Evaluation of the Global S-Entropy Production in Membrane Transport of Aqueous Solutions of Hydrochloric Acid and Ammonia

The results of experimental studies of volume osmotic fluxes (Jvkr) and fluxes of dissolved substances (Jkr) in a system containing a synthetic Nephrophan® membrane (Orwo VEB Filmfabrik, Wolfen, Germany) set in a horizontal plane are presented. The membrane separated water and aqueous HCl or ammonia solutions or aqueous ammonia and HCl solutions. It was found that for the homogeneity conditions of the solutions Jvk and Jk depend only on the concentration and composition of the solutions. For concentration polarization conditions (where concentration boundary layers are created on both sides), Jvkr and Jkr depend on both the concentration and composition of the solutions and the configuration of the membrane system. The obtained results of the Jvk and Jk flux studies were used to assess the global production of entropy for the conditions of homogeneity of solutions (ΦSk), while Jvkr and Jkr—to assess the global production of entropy for concentration polarization conditions (ΦSkr). In addition, the diffusion-convective effects and the convection effect in the global source of entropy were calculated. The concentration polarization coefficient ζir was related to modified concentration Rayleigh number, e.g., the parameter controlling the transition from non-convective (diffusive) to convective state. This number acts as a switch between two states of the concentration field: convective (with a higher entropy source value) and non-convective (with a lower entropy source value). The operation of this switch indicates the regulatory role of earthly gravity in relation to membrane transport.


Introduction
Membrane transport processes belong to the group of basic phenomena occurring at the level of organization of physicochemical systems, in which the membrane constitutes a selective barrier separating the interior of the system from its surroundings [1][2][3]. The driving forces of these transport phenomena are a consequence of the occurrence of various types of physical fields, such as concentration, pressure, temperature or electric potential fields, participating in shaping the field constitution of nature [4]. The flows resulting from the action of these forces, such as diffusion or osmosis, modify the physical fields, an example of which in the case of the concentration field is concentration polarization [5][6][7][8]. This modification consists in minimizing the concentration gradients, which results in minimizing, inter alia, the osmotic and diffusion fluxes of dissolved substances and the membrane potentials [8,9]. Under certain conditions depending on the composition of solutions and the orientation of the membrane with respect to the gravity vector, concentration gradients can be In thermodynamic systems, including membrane systems, internal energy can be converted into free energy and dissipated energy. The energy dissipated is the product of absolute temperature (T) and S-entropy (S). The rate of entropy changes of the system (dS/dt) is the sum of the rate of entropy exchanged between the system and the environment (dS e /dt) and the rate of entropy formation inside the system (dS i /dt) [1,15]. The rate of formation or production of entropy inside the system is determined by the expression dS i /dt = ϕ S dV, where ϕ S = (1/T·V)/(dS i /dt) ≥ 0-denotes the source of entropy that is the rate of S-entropy formation in the volume unit (V) of the tested system, (ϕ S > 0-in an irreversible process, and ϕ S = 0-in a reversible process) [3]. Moreover, the source of entropy (ϕ S ) satisfies the relation ϕ S = k X k J k 0. This relation shows that the set of thermodynamic force (X k ) causes irreversible flows conjugated with them and opposite to them, which are measured by the J k fluxes, reducing the value of X k and leading the system to the state of thermodynamic equilibrium [1,3]. For a membrane system where a ∆x thick membrane separates two homogeneous electrolyte solutions of different concentrations, the entropy source of the membrane itself is Φ S = ∆x 0 ϕ S dx [17]. If the solutions contain a solvent and k solutes, then the global source of entropy is described by the following equation: where Φ S -global entropy source for the conditions of the homogeneous concentration field of solutions; (Φ S ) J vk , (Φ S ) J k and (Φ S ) I -the S-entropy produced by J vk , J k and I, respectively; J vk and J k -fluxes, respectively, volume solution and k-th solute for the conditions of homogeneity of solutions, I-electric current, ∆P and ∆π k = RT∆C k -differences of hydrostatic and osmotic pressures, respectively (RT-the product of the gas constant and temperature, ∆C k -difference of the concentrations of the solutions), C k = (C hk − C lk ) ln C hk C lk −1 −1 -the average concentration of solutes in the membrane (M). Equation (1) is reduced to the written expression for nonelectrolyte solutions when I = 0 and E = 0 [17].
J vk , J k and I fluxes can be described by the appropriate Kedem-Katchalsky equations for the homogeneity conditions of electrolyte solutions [17]: where L p , σ k and ω ks -hydraulic permeability, reflection and solute permeability coefficients, ε k (1 ≤ ε k ≤ 2)-stands for the Vant Hoff coefficient, β-electroosmotic coefficient, i-represent electric current through the membrane, τ k -transference number of ions, z k -valence of ions, F-Faraday number, κ-conductance coefficient, ∆E-electromotive force difference. Equations (2)-(4) reduces to the expression for nonelectrolyte when I = 0. Due to the lack of accumulation or depletion of ions in the electroneutral membrane and due to the electroneutrality of the solution, it can be concluded that J + = J − = J k (k = 1 or 2). Under real conditions, the homogeneity of the solution concentration field may be disturbed by concentration polarization. As a result, concentration boundary layers are spontaneously formed on both sides of the membrane. For the conditions of concentration polarization, and for I = 0 or E = 0, Equation (1) takes the form: where Φ r S -global entropy source for the conditions of concentration polarization, Φ r S J r vk is the S-entropy produced by J r vk , Φ r S J r k is the S-entropy produced by J r k , J r vk and J r k -the volume and k-th solute fluxes, respectively, for the concentration polarization conditions of the solutions, r = A or B means the configuration of the membrane system. The Kedem-Katchalsky equations for the fluxes J r vk and J r k and for I = 0 can be written as: J r k = k,s ζ r ks ω ks ∆π k + J r vk (1 − ζ r a σ k ) C k (7) where ζ r p , ζ r vk , ζ r ks and ζ r a are the hydraulic, osmotic, diffusive and adjective concentration polarization coefficients, respectively [23]. As in the previous case, due to the lack of accumulation or depletion of ions in the electroneutral membrane and the electroneutrality of the solutions, it can be assumed that J r + = J r − = J r k (k = 1 or 2). For this reason, in the vicinity of the electroneutral membrane, there only a phenomenon of concentration polarization of the membrane having an important influence on substances "1" and/or "2" transport through the membrane. Due to the electroneutrality of the concentrated electrolyte solutions, the electric current through the membrane (electroneutral membrane without bounded ions) during the measurement is negligible (I = 0) [17,24]. In [4,8] it was shown that J r vk and J r k depend on the transport properties of the membrane, the configuration of the membrane system as well as the physicochemical properties and composition of solutions separated by the membrane. The value of these fluxes is greater under convective than in non-convective conditions. In the case of ternary solutions (consisting of water and two dissolved substances, one of which causes an increase in density and the other a decrease in density as their concentration increases), the J r vk and J r k fluxes are non-linear functions of the concentration difference. Due to Equation (2), the global source of entropy for the conditions of concentration polarization (Φ r S ), is a non-linear function of J r vk and J r k [23,25]. The aim of the present study was to determine J r vk , J r k , J vk and J k in a single-membrane system, in which the hemodialyzer biomembrane Nephrophan ® (Orwo VEB Filmfabrik, Wolfen, Germany) situated in the horizontal plane separates water and a ternary solution consisting of water, ammonia and/or HCl. In order to achieve this goal, the influence of the concentration of individual components of the solutions and the configuration of the membrane system on the value of J r vk , J r k , J vk and J k fluxes under the conditions of concentration polarization, respectively, and under the conditions of homogeneity of solutions were investigated. Based on the results of the J r vk and J v tests, the sources of entropy (Φ Sk , Φ r Sk ), the diffusion-convective effects (∆Φ r Sk = Φ Sk − Φ r Sk ) and the convective effects in the global entropy source (k = 1, 2 represents the component number of the solution and r = A, B-configuration of the membrane system). The experiments were performed under the conditions of E = 0 and I = 0.

