## 2 Materials and Methods
### Substantiation of the Model  
Let us consider a sample of a capillary-porous material of mass \(M\) (1). Drying is performed at a temperature \(T\)\({}^{\circ}\)C. Over time \(t\), due to a decrease in the moisture content of the material, the values \(M_{water}\) and \(M\) decrease by the same value \(\Delta M_{water}\). Then at the moments of time \(t\) and \(\tilde{t}=t+\Delta t\), the mass of moisture is \(M_{water}\) and \((M_{water}-\Delta M_{water})\), respectively; the mass of a sample at the same  
Figure 1: The relationship between moisture values determined on the wet basis and on the dry basis.  
times is equal to \(M\) and \((M-\Delta M_{water})\). At the same moments of time, relative moisture content (2) is determined by relations (9) and (10), respectively:  
\[C_{water}^{(w.b.)}=\frac{M_{water}}{M} \tag{9}\]  
\[\tilde{C}_{water}^{(w.b.)}=\frac{M_{water}-\Delta M_{water}}{M-\Delta M_{water}} \tag{10}\]  
For a sufficiently small value of \(\Delta t\), we can assume that the value of \(\Delta M_{water}\) is proportional to \(\Delta t\). In addition, the value of \(\Delta M_{water}\) is proportional to the amount of water \(M_{water}\). The total influence of other technological factors will be taken into account by the coefficient \(\tau\). Thus:  
\[\Delta M_{water}=\frac{\Delta t}{\tau}M_{water} \tag{11}\]  
The coefficient \(\tau\) has the dimension of time; its value is determined experimentally and remains constant, but only within the framework of solving a specific problem.  
Let's move on to dimensionless parameters. Let's write:  
\[\theta=\frac{t}{\tau} \tag{12}\]  
\[\Delta\theta=\frac{\Delta t}{\tau} \tag{13}\]  
Then instead of (11) we get  
\[\Delta M_{water}=\Delta\theta M_{water} \tag{14}\]  
Using (2) and (14), we transform (10) to the form:  
\[\tilde{C}_{water}^{(w.b.)}=\frac{C_{water}^{(w.b.)}-\Delta\theta C_{water}^{(w.b.)}}{1-\Delta\theta C_{water}^{(w.b.)}} \tag{15}\]  
Taking into account (9) and (15), we determine the change in relative moisture content over the time interval \(\Delta t\), that is \(\Delta C_{water}^{(w.b.)}=\tilde{C}_{water}^{(w.b.)}-C_{water}^{(w.b.)}\). After transforming this equality, taking into account relations (1) and (4), neglecting the second-order value \(\Delta\theta\Delta C_{water}^{(w.b.)}\approx 0\), we obtain:  
\[\tilde{C}_{water}^{(w.b.)}=\frac{C_{water}^{(w.b.)}-\Delta\theta C_{water}^{(w. b.)}}{1-\Delta\theta C_{water}^{(w.b.)}} \tag{16}\]  
With \(\Delta\theta\to 0\), instead of (16), we obtain a differential equation, which can be written in the form:  
\[\frac{dC_{water}^{(w.b.)}}{C_{water}^{(w.b.)}(1-C_{water}^{(w.b.)})}=-d\theta \tag{17}\]  
Integrating both sides of equality (17), we get \(\ln\frac{C_{water}^{(w.b.)}}{C_{water}^{(w.b.)}-1}=-\theta+A\). The constant of integration \(A\) is found from the condition that the initial moisture content of the material \(C_{water,start}^{(w.b.)}\) is known, i.e., if \(\theta\)= 0, then \(C_{water}^{(w.b.)}=C_{water,start}^{(w.b.)}\). After transformations, we will find \(e^{\theta}=\frac{C_{water}^{(w.b.)}\left(1-C_{water,start}^{(w.b.)}\right)}{\left(1 -C_{water}^{(w.b.)}\right)C_{water,start}^{(w.b.)}}\). From here we express \(C_{water}^{(w.b.)}\) as follows:  
\[C_{water}^{(w.b.)}=\frac{C_{water,start}^{(w.b.)}}{C_{water,start}^{(w.b.)}(1-e^{ \theta})+e^{\theta}} \tag{18}\]  
From (18) it follows that the normalized moisture \((C_{water}^{(w.b.)}/C_{water,start}^{(w.b.)})\) directly depends on the initial moisture \(C_{water,start}^{(w.b.)}\). Relation (18) can be converted to the form:  
\[C_{water}^{(w.b.)}=\frac{e^{-\theta}}{\left(C_{water,start}^{(w.b.)}\right)^{-1} +e^{-\theta}-1} \tag{18a}\]  
From (18a) it follows: if \(\theta\)\(\rightarrow\)\(\infty\), then \(C_{water}^{(w.b.)}\)\(\rightarrow\)0.