Thermo-osmosis

Thermo-osmosis (or ihcrmo diffusion) is a process where a porous or nonporous membrane separates two phases different in temperature. Because of the temperature difference, a volume flux exists from the warm side to the cold side until thermodynamic equilibrium is attained. This has been described as an example of coupled flow in chapter IV. There is a considerable difference between thermo-osmosis and membrane distillation, because the membrane determines the separation performance in the former process, whereas in the latter case the membrane is just a barrier between two non-wettable liquids and the selectivity is determined by the vapour-liquid equilibrium. However, the temperature difference is the driving force in both processes. 

In all cases the charged membrane constitute a selective barrier where ions are either repelled or transponed dependent on the ionic charge and membrane charge. The first three processes require an electrical potential difference as driving force whereas the last process, fuel cells convert chemical energy into electrical energy in a more efficient way than conventional processes by combustion. 

The principle of the electrodialysis process is depicted in figure VI - 60. In this process elcctncally charged membranes are used to remove ions from an aqueous solution. A 

The following electrode rections may occur, cathode 2HiO +2e = H2 +2 OH anode  

In commercial applications several hundreds of cell pairs are assembled in a stack and in this way the applied driving force is used very effectively. By using the concept of an electrical potential difference in combination with electrically charged membranes, a 

---

Po roc hem othe rm oelastic Poro thermo clastic No thermo-osmosis... 

Ion exchange membranes have been used in various industrial fields, and have great potential for use in new fields due to their adaptable polymer membrane. As mentioned in the Introduction, membranes are characterized mainly by ion conductivity, hydrophilicity and the existence of carriers, which originate from the ion exchange groups of the membrane. Table 6.1 shows reported examples of applications of ion exchange membranes and the membrane species used in various fields. Various driving forces are usable for separation electrochemical potential, chemical potential, hydraulic pressure such as piezodialysis and pervaporation, temperature difference (thermo-osmosis), etc. Of these, the main applications of the membrane are to electrodialysis, diffusion dialysis, as a separator for electrolysis and a solid polymer electrolyte such as in fuel cells. 

Attempts to concentrate acetic acid by thermo-osmosis have employed various anion exchange membranes acetic acid is concentrated by 1.5 times in concentrated steam on the hot side using diethylaminated polystyrene membrane groups.213 Sodium chloride solution is concentrated to the hot side using an amphoteric ion exchange membrane.214... 

R. Kiyono, A. Komoto, M. Tasaka, T. Yamaguchi and T, Sata, Membrane phenomena in nonisothermal systems Part 2. Effect of hydrophilicity of ion-exchange groups of anion-exchange membranes on thermo-osmosis, Bull. Chem. Soc, Jpn., 1997, 790, 1015-1020. 

Open system is always in non-equilibrium. A closed system can be in non-equilibrium depending on the circumstances. It may have subsystems between which exchange of matter and energy can take place or in the system itself, thermodynamic variables may not be constant in space. A typical example of the former type is thermo-osmosis, which is discussed in Chapter 3, where the two subsystems are separated by a membrane. Example of the latter type is thermal diffusion, which has been discussed in Chapter 5. When the flows and counter-flows in opposite directions are generated by corresponding gradients, steady state is obtained. Both equilibrium and non-equilibrium steady states are time-invariant states, but in the latter case both flows and gradients are present. 

Onsager relations are satisfied, showing that free electron gas theory is consistent with thermodynamic theory. The free electron theory correctly predicts the temperature dependence of thermo-electric power. Similarly, the interpretation of the phenomenon of thermo-osmosis of gases on the basis of non-equilibrium thermodynamics and kinetic theory of gases is mutually consistent. 

Chapter 3 deals with theoretical and experimental studies of thermo-osmosis of liquids and gases along with thermo-osmotic concentration differences. Correlation with kinetic theory has also been attempted. Chapter 4 is concerned with experimental and theoretical studies of electro-kinetic phenomena, e.g. electro-osmosis and streaming in a system containing two subsystems separated by a membrane. Relationship with Helmholtz double layer theory has been examined with a view to provide physical interpretation of phenomenological coefficients. Theory and experiment have been compared to assess the range of validity of thermodynamic theory. Chapters 3 and 4 are concerned with discontinuous systems involving a membrane as barrier. 