Model of the Electrochemical Membrane Cell
The subject of considerations, as well as several of our previous works, is transport in a membrane system illustrated schematically in Figure 1 [4,26]. This figure shows a model of a membrane system in which the membrane (M), situated in the horizontal plane, separates two solutions with the initial concentrations C hk and C lk (C hk > C lk , k = 1, 2). In configuration A, in the compartment above the membrane there is a solution with a concentration of C lk , and in the compartment under the membrane-a solution with a concentration of C hk . In configuration B-solutions with the concentration of C lk , and C hk are changed places. If we assume that the driving force for osmotic flows is the difference in concentrations between the solutions filling the upper and lower compartments, then ∆C k for configuration A has a negative sign, and for configuration B-positive. The aim of the present study was to determine , , and in a single-membrane system, in which the hemodialyzer biomembrane Nephrophan ® (Orwo VEB Filmfabrik, Wolfen, Germany) situated in the horizontal plane separates water and a ternary solution consisting of water, ammonia and/or HCl. In order to achieve this goal, the influence of the concentration of individual components of the solutions and the configuration of the membrane system on the value of , , and fluxes under the conditions of concentration polarization, respectively, and under the conditions of homogeneity of solutions were investigated. Based on the results of the and tests, the sources of entropy ( , ), the diffusion-convective effects (∆ = − ) and the convective effects ( = − ) in the global entropy source (k = 1, 2 represents the component number of the solution and r = A, B-configuration of the membrane system). The experiments were performed under the conditions of E = 0 and I = 0.

Model of the Electrochemical Membrane Cell
The subject of considerations, as well as several of our previous works, is transport in a membrane system illustrated schematically in Figure 1 [4,26]. This figure shows a model of a membrane system in which the membrane (M), situated in the horizontal plane, separates two solutions with the initial concentrations Chk and Clk (Chk > Clk, k = 1, 2). In configuration A, in the compartment above the membrane there is a solution with a concentration of Clk, and in the compartment under the membrane-a solution with a concentration of Chk. In configuration Bsolutions with the concentration of Clk, and Chk are changed places. If we assume that the driving force for osmotic flows is the difference in concentrations between the solutions filling the upper and lower compartments, then ΔCk for configuration A has a negative sign, and for configuration B-positive.
According to the laws of diffusion, water and substances dissolved in it, penetrating through the membrane, causing the phenomenon of concentration polarization, form, on both its sides, concentration boundary layers and (r = A, B) with thicknesses respectively and . The consequence of the formation of these layers is the reduction of the concentration difference from the value of Chk-Clk to the value of − , where > , Chk > and > Clk. In the case when a solution with a lower density is placed in the compartment under the membrane, and a solution with a higher density in the compartment above the membrane, the system /M/ loses hydrodynamic stability and, consequently, gravitational convection may occur in the concentration boundary layers region [27][28][29][30][31][32]. It appears when the thickness of the boundary concentration layers ( , ) exceeds the critical value ( ) and/or the concentration polarization coefficients ( ) exceeds the critical value ( ) and when the concentration Rayleigh number ( Figure 1. The model of single-membrane system: M-membrane, g-gravitational acceleration, l A l and l A h -the concentration boundary layers in configuration A, l B l and l B h -the concentration boundary layers in configuration B, P h and P l -mechanical pressures, C kh and C kl -global solution concentrations (C hk > C lk ), C A lk , C A hk , C B lk and C B hk -local (at boundaries between membrane and CBLs) solution concentrations, J A vk -solute and volume fluxes in configuration A, J B vk -solute and volume fluxes in configuration B, (k = 1 or 2). According to the laws of diffusion, water and substances dissolved in it, penetrating through the membrane, causing the phenomenon of concentration polarization, form, on both its sides, concentration boundary layers l r h and l r l (r = A, B) with thicknesses respectively δ r h and δ r l . The consequence of the formation of these layers is the reduction of the concentration difference from the value of C hk-C lk to the value of C r hk − C r lk , where C r hk > C r lk , C hk > C r hk and C r lk > C lk . In the case when a solution with a lower density is placed in the compartment under the membrane, and a solution with a higher density in the compartment above the membrane, the system l r h /M/l r l loses hydrodynamic stability and, consequently, gravitational convection may occur in the concentration boundary layers region [27][28][29][30][31][32]. It appears when the thickness of the boundary concentration layers (δ r h , δ r l ) exceeds the critical value (δ) and/or the concentration polarization coefficients (ζ r k ) exceeds the critical value (ζ k ) and when the concentration Rayleigh number (R Ck ) that control the process of the appearance of gravitational convection, will exceed their critical values [28,33,34]. The concentration Rayleigh number for membrane transport processes of ternary solutions can be represented by the expressions [35,36]: where R C1 -concentration Rayleigh Number, ρ 0 -mass density, ν 0 -kinematic viscosity of solution, RT-product of the gas constant and temperature, ω 1 -solute permeability coefficient, g-gravitational acceleration, ∂ρ/∂C k -variation of density with concentration, ζ 1 -concentration polarization coefficient, D 1 -diffusion coefficient, (k = 1, 2). It is worth noting that Equation (8) does not contain the concentration thickness of the boundary layer (δ). To get R C2 it is enough to change the index "1" to "2". Over time, the destructive effect of gravitational convection limits the growth of δ r h and δ r l and accelerates the diffusion of substances beyond the layers, which extends the effect of convection to the entire volume of the solution. Under certain conditions, even liquid structuring may occur, which is manifested in the appearance of "plum structures" [37,38].
The process of creating concentration boundary layers is accompanied by a decrease in the volume osmotic fluxes from J vk to J r vk and the solute fluxes from J k to J r k [7]. Using Equations (1) and (5), the global source of entropy for ternary solutions can be represented as: To calculate the sources of entropy Φ Sk and Φ r Sk , it is enough to experimentally determine the concentration dependences of the fluxes J r vk , J vk , J r k and J k .

