the absorption process was observed for gels obtained from pectins extracted from black and red currants. In both cases, gels were obtained from solutions with a concentration higher than the first critical concentration, which is 0.78 g\(\cdot\)dL\({}^{-1}\) for red currant pectin and 0.43 g\(\cdot\)dL\({}^{-1}\) for black currant pectin (Table 1). First of all, it can be observed that, in the studied time period, the \(W(t)\) values are generally lower as compared to the apple pectin gel. The exception is the first hour of the experiment, during which the initial values of the rates are similar to those obtained for the 3% apple pectin gel and greater than those determined for 1.5%. After one hour, the maximum for \(W_{t}\) is observed, which means that the gel beads are fully saturated with water; after it is reached, these values decrease, and the beads disintegrate. This phenomenon was also observed by [PERSON] et al. [10] who investigated the swelling of 2% citrus pectin gels (DM = 38%) and [PERSON] et al. [12] for 1.5% gels and 2% of apple pectin swelling in distilled water.