Discontinuous systems (membrane phenomena), where two or more homogeneous systems are separated by a boundary. In such a system, the intrinsic properties are discontinuous at the boundary of homogenous systems. Typical example of a discontinuous system is the one, which has two sub-systems I and II containing a single gas separated by a membrane displaying the non-equilibrium phenomenon of thermo-osmosis (Fig. 2.2). In this case, Pj > Pi and T2> Tj. Further volume flux (thermo-osmotic flow)... 

Depending on the number of fluxes in the system, one can have coupling of flows with some restrictions. For example, in case of thermo-osmosis, coupling of heat flow and mass flow takes place, since a membrane separates two compartments... 

Thermo-osmosis Heat flux and volume Temperature and pressure... 

Thermo-osmosis is a phenomenon in which matter is driven through a membrane or an orifice from one chamber to another on account of the temperature difference between the two chambers. This can occur for a single fluid or a mixture of fluids. 

Theories based on non-equilibrium thermodynamics [3-8] have been applied extensively to elucidate the phenomenon of thermo-osmosis. The methodology of nonequilibrium thermodynamics essentially involves the evaluation of entropy production by the application of the laws of conservation of mass and energy and Gibbs equation. Appropriate fluxes and forces are chosen by suitably splitting the expression for entropy production and subsequently, thermodynamic transport equations are written. The theory of thermo-osmosis based on non-equilibrium thermodynamics is discussed below. 

The above equations are interesting from the view point of estimating the sluft from thermodynamics equilibrium due to thermo-osmosis. Such an estimate has been made for the reaction N2O4 2NO4 using the available equilibrium data on thermal dissociation to estimate the magnitude of the shift from thermodynamic equilibrium [11], The result reveals appreciable deviation from equilibrium depending on the temperature coefficient of reaction rate. 

Thermodynamic theory of thermo-osmosis of gaseous non-reacting mixtures... 

For the thermo-osmosis of a single gas which does not under go any chemical reaction, Eq. (3.87) yields... 

A membrane is a heterogeneous barrier between otherwise two homogeneous systems. It consists of a complicated network of pores which may be connected to each other in a complex manner. The mechanism of transport depends on (i) the size and shape of the pores, and (ii) nature of the permeant. The phenomenon of thermo-osmosis can occur only when the diameter of pores is comparable to mean free path of the permeating species. For gaseous systems, the mean free path can be controlled by controlling the mean pressure. In view of the membrane being made up of a complex network of pores, some pores may have diameters considerably less than the mean free path while some others may have pore diameters considerably larger than the mean free path. In the latter case, viscous flow can occur and the net flow is a composite flow made up of... 

For the sake of simplicity, we discuss below thermo-osmosis of a Knudsen gas. 

On combining Eq. (3.123) with Eq. (3.122), Eq. (3.188) is obtained. It thus follows that the kinetic theory of thermo-osmosis is consistent with the thermodynamic theory of thermo-osmosis. 

Thermo-osmosis was the first non-equilibrium phenomenon which was extensively studied from experimental and theoretical angles, both for the case of liquids, gases and gaseous mixtures. 

Haase [17] has reported some observations on thermo-osmosis of water through cellophane membrane with and without deposition of copper ferrocyanide in the pores. A well-authenticated instance of thermal migration of a liquid against a hydrostatic pressure through a permeable barrier is the fountain effect in liquid He II. Like thermoosmosis, this process gives rise to a well-defined stationary pressure difference. 

There are a number of factors, which govern the occurrences of the phenomenon of thermo-osmosis. It is essential to choose a system such that the dimensions of the pores of the membrane are comparable to the mean free path of the permeating molecules. The deficiency is all the more serious in case of liquids. In case of gases, appreciable... 

Themo-osmosis of water through a cellophane membrane has been reported by Rastogi, Blokhra and Agrawal [21], Experimental studies on thermo-osmosis of liquids (methanol and water) across Du pont 600 cellophane were reported for the first time by Rastogi and Singh [22],... 

It may be noted that thermo-osmosis of water and methanol occurs through cellophane membrane but not for ethyl alcohol or toluene. Thermo-osmosis occurs if the radii of the pores are smaller than the Van der Waals radii, but not if the pore size is greater than the molecular radii but smaller than the mean free path. Since the mean free path of the molecules in the liquid is of molecular dimensions, the range of pore size for thermo-osmosis to occur is limited. The size of ethyl alcohol molecules appears to be comparable to the pore size, whereas for toluene the pore size is perhaps greater than the molecular radii and the mean free path. Probably for methyl alcohol and water the pore diameter of the membrane is between the mean free path and the Van der Waals radii. However, there is no independent evidence for the magnitude of mean free path of liquid water. 