Methodology for Measuring the Volume Osmotic and Solute Fluxes
The study of volume osmotic transport and transport of dissolved substances was carried out using the measuring set described in a previous paper [29]. The set consisted of two cylindrical measuring vessels with a volume of 200 cm 3 each. One of the vessels contained the tested binary solution (aqueous HCl or NH 3 ·H 2 O solution) or ternary (aqueous solution of HCl and NH 3 ·H 2 O). In turn, the second vessel in all experiments contained an aqueous solution of HCl and/or NH 3 ·H 2 O (NH 4 OH) with a constant concentration C l1 = C l2 = 1 mol m −3 . The solutions in the vessels were separated by the Nephrophan ® (Orwo VEB Filmfabrik, Wolfen, Germany) biomembrane, set in a horizontal plane, with an area of A = 3.36 cm 2 and transport properties determined by the following factors: hydraulic permeability (L p ), reflection (σ) and diffusion permeability (ω). The values of these coefficients for HCl (index 1) and NH 3 ·H 2 O (index 2), determined in a series of independent experiments carried out according to the procedure described in paper [16], were: L p = 5 × 10 −12 m 3 N −1 s −1 , σ 1 = 0.06, σ 2 = 0.01, ω 11 = 1.24 × 10 −9 mol N −1 s −1 , ω 12 = 1.4 × 10 −12 mol N −1 s −1 , ω 22 = 2.68 × 10 −9 mol N −1 s −1 and ω 21 = 2.5 × 10 −12 mol N −1 s −1 . Nephrophan ® (Orwo VEB Filmfabrik, Wolfen, Germany) is a microporous, highly hydrophilic and electroneutral membrane made of regenerated cellulose [39].
A graduated (every 0.5 mm 3 ) pipette set in a plane parallel to the plane of the membrane was connected to the vessel containing the higher concentration. The change in volume (∆V r ) of the solution in this vessel of the plumbing system was measured with this pipette. In turn, the second vessel was connected to a reservoir of an aqueous solution of HCl and/or NH 4 OH (NH 3 ·H 2 O) with a concentration of C l1 = C l2 = 1 mol m −3 , with adjustable height relative to the pipette. This made it possible to compensate for the hydrostatic pressure (∆P = 0) present in the measurement set. The measurements were performed according to the procedure described in [8], which consisted of two stages. In the first stage, the increases of ∆V r were measured under the conditions of intensive mechanical stirring of the solutions with an angular speed of 500 rpm. The second stage started as soon as steady-state flows were achieved, and the stirring of the solutions was turned off. In this step, the increases of ∆V r were also measured until the steady state of the flows was obtained. Each experiment was performed for configurations A and B of the membrane system. In configuration A, the test solution was filled into the vessel under the membrane, and in configuration B-the vessel over the membrane. It should be noted that the volume flows took place from the vessel with a lower concentration of solutions to the vessel with a higher concentration of solutions, and the flows of dissolved substances in the opposite direction. Therefore, it was assumed that in the configuration A the fluxes J r vk , J vk , J r k and J k and the concentration differences ∆C k (k = 1, 2) are negative (J r vk , J vk -directed vertically downwards, J r k and J k -vertically upwards), and in configuration B-positive (J r vk , J vk -vertically upwards, J r k , J k -vertically downwards).
The tests were carried out in isobaric-isothermal conditions for T = 295 K and ∆P = 0. The volume flow was calculated on the basis of the volume changes (∆V r ) in the pipette over time ∆t through the membrane surface S, using the formula J r vk = (∆V r )S −1 (∆t) −1 (r = A, B). Flows of dissolved substances were calculated on the basis of the formula J r k = ∆C r k V u S −1 (∆t) −1 (k = 1, 2; r = A, B), V u -volume of the measuring vessel, ∆C r k -global concentration exchanes in the solutions studied was performer by the standard physico-chemical method [40,41]. In this expression, due to the lack of accumulation or depletion of ions inside the electroneutral membrane and in its surroundings (electroneutral solutions), we assume that J r The study of volume flows and flows of dissolved substances in both configurations consisted in determining the characteristics J vk = f (t), J r vk = f (t), J k = f (t) and J r k = f (t), (k = 1, 2; r = A, B) for different concentrations of solutions. Each measurement series was repeated 3 times. The relative error in determining J vk , J r v , J k and J r k was not greater than 5%. Based on the characteristics J vk = f (t), J r vk = f (t), J k = f (t) and J r k = f (t) for the steady state, the characteristics J v1 = f (∆C 1 , . Based on these characteristics, the concentration source of entropy was calculated:

Concentration Dependencies of the Volume Osmotic Flux
The results of the volume osmotic flux tests for the concentration polarization conditions of the solutions separated by the membrane are shown in Figures 2 and 3. Figure 2 shows the experimental dependencies J r v1 = f (∆C 1 , ∆C 2 = constant), and in Figure 3-the experimental dependencies J r v2 = f (∆C 2 , ∆C 1 = constant). The graphs in the third quadrant of the coordinate system (1A, 2A, 3A) refer to configuration A of the membrane system). On the other hand, the graphs in the first quadrant of the coordinate system (1B, 2B, 3B) refer to configuration B of the membrane system.
Lines 1A and 1B shown in Figure 2 show that in the case of ∆C 1 < 0 and ∆C 1 > 0 (for ∆C 2 = 0) in binary solutions it causes a linear decrease (graph 1A) or a linear increase (graph 1B) of the J r v1 flux value, but the slope of line 1A is less than line 1B. This is because for ∆C 1 < 0 the concentration polarization minimizes ∆C 1 and consequently also J r v1 . On the other hand, for ∆C 1 > 0, gravitational convection partially restores ∆C 1 , which in turn gives higher values of J r v1 . On the other hand, graphs 1A and 1B presented in Figure 3 show that in the case of ∆C 2 < 0 and ∆C 2 > 0 (for ∆C 1 = 0) in binary solutions it causes a linear increase (diagram 1A) or a linear decrease (diagram 1B) of J r v2 fluxes, but this time the slope of line 1A is greater than line 1B. In this case, for ∆C 2 > 0, the concentration polarization minimizes ∆C 2 and consequently also J r v2 . On the other hand, for ∆C 2 < 0, gravitational convection partially restores ∆C 2 , which in turn gives higher values of J r v2 . Lines 2A and 3A as well as 2B and 3B shown in Figure 2 show that in the case of ΔC1 < 0 and ΔC1 > 0 (for ΔC2 = 250 mol m −3 and ΔC2 = 500 mol m −3 ) in ternary solutions, changes in ΔC1 cause various changes of fluxes. These graphs show that for ΔC1 < 0 an initial decrease and then a non-linear increase in the value of fluxes are observed. Graphs 2B and 3B show that for ΔC1 > 0, after the initial small linear, there is a non-linear increase in the value of the flux . Moreover, comparing the graphs 1A, 2A and 3A for the test results presented in this figure, the following relationships are satisfied: . On the other hand, the comparison of the graphs 1B, 2B and 3B shows that (for ΔC2 = 0) > (for ΔC2 = 250 mol m −3 ) > (for ΔC2 = 500 mol m −3 ). The jump in the value of is caused by the transition of the system from non-convective to convective state. In turn, the abrupt decrease in the value of is caused by the transition of the system from convective to non-convective state.
