# Some Aspects of the Modelling of Dried Red Beets Rehydration Process
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model No.** & **Model Name** & **Parameter Equation** \\ \hline (1) & [PERSON] & \(A_{1}=-0.61102v_{d}+4.35955L-0.0423 LT_{r}\) \\  & & \(A_{2}=0.00055v_{d}{}^{2}-0.0097L^{2}+0.00151T_{d}L\) \\ \hline (2) & [PERSON] ([PERSON]) & \(k=0.00872v_{d}+6.1\times 10^{-6}T_{d}{}^{2}-0.0004v_{d}{}^{2}+2.9\times 10^{-6}T _{r}{}^{2}-10^{-4}T_{d}v_{d}-6\times 10^{-5}T_{d}L\) \\ \hline (3) & Henderson–Pabis & \(k=4.1\times 10^{-5}T_{d}v_{d}+9.6\times 10^{-6}T_{d}T_{r}-5\times 10^{-5}v_{d}T_{r}-6 \times 10^{-5}LT_{r}\) \\  & & \(a=0.92777-0.0019T_{d}-0.0046v_{d}-6\times 10^{-5}T_{r}{}^{2}+8.6\times 10^{-5}T _{d}T_{r}\) \\ \hline (4) & Page & \(k=0.05908+0.03112v_{d}-0.0032v_{d}{}^{2}-0.0003T_{d}L+2.6\times 10^{-5}T_{d}T_{r}\) \\  & & \(n=-0.0514v_{d}+0.38982L+0.00646v_{d}{}^{2}-0.049L^{2}-2\times 10^{-5}T_{r}{}^{2}\) \\ \hline (5) & Modified Page & \(k=0.00028T_{d}+0.00295v_{d}-0.0004v_{d}{}^{2}-5\times 10^{-5}T_{d}L+3.7\times 10^{-6}T _{d}T_{r}\) \\  & & \(n=-0.056v_{d}+0.39677L+0.007v_{d}{}^{2}-0.05L^{2}-2\times 10^{-5}T_{r}{}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Parameter equations for the models adopted to volume changes during rehydration of dried red beets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model No.** & **Model Name** & **Parameter Equation** \\ \hline (1) & Peleg & \(A_{1}=355.113-6.996T_{d}-91.017L+1.46026v_{d}{}^{2}+0.01411\)\(T_{r}{}^{2}+2.64528T_{d}L-5.2259\)\(v_{d}L-0.7968 LT_{r}\) \\  & & \(A_{2}=-12.927+0.00792T_{d}+0.04094v_{d}{}^{8}+8.57966L-0.0077v_{d}{}^{2}-1.1362L^{ 2}+0.00014T_{r}{}^{2}-0.0002T_{d}T_{r}\) \\ \hline (2) & Lewis (Newton) & \(k=0.00028T_{d}+0.00688v_{d}+0.0008v_{d}{}^{2}+1.2\times 10^{-6}T_{r}{}^{2}-0.00002 LT_{r}\) \\  & & \(k=0.01533+0.00624v_{d}-0.0008v_{d}{}^{2}+1.2\times 10^{-5}T_{r}{}^{2}-0.0001 LT_{r}\) \\  & & \(a=2.03326-0.6471L+0.08638L^{2}-0.0046\)\(v_{d}{}^{2}L^{2}+0.00028v_{d}T_{r}\) \\ \hline (4) & Page & \(k=0.00157T_{d}-0.0003T_{d}L+1.7\times 10^{-5}T_{d}T_{r}+0.00035\)\(v_{d}T_{r}\) \\  & & \(n=0.6762+0.00538L^{2}-0.0094v_{d}L\) \\ \hline (5) & Modified Page & \(k=0.01813v_{d}+0.00517L-0.0014v_{d}{}^{2}+1.5\times 10^{-5}T_{r}{}^{2}-0.0029v_{d}L-0.0002 LT_{r}\) \\  & & \(n=0.04846v_{d}+0.38198L-0.0421L^{2}-0.0266v_{d}L\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameter equations for the models adopted to dry matter changes during rehydration of dried red beets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model No.** & **Model Name** & **Parameter Equation** \\ \hline (1) & [PERSON] & \(A_{1}=0.53319v_{d}{}^{2}-0.0655T_{d}v_{d}+0.1076T_{d}L-0.0603 LT_{r}\) \\  & & \(A_{2}=-0.952+0.68791L+0.00142v_{d}{}^{2}-0.0892L^{2}-0.0001T_{d}v_{d}\) \\ \hline (2) & Lewis (Newton) & \(k=0.00028T_{d}+0.00565v_{d}+0.00376L-0.0006v_{d}{}^{2}+3.1\times 10^{-6}T_{r}{}^{2}-10^{-4}T _{d}L-0.0006v_{d}L\) \\ \hline (3) & Henderson–Pabis & \(k=0.01115+0.00224v_{d}-0.0003v_{d}{}^{2}-4\times 10^{-5}T_{d}L+4.2\times 10^{-6}T _{d}T_{r}\) \\  & & \(a=-0.0191v_{d}+0.49871L+0.00221v_{d}{}^{2}-0.0651L^{2}-5\times 10^{-5}T_{r}{}^{2}+6.9 \times 10^{-5}T_{d}T_{r}\) \\ \hline (4) & Page & \(k=0.03324v_{d}-0.0035v_{d}{}^{2}-4\times 10^{-5}T_{r}{}^{2}-0.0003T_{d}L+8.3\times 10^{-5}T _{d}T_{r}\) \\  & & \(n=0.64387-0.08v_{d}+0.00943v_{d}{}^{2}+0.00074T_{d}L-3\times 10^{-5}T_{d}T_{r}\) \\ \hline (5) & Modified Page & \(k=0.00361v_{d}+0.00786L-0.00055v_{d}{}^{2}-0.00112^{2}-5\times 10^{-5}T_{d}L+4.9 \times 10^{-6}T_{d}T_{r}\) \\  & & \(n=0.70781-0.0011T_{d}-0.0854v_{d}{}+0.01119v_{d}{}^{2}+0.00075T_{d}L-3 \times 10^{-5}T_{d}T_{r}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameter equations for the models adopted to \(m\) changes during rehydration of dried red beets. The rehydration rate constants \(k\) for four of the considered models used for the description of volume increase (Table 6) depended (in a statistically significant way) on all investigated parameters: \(T_{d}\), \(v_{d}\), \(L\), \(T_{r}\).