The thermo-osmotic permeability and the ordinary permeability of water is greater than that for methanol. For these reasons, thermo-osmosis of water could not be detected... 

Detailed studies on thermo-osmosis using highly selective cellulose acetate membrane in the presence and absence of osmotic pressure difference have also been carried out [25]. Using general description of thermo-osmosis based on irreversible thermodynamics, it was shown that coupling between the flow of heat and the flow of water is quite loose possibly on account of thermal leak between the compartments. Whatever the detailed stmctural interpretation, it was argued that in annealed, less-permeable membranes, the water-matrix interaction is increased relative to the water-water interaction and with only this type of interaction strong thermo-osmosis is expected. 

Studies on thermo-osmosis of water through cellulose acetate membrane [26] support predictions by Rastogi and Singh [27] based on correlation between the existence of themo-osmosis and the membrane pore size. 

Extensive studies on thermo-osmosis have been carried out using various hydrophobic and hydrophilic membranes [29]. Using non-equilibrium thermodynamic principles, it was concluded that water is transferred through hydrophilic polymer membranes from the cold side to the hot side because the transported entropy of water in the membrane is smaller than molar entropy of water in the external free solutions. In contrast, water is transferred through hydrophobic polymer membranes from the hot side to the cold side because the transported entropy of water in the membrane is larger than the molar entropy of water in the external free solutions. 

During the study of phenomenon of thermo-osmosis, major difficulty in encountered in testing the validity of ORR. According to Eq. (3.79), formerly discussed in Section 3.3, the heat flux equations can be written as... 

Number of experimental smdies on thermo-osmosis of gases have been reported in literature [32], The steady-state relation is found to be satisfied in all cases studied within a limited range of non-equilibrium. A typical experimental set-up used for studying thermo-osmosis is shown in Fig. 3.9 [33]. 

Typical thermo-osmotic pressure data for COj using unglazed porcelain membrane at various AT/T1T2 are presented in Fig. 3.13. The result are in conformity with the steady-state relation. This also implies that heat of transport Q is independent of mean temperature within the range of investigation. Heat of transport was also found to be independent of difference of temperature up to AT = 130°C. It shows that, so far as thermo-osmosis of gases is concerned, thermodynamic predictions have a wide range of validity. 

Rastogi and Singh [34] studied for the first time phenomenon of thermo-osmosis in gaseous mixtures. Measurements of thermo-osmotic pressure difference were carried out using the experimental set-up already shown in Fig. 3.9 for mixtures of CO2 and O2 of different composition through unglazed porcelain membrane. Measurement were also carried out using... 

Thermo-osmosis in biological systems has received scant attention [39], although it is realized that fluxes of thermal energy through biological membranes can occur owing... 

Steady states, as we have seen in Part One, are obtained when fluxes in opposite directions are involved. In electro-osmosis, hydrodynamic flow is opposed by electro-osmotic flux. In thermo-osmosis, hydrodynamic flow is opposed by thermo-osmotic flux. In case of chemical reactions, such situations can arise when positive feedback is opposed by negative feedback. For example, when autocatalysis is opposed by inhibitory reaction, steady state can be attained. However, the reaction rates are non-linear and have only non-linear steady states in practice. We illustrate this point by the following example. 

Let us try to examine these phenomena from the angle of causality principle. Taking the example of thermo-osmosis (Chapter 3), temperature difference is the starting cause, the effect of which is thermo-osmotic fluid flow, which in turn generates another cause, viz. pressure difference under specific circumstances (e.g. experimental set-up), the effect of which is hydrodynamic fluid flow in the reverse direction. Normally, both these causes and effects operate simultaneously. However, when two opposing flows are balanced, a steady state is reached. Similar type of situation occurs in other steady-state phenomena discussed in Chapters 4-6 including mechano-caloric effect. 

For simpler phenomena such as thermo-osmosis, electro-kinetic phenomena, thermal diffusion and Dufour effect, the linear thermodynamics of irreversible processes is valid in a wide range as indicated by the experimental results discussed in Chapters 3-5. It may be noted that Onsager relations for thermal diffusion can be proved by ETT [2]. 

---