Comparing the curves 2A and 2B as well as 3A and 3B shown in Figure 2, it can be seen that in the case of the first pair of curves, for ΔC1 = ±107.7 mol m −3 , the fluxes are equal in value ( = ±1.29 × 10 −8 m s −1 ), but directed in the opposite direction. On the other hand, in the case of the second pair of curves, the fluxes are equal in value ( = ±1.46 × 10 −8 m s −1 ) and directed opposite for ΔC1 = ±206.2 mol m −3 . The equality of the volume osmotic flux means that the volume osmotic flux is independent of the configuration of the membrane system. This means that the diaphragm system −3
Lines 2A and 3A as well as 2B and 3B shown in Figure 2 show that in the case of ∆C 1 < 0 and ∆C 1 > 0 (for ∆C 2 = 250 mol m −3 and ∆C 2 = 500 mol m −3 ) in ternary solutions, changes in ∆C 1 cause various changes of J r v1 fluxes. These graphs show that for ∆C 1 < 0 an initial decrease and then a non-linear increase in the value of J r v1 fluxes are observed. Graphs 2B and 3B show that for ∆C 1 > 0, after the initial small linear, there is a non-linear increase in the value of the flux J r v1 . Moreover, comparing the graphs 1A, 2A and 3A for the test results presented in this figure, the following relationships are satisfied: . On the other hand, the comparison of the graphs 1B, 2B and 3B shows that J r v1 (for . The jump in the value of J r v1 is caused by the transition of the system from non-convective to convective state. In turn, the abrupt decrease in the value of J r v1 is caused by the transition of the system from convective to non-convective state. Comparing the curves 2A and 2B as well as 3A and 3B shown in Figure 2, it can be seen that in the case of the first pair of curves, for ∆C 1 = ±107.7 mol m −3 , the J r v1 fluxes are equal in value (J r v1 = ±1.29 × 10 −8 m s −1 ), but directed in the opposite direction. On the other hand, in the case of the second pair of curves, the J r v1 fluxes are equal in value (J r v1 = ±1.46 × 10 −8 m s −1 ) and directed opposite for ∆C 1 = ±206.2 mol m −3 . The equality of the volume osmotic flux means that the volume osmotic flux is independent of the configuration of the membrane system. This means that the diaphragm system does not discriminate in the gravity direction. Moreover, for ∆C 1 > −107.7 mol m −3 and ∆C 1 > −206.2 mol m −3 , membrane transport in configuration A of the membrane system and for ∆C 1 > 107.7 mol m −3 and ∆C 1 > 206.2 mol m −3 (for configuration B) takes place under the conditions of concentration polarization destruction by free convection and is osmotic-diffusion-convective in nature. In turn, for ∆C 1 < −107.7 mol m −3 and ∆C 1 < −206.2 mol m −3 in the membrane transport (in configuration A) of the membrane system and for ∆C 1 > 107.7 mol m −3 and ∆C 1 < 206.2 mol m −3 (in configuration A) B of the membrane system) takes place under the conditions of concentration polarization and is osmotic and diffusive.
Plots 2A and 3A as well as 2B and 3B shown in Figure 3 show that in the case of ∆C 2 < 0 and ∆C 2 > 0 (for ∆C 1 = 200 mol m −3 and ∆C 1 = 300 mol m −3 ) in ternary solutions, changes in ∆C 2 cause different changes of J r v2 fluxes. These graphs show that for ∆C 2 < 0, an initial slight linear and then a non-linear decrease in the values of J r v2 fluxes is observed. Graphs 2B and 3B show that for ∆C 2 > 0, with an increase in the value of ∆C 2 , there is a non-linear decrease in the value of the flux J r v2 . Moreover, comparing the graphs 1A, 2A and 3A for the test results presented in this figure, the relations between J r v2 (for ∆C 1 = 0), J r v2 (for ∆C 1 = 200 mol m −3 ) and J r v2 (for ∆C 1 = 300 mol m −3 ) are different depending on the ∆C 2 range. On the other hand, the comparison of graphs 1B, 2B and 3B shows that . As in the previous case, the jump or decrease in the value of J r v2 is caused by the transition of the system from non-convective to convective state or the other way.  Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 3, it can be seen that in the case of the first pair of curves, for ΔC2 = ±476.  Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 3, it can be seen that in the case of the first pair of curves, for ∆C 2 = ±476.7 mol m −3 , the J r v2 fluxes are equal in value (J r v2 = ±1.5 × 10 −8 m s −1 ), but directed in the opposite direction. On the other hand, in the case of the second pair of curves, the J r v2 fluxes are equal in value (J r v2 = ±2.19 × 10 −8 m s −1 ) and directed opposite for ∆C 2 = ±664 mol m −3 . The equality of the volume osmotic fluxes means that the volume osmotic flux is independent of the configuration of the membrane system and thus of the gravity direction. Moreover, for ∆C 2 > −476.7 mol m −3 and ∆C 2 > −664 mol m −3 , membrane transport in configuration A of the membrane system and for ∆C 2 < 476.7 mol m −3 and ∆C 2 < 664 mol m −3 (for configuration B) takes place under the conditions of concentration polarization destruction by gravitational convection and is osmotic-diffusion-convective in nature. In turn, for ∆C 2 > −476.7 mol m −3 and ∆C 2 > −664 mol m −3 in the membrane transport (in configuration A) of the membrane system and for ∆C 2 < 476.7 mol m −3 and ∆C 2 < 664 mol m −3 (in B of the membrane system) takes place under the conditions of concentration polarization and is osmotic and diffusive. Figures 4 and 5 show the results of the volume osmotic flux tests for the uniformity conditions of the solutions. Figures 4 and 5 show that changing the sign of ∆C 1 and/or ∆C 2 changes the sign of J v1 and J v2 but does not change the value. This means that J v1 and J v2 do not depend on the configuration of the diaphragm system. Moreover, J v1 is a linear (except for the initial section of plots 2 and 3) a function of ∆C 1 , with a fixed value of ∆C 2 . It should be noted that for the test results presented in Figure 4, non-zero values of ∆C 2 , and for the test results presented in Figure 5, non-zero values of ∆C 1 , cause a parallel shift of graphs 2 and 3 in relation to graph 1, while 1 is greater than plot 3 relative to 2. This is due to a 2-fold increase in the osmotic pressure difference ∆π 2 due to complete dissociation of NH 3 ·H 2 O (NH 4 OH) in the presence of HCl. Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 3, it can be seen that in the case of the first pair of curves, for ΔC2 = ±476.7 mol m −3 , the fluxes are equal in value ( = ±1.5 × 10 −8 m s −1 ), but directed in the opposite direction. On the other hand, in the case of the second pair of curves, the fluxes are equal in value ( = ±2.19 × 10 −8 m s −1 ) and directed opposite for ΔC2 = ±664 mol m −3 . The equality of the volume osmotic fluxes means that the volume osmotic flux is independent of the configuration of the membrane system and thus of the gravity direction. Moreover, for ΔC2 > −476.7 mol m −3 and ΔC2 > −664 mol m −3 , membrane transport in configuration A of the membrane system and for ΔC2 < 476.7 mol m −3 and ΔC2 < 664 mol m −3 (for configuration B) takes place under the conditions of concentration polarization destruction by gravitational convection and is osmotic-diffusion-convective in nature. In turn, for ΔC2 > −476.7 mol m −3 and ΔC2 > −664 mol m −3 in the membrane transport (in configuration A) of the membrane system and for ΔC2 < 476.7 mol m −3 and ΔC2 < 664 mol m −3 (in B of the membrane system) takes place under the conditions of concentration polarization and is osmotic and diffusive.   Figures 4 and 5 show that changing the sign of ΔC1 and/or ΔC2 changes the sign of and but does not change the value. This means that and do not depend on the configuration of the diaphragm system. Moreover, is a linear (except for the initial section of plots 2 and 3) a function of ΔC1, with a fixed value of ΔC2. It should be noted that for the test results presented in Figure 4, non-zero values of ΔC2, and for the test results presented in Figure 5, non-zero

Concentration Dependencies of Solute Fluxes
The results of the study of the flux of dissolved substances for the conditions of concentration polarization of the solutions separated by the membrane are shown in Figures 6 and 7. Figure 6 shows the experimental dependences J r 1 = f (∆C 1 , ∆C 2 = constant), and in Figure 7, the experimental dependencies J r 2 = f (∆C 2 , ∆C 1 = constant). The graphs in the third quadrant of the coordinate system (1A, 2A, 3A) refer to configuration A of the membrane system. In turn, the graphs in the first quadrant of the coordinate system (1B, 2B, 3B) refer to the configuration B of the membrane system. Graphs 1A and 1B shown in Figure 6 show that in the case of ∆C 1 < 0 and ∆C 1 > 0 (for ∆C 2 = 0) in binary solutions it causes a linear decrease (graph 1A) or a linear increase (graph 1B) of the J r 1 . flux value, but the slope of line 1A is less than line 1B. This is because for ∆C 1 < 0 the concentration polarization minimizes ∆C 1 and consequently also J r 1 . On the other hand, for ∆C 1 > 0, gravitational convection partially restores ∆C 1 , which consequently gives higher values of J r 1 . On the other hand, graphs 1A and 1B presented in Figure 7 show that in the case of ∆C 2 < 0 and ∆C 2 > 0 (for ∆C 1 = 0) in binary solutions it causes a linear increase (graph 1A) or a linear decrease (graph 1B) of J r 2 fluxes, but this time the slope of line 1A is greater than line 1B. In this case, for ∆C 2 > 0, the concentration polarization minimizes ∆C 2 and consequently also J r 2 . On the other hand, for ∆C 2 < 0, gravitational convection partially restores ∆C 2 , which consequently gives higher values of J r 2 .
Entropy 2020, 22, x 10 of 21 250 mol m −3 ) > (ΔC2 = 500 mol m −3 ). The jump in the value of is caused by the transition of the system from non-convective to convective states. In turn, the abrupt decrease in the value of is caused by the transition of the system from convective to non-convective state. Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 6, it can be seen that in the case of the first pair of curves, for ΔC1 = ±106.  . The jump in the value of is caused by the transition of the system from non-convective to convective states. In turn, the abrupt decrease in the value of is caused by the transition of the system from convective to non-convective state. Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 6, it can be seen that in the case of the first pair of curves, for ΔC1 = ±106.    Graphs 2A and 3A as well as 2B and 3B shown in Figure 6 show that in the case of ∆C 1 < 0 and ∆C 1 > 0 (for ∆C 2 = 250 mol m −3 and ∆C 2 = 500 mol m −3 ) in ternary solutions, changes in ∆C 1 cause different changes of J r 1 fluxes. These graphs show that for ∆C 1 < 0 an initial decrease and then a non-linear increase in the values of J r 1 fluxes are observed. Graphs 2B and 3B show that for ∆C 1 > 0, after the initial small linear, there is a non-linear increase in the value of the flux J r 1 . Moreover, comparing the graphs 1A, 2A and 3A for the test results presented in this figure, the following dependences are fulfilled: J r 1 (for ∆C 2 = 0) > J r 1 (for ∆C 2 = 250 mol m −3 ) > J r 1 (for ∆C 2 = 500 mol m −3 ). On the other hand, the comparison of the graphs 1B, 2B and 3B allows to conclude that J r 1 (for ∆C 2 = 0) > J r 1 (for ∆C 2 = 250 mol m −3 ) > J r 1 (∆C 2 = 500 mol m −3 ). The jump in the value of J r 1 is caused by the transition of the system from non-convective to convective states. In turn, the abrupt decrease in the value of J r 1 is caused by the transition of the system from convective to non-convective state. Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 6, it can be seen that in the case of the first pair of curves, for ∆C 1 = ±106.  Figure 7 shows the results of the J r 2 flux generated by the constant difference in concentrations ∆C 2 = 250 mol m −3 (graphs 2A and 2B) and ∆C 2 = 500 mol m −3 (graphs 3A and 3B) for a variable value of ∆C 1 . Hence, J r 2 should be constant. However, adding HCl to aqueous solutions of ammonia causes an increase in the density of the solution, which in turn induces convective movements causing partial destruction of CBLs and leads to an increase in the value of J r 2 , depending on ∆C 1 . Graphs 2A and 3A as well as 2B and 3B shown in Figure 8 show that in the case of ∆C 2 < 0 and ∆C 2 > 0 (for ∆C 1 = 200 mol m −3 and ∆C 2 = 300 mol m −3 ) in ternary solutions, changes in ∆C 2 cause different changes of J r 2 fluxes. These graphs show that for ∆C 2 < 0, an initial slight linear and then a non-linear decrease in the values of J r 2 fluxes is observed. Graphs 2B and 3B show that for ∆C 2 > 0, with an increase in the value of ∆C 2 , there is a non-linear decrease in the value of the flux J r 2 . Moreover, comparing the graphs 1A, 2A and 3A for the test results presented in this figure, the relations between J r 2 (for ∆C 2 = 0), J r 2 (for ∆C 1 = 200 mol m −3 ) and J r 2 (for ∆C 1 = 300 mol m −3 ) are different depending on the ∆C 2 range. On the other hand, the comparison of graphs 1B, 2B and 3B shows that J r 2 (for ∆C 1 = 0) < J r 2 (for ∆C 1 = 200 mol m −3 ) < J r 2 (for ∆C 2 = 300 mol m −3 ). As in the previous case, the abrupt increase or decrease in the value of J r 2 is caused by the transition of the system from non-convective to convective state or the other way.
Comparing the curves 2A and 2B as well as 3A and 3B presented in Figure 8, it can be seen that in the case of the first pair of curves, for ∆C 2 = ±476.8 mol m −3 , the J r 2 fluxes are equal in value (J r 2 = ±25.1 × 10 −5 mol m −2 s −1 ), but in the opposite direction. In turn, in the case of the second pair of curves, the fluxes J r 2 are equal in value (J r 2 = ±35.2 × 10 −5 mol m −2 s −1 ) and directed opposite for ∆C 2 = ±664 mol m −3 . The equality of the volume osmotic flux means that the volume osmotic flux is independent of the configuration of the membrane system. Moreover, for ∆C 2 > −476.8 mol m −3 and ∆C 2 > −664 mol m −3 , membrane transport in configuration A of the membrane system and for ∆C 2 < 476.8 mol m −3 and ∆C 2 < 664 mol m −3 (for configuration B) takes place under the conditions of concentration polarization destruction by gravitational convection and is diffusive-convective in nature. In turn, for ∆C 2 > −476.8 mol m −3 and ∆C 2 > −664 mol m −3 in the membrane transport (in configuration A) of the membrane system and for ∆C 2 < 476.8 mol m −3 and ∆C 2 < 664 mol m −3 (in B of the membrane system) takes place in the conditions of concentration polarization and is diffusive. different changes of fluxes. These graphs show that for ΔC2 < 0, an initial slight linear and then a non-linear decrease in the values of fluxes is observed. Graphs 2B and 3B show that for ΔC2 > 0, with an increase in the value of ΔC2, there is a non-linear decrease in the value of the flux . Moreover, comparing the graphs 1A, 2A and 3A for the test results presented in this figure, the relations between (for ΔC2 = 0), (for ΔC1 = 200 mol m −3 ) and (for ΔC1 = 300 mol m −3 ) are different depending on the ΔC2 range. On the other hand, the comparison of graphs 1B, 2B and 3B shows that (for ΔC1 = 0) < (for ΔC1 = 200 mol m −3 ) < (for ΔC2 = 300 mol m −3 ). As in the previous case, the abrupt increase or decrease in the value of is caused by the transition of the system from non-convective to convective state or the other way.  Figure 9 shows the results of the flux generated by the constant difference in concentrations ∆ = 200 mol m −3 (graphs 2A and 2B) and ∆ = 300 mol m −3 (graphs 3A and 3B ) for a variable value of ∆ . Hence, should be constant. However, adding ammonia to aqueous HCl solutions reduces the density of the solution, which in turn causes convective movements causing partial destruction of CBLs and leads to an increase in the value of , depending on ∆ . Figures 10 and 11 show the results of the solute flux tests for the uniformity conditions of the solutions. These figures show that changing the sign of ΔC1 and/or ΔC2 changes the sign of and but does not change the value. This means that and do not depend on the configuration of the diaphragm system. Moreover, is a linear function of ΔC1, almost independent of the value of ΔC2.        It should be noted that the addition of 200 mol m −3 HCl to aqueous ammonia solutions increases the value of by a factor of 2, which is caused by complete dissociation of NH3·H2O (NH4OH) in the presence of HCl. Increasing the HCl concentration to 300 mol m −3 does not cause a significant    It should be noted that the addition of 200 mol m −3 HCl to aqueous ammonia solutions increases the value of by a factor of 2, which is caused by complete dissociation of NH3·H2O (NH4OH) in the presence of HCl. Increasing the HCl concentration to 300 mol m −3 does not cause a significant For isothermal conditions, due to the density category, binary solutions consisting of water and one dissolved substance can be classified into one of two categories. The first category includes solutions whose density is inversely proportional to their concentration. Examples belonging to this group are aqueous solutions of first order alcohols (methanol, ethanol etc.) and ammonia. The second category is solutions whose density is proportional to their concentration. This category comprises solution not belonging to the first category. Unlike binary solutions, the density of ternary solutions, composed of a solvent and substances causing an increased and decreased solution density (i.e., glucose and ethanol, CuSO 4 and ethanol, KCl and ammonia or HCl and ammonia, etc.) may be lower than, equal to or greater than that of the solvent [4,8,31].  = 1, 2). Figures 12 and 13 show the dependencies Φ r S1 = f (∆C 1 , ∆C 2 = constant) and Φ r S2 = f (∆C 2 , ∆C 1 = constant), calculated on the basis of Equation (9) and the experimental These trends are evidenced by the same shape of the concentration characteristics of the fluxes for the conditions of concentration polarization. The research shows that the volume fluxes and fluxes of dissolved substances depend on the concentration and composition of solutions (binary or ternary) and the configuration of the membrane system. The presence of alcohol (ethanol, methanol) or ammonia in a ternary solution determines the specificity of the appropriate characteristics for ternary solutions in relation to the appropriate characteristics for binary solutions. It seems that the characteristics for solutions containing HCl and ammonia should be unusual. Because the chemical reaction of HCl + NH3·H2O = NH4Cl + H2O and H + + Cl − + OH − = NH4 + + Cl − + H2O. That is, the product is ammonium chloride. Due to the fact that the density of the aqueous ammonium chloride solution is directly proportional to the concentration, the characteristic should be linear. Research shows otherwise. The concentration characteristics of the streams in the system containing aqueous HCl and NH3·H2O solutions are of the same type as the concentration characteristics of the fluxes in the system containing aqueous solutions of glucose and ethanol, KCl and ammonia or CuSO4 and ethanol.

Concentration Dependencies of the Global Source of Entropy and
Equations (1) and (5)   Graph 1B presented in Figure 12 shows that increases linearly with the increase of the value of ∆ . On the other hand, graph 1A shows that changing the sign of ∆ from positive to negative Figure 12. Graphic illustration of the dependence Φ r S1 = f (∆C 1 , ∆C 2 = constant), for HCl solutions in NH 4 OH aqueous solution and concentration polarization conditions. Graphs 1A and 1B were obtained for ∆C 2 = 0, graphs 2A and 2B-for ∆C 2 = 250 mol m −3 and graphs 3A and 3B-for ∆C 2 = 500 mol m −3 . also causes a linear increase of but its values, in the case of negative ∆ , are much smaller compared to the value of for positive ∆ . The dependence = (∆ , ∆ = constant), Illustrated by the curves 2B and 3B, have a similar shape and are nonlinear. Two areas can be separated in the course of these curves. The first, where is weakly dependent on ∆ , related to the osmotic-diffusion production of entropy, and the second, where is strongly dependent on ∆ , related to the osmotic-diffusion-convective production of entropy.
The dependences = (∆ , ∆ = constant), illustrated by the curves 2A and 3A, have a similar shape and are nonlinear. Two areas can also be separated in the course of these curves. The first, where is strongly dependent on ∆ , related to the osmotic-diffusion-convective production of entropy, and the second, where is weakly dependent on ∆ , related to the osmotic-diffusion production of entropy. Moreover, it can be seen from Figures 12 and 13 that the Charts 1A, 2A, 3A are asymmetric with respect to the Charts 1B, 2B and 3B with respect to the vertical axis passing through the zero point.
Graph 1B presented in Figure 13 shows that increases linearly with the increase of the value of ∆ . Graph 1A, in turn, shows that the change of the sign of ∆ from positive to negative also causes a linear increase of , but its values, in the case of negative ∆ , are much larger compared to the value of for positive ∆ . The dependences = (∆ , ∆ = constant), Illustrated by the curves 2B and 3B, have a similar shape and are nonlinear. Two areas can be separated in the course of these curves. The first, where are strongly dependent on ∆ , related to the osmoticdiffusion-convective production of entropy, and the second, where is weakly dependent on ∆ , related to the osmotic-diffusion production of entropy. The dependences = (∆ , ∆ = constant), illustrated by the curves 2A and 3A, have a similar shape and are non-linear. Two areas can also be separated in the course of these curves. The first, where is weakly dependent on ∆ , related to the osmotic-diffusion production of entropy, and the second, where is strongly dependent on ∆ , related to the osmotic-diffusion-convective production of entropy.  Graph 1B presented in Figure 12 shows that Φ r S1 increases linearly with the increase of the value of ∆C 1 . On the other hand, graph 1A shows that changing the sign of ∆C 1 from positive to negative also causes a linear increase of Φ r S1 but its values, in the case of negative ∆C 1 , are much smaller compared to the value of Φ r S1 for positive ∆C 1 . The dependence Φ r S1 = f (∆C 1 , ∆C 2 = constant), Illustrated by the curves 2B and 3B, have a similar shape and are nonlinear. Two areas can be separated in the course of these curves. The first, where Φ r S1 is weakly dependent on ∆C 1 , related to the osmotic-diffusion production of entropy, and the second, where Φ r S1 is strongly dependent on ∆C 1 , related to the osmotic-diffusion-convective production of entropy.
The dependences Φ r S1 = f (∆C 1 , ∆C 2 = constant), illustrated by the curves 2A and 3A, have a similar shape and are nonlinear. Two areas can also be separated in the course of these curves. The first, where Φ r S1 is strongly dependent on ∆C 1 , related to the osmotic-diffusion-convective production of entropy, and the second, where Φ r S1 is weakly dependent on ∆C 1 , related to the osmotic-diffusion production of entropy. Moreover, it can be seen from Figures 12 and 13 that the Charts 1A, 2A, 3A are asymmetric with respect to the Charts 1B, 2B and 3B with respect to the vertical axis passing through the zero point.
Graph 1B presented in Figure 13 shows that Φ r S2 increases linearly with the increase of the value of ∆C 2 . Graph 1A, in turn, shows that the change of the sign of ∆C 1 from positive to negative also causes a linear increase of Φ r S2 , but its values, in the case of negative ∆C 2 , are much larger compared to the value of Φ r S2 for positive ∆C 2 . The dependences Φ r S2 = f (∆C 2 , ∆C 1 = constant), Illustrated by the curves 2B and 3B, have a similar shape and are nonlinear. Two areas can be separated in the course of these curves. The first, where Φ r S2 are strongly dependent on ∆C 2 , related to the osmotic-diffusion-convective production of entropy, and the second, where Φ r S2 is weakly dependent on ∆C 2 , related to the osmotic-diffusion production of entropy. The dependences Φ r S2 = f (∆C 2 , ∆C 1 = constant), illustrated by the curves 2A and 3A, have a similar shape and are non-linear. Two areas can also be separated in the course of these curves. The first, where Φ r S2 is weakly dependent on ∆C 2 , related to the osmotic-diffusion production of entropy, and the second, where Φ r S2 is strongly dependent on ∆C 2 , related to the osmotic-diffusion-convective production of entropy. Figures 14 and 15 show the dependencies Φ S1 = f (∆C 1 , ∆C 2 = constant) and Φ S2 = f (∆C 2 , ∆C 1 = constant), respectively, for the conditions homogeneity of solutions, calculated on the basis of Equation (10) and the experimental dependencies J v1 = f (∆C 1 , ∆C 2 = constant), J v2 = f (∆C 2 , ∆C 1 = constant), J 1 = f (∆C 1 , ∆C 2 = constant) i J 2 = f (∆C 2 , ∆C 1 = constant). Graphs 1B, 2B and 3B shown in Figure 14 show that Φ S1 increases with the increase of the value of ∆C 1 . Changing the sign of ∆C 1 does not change the value of Φ S1 . Adding a constant amount of NH 4 OH to aqueous HCl solutions causes a shift of plots 2A and 2B with respect to plots 1A and 1B and plots 3A and 3B against plots 2A and 2B.      Graphs 1B, 2B and 3B shown in Figure 15 show that Φ S2 increases with the increase of the value of ∆C 2 . Changing the sign of ∆C 2 does not change the value of Φ S2 . Adding a constant amount of HCl to aqueous NH 4 OH solutions causes a shift of plots 2A and 2B with respect to plots 1A and 1B, and plots 3A and 3B against plots 2A and 2B. The comparison of the graphs presented in Figures 12 and 13 shows that the graphs 1A, 2A, and 3A are symmetrical to the graphs 1B, 2B and 3B about the vertical axis passing through the zero point. There are relations between the above-mentioned quantities Φ S1 > Φ r S1 ,

Concentration Dependences Diffusion-Convective Effect ∆Φ r Sk
To calculate the difference (∆Φ r Sk ) between the entropy source for the uniformity conditions of the solutions (Φ Sk ) and the concentration polarization conditions (Φ r Sk ) we use the following equation: (11) and the dependencies Φ S1 = f (∆C 2 , Sk is a measure of the diffusion-convective effect. Figure 16 shows the dependencies ∆Φ r S1 = f (±∆C 1 , ±∆C 2 = const.), calculated on the basis of Equation (11), taking into account the dependencies Φ S1 = f (∆C 1 , ∆C 2 = const.) and Φ r S1 = f (∆C 1 , ∆C 2 = const.), presented in Figures 10 and 12. The figures shows that the curves 1A, 2A and 3A are asymmetric with respect to the curves 1B, 2B and 3B with respect to the vertical axis crossing zero. Figure 17 shows the dependencies ∆Φ r S2 = f (∆C 2 , ∆C 1 = constant), calculated on the basis of Equation (12), taking into account the dependencies Φ S2 = f (∆C 2 , ∆C 1 = constant) and Φ r S2 = f (∆C 2 , ∆C 1 = constant), presented in Figures 11 and 13. This figure shows that the curves 1A, 2A and 3A are asymmetric with respect to the curves 1B, 2B and 3B with respect to the vertical axis passing through zero. asymmetric with respect to the curves 1B, 2B and 3B with respect to the vertical axis crossing zero. Figure 17 shows the dependencies ∆ = (∆ , ∆ = constant), calculated on the basis of Equation (12), taking into account the dependencies = (∆ , ∆ = constant) and = (∆ , ∆ = constant), presented in Figures 11 and 13. This figure shows that the curves 1A, 2A and 3A are asymmetric with respect to the curves 1B, 2B and 3B with respect to the vertical axis passing through zero.

Concentration Dependencies of the Convective Polarization Effect
To calculate the convective effects we use Equation (12):

Concentration Dependencies of the Convective Polarization Effect
To calculate the convective effects we use Equation (12):

Concentration Dependencies of the Convective Polarization Effect
To calculate the convective effects α k we use Equation (12): Concentration dependencies of the source of entropy α 1 = f (∆C 1 , ∆C 2 = constant) and α 2 = f (∆C 2 , ∆C 1 = constant), illustrated by graphs 1A, 2A, 3A and 1B, 2B and 3B are shown in Figures 10  and 11. The calculation results are presented in Figures 18 and 19. Figures 18 and 19 show that the relationships α 1 = f (∆C 1 , ∆C 2 = 0) and α 2 = f (∆C 2 , ∆C 1 = 0), are linear, as illustrated by graphs 1, where α 1 > 0, while α 2 < 0 and α 1 < |α 2 | in the whole range of tested solution concentration differences. Negative α 1 means that the convection currents are directed vertically downwards. In turn, positive α 2 informs that convection currents are directed vertically upwards. In the case of the dependences α 1 = f (∆C 1 , ∆C 2 > 0) and α 2 = f (∆C 2 , ∆C 1 > 0), both α 1 and α 2 can be negative, positive or equal to zero. This means that with a change in the sign of α 1 or α 2 , the sense of convection currents changes: in the case of α 1 , from vertical up to vertical down, and in the case of α 2 -from vertical down to vertical up. Similar results as in Figures 18 and 19 were obtained for aqueous CuSO 4 and/or ethanol solutions [4]. directed vertically downwards. In turn, positive informs that convection currents are directed vertically upwards. In the case of the dependences = (∆ , ∆ > 0) and = (∆ , ∆ > 0), both and can be negative, positive or equal to zero. This means that with a change in the sign of or , the sense of convection currents changes: in the case of , from vertical up to vertical down, and in the case of -from vertical down to vertical up. Similar results as in Figures 18 and  19 were obtained for aqueous CuSO4 and/or ethanol solutions [4].   Figure 20 shows that the relationships 2A and 2B intersect at the coordinates = 0.042 and ΔC1 = 105.85 mol m −3 , while the relationships 3A and 3B-at the point with the coordinates = 0.045 and ΔC1 ≈ 190 mol m −3 . These points correspond to the points where the convective effect disappears, as measured by the coefficient . Figure 18 shows that = 0 for ΔC1 ≈ 106 mol m −3 and ΔC1 ≈ 188 mol m −3 . As already mentioned, the convective effect appears for < 0 and > 0. vertically upwards. In the case of the dependences = (∆ , ∆ > 0) and = (∆ , ∆ > 0), both and can be negative, positive or equal to zero. This means that with a change in the sign of or , the sense of convection currents changes: in the case of , from vertical up to vertical down, and in the case of -from vertical down to vertical up. Similar results as in Figures 18 and  19 were obtained for aqueous CuSO4 and/or ethanol solutions [4].   Figure 20 shows that the relationships 2A and 2B intersect at the coordinates = 0.042 and ΔC1 = 105.85 mol m −3 , while the relationships 3A and 3B-at the point with the coordinates = 0.045 and ΔC1 ≈ 190 mol m −3 . These points correspond to the points where the convective effect disappears, as measured by the coefficient . Figure 18 shows that = 0 for ΔC1 ≈ 106 mol m −3 and ΔC1 ≈ 188 mol m −3 . As already mentioned, the convective effect appears for < 0 and > 0.  Figures 20 and 21 show the concentration dependencies of the concentration polarization coefficients of the dependence ζ r 1 and ζ r 2 . These coefficients are defined by the expressions: ζ r 1 = J r v1 /J v1 = J r 1 /J 1 and ζ r 2 = J r v2 /J v2 = J r 2 /J 2 . The dependencies ζ r 1 = f (∆C 1 , ∆C 2 = constant) and ζ r 2 = f (∆C 2 , ∆C 1 = constant), calculated on the basis of the test results shown in Figures 2-11. Figure 20 shows that the relationships 2A and 2B intersect at the coordinates ζ 1 = 0.042 and ∆C 1 = 105.85 mol m −3 , while the relationships 3A and 3B-at the point with the coordinates ζ 1 = 0.045 and ∆C 1 ≈ 190 mol m −3 . These points correspond to the points where the convective effect disappears, as measured by the coefficient α 1 . Figure 18 shows that α 1 = 0 for ∆C 1 ≈ 106 mol m −3 and ∆C 1 ≈ 188 mol m −3 . As already mentioned, the convective effect appears for α 1 < 0 and α 1 > 0. Figure 21 shows that the graphs 2A and 2B intersect at the coordinates ζ 2 ≈ 0.045 and ∆C 2 ≈ 480 mol m −3 , while the relationships 3A and 3B−at the coordinates ζ 2 ≈ 0.045 and ∆C 2 ≈ 670 mol m −3 . These points correspond to the points where the convective effect disappears, as measured by the coefficient α 2 . Figure 19 shows that α 2 = 0 for ∆C 2 ≈ 483 mol m −3 and ∆C 2 ≈ 672 mol m −3 . In this case, the convective effect appears for α 2 > 0 and α 2 < 0. This means that the points where α 1 = 0 and α 2 = 0 are compatible with the critical value of the coefficient ζ 1 and/or ζ 2 . Typically, the Rayleigh concentration number (R r Ck ) is used as the control parameter. We propose to call this expression the Katchalsky number (Ka). Let us consider Equation (7) and transform it to the form:  Figure 21 shows that the graphs 2A and 2B intersect at the coordinates ≈ 0.045 and ΔC2 ≈ 480 mol m −3 , while the relationships 3A and 3B−at the coordinates ≈ 0.045 and ΔC2 ≈ 670 mol m −3 . These points correspond to the points where the convective effect disappears, as measured by the coefficient . Figure 19 shows that = 0 for ΔC2 ≈ 483 mol m −3 and ΔC2 ≈ 672 mol m −3 . In this case, the convective effect appears for > 0 and < 0. This means that the points where = 0 and = 0 are compatible with the critical value of the coefficient and/or . Typically, the Rayleigh concentration number ( ) is used as the control parameter. We propose to call this expression the Katchalsky number (Ka). Let us consider Equation (7) and transform it to the form:
The ζ r k coefficient may take values in the range 0 ≤ ζ r k ≤ 1. For 0 ≤ ζ r k ≤ ζ k we are dealing with a gravitational convection. If ζ r k takes values in the range ζ k < ζ r k ≤ (ζ r k ) max , the state of gravitational convection occurs in the membrane system. If, on the other hand, ζ r k takes values in the range (ζ r k ) max < ζ r k ≤ 1, the system is in the state of forced convection. This means that the greater the value of ζ r k , the smaller the value of Ka.

Conclusions
In the paper, the authors present the results of research on the effects of the concentration and orientation of aqueous HCl and/or ammonia solutions in relation to a horizontally oriented membrane, under Earth gravity conditions, on the value of osmotic volume fluxes (J r vk ) and dissolved substances (J r k ). It has been shown that for the polarization conditions of the concentration and of aqueous HCl