Thermo-osmotic pressure difference

Equation (3.87) is a set of n relations which can be solved to yield thermo-osmotic pressure difference, AP and thermo-osmotic concentration difference Ac (j = 1,2,..., ) as a function of temperature difference AT. 

Experimental set-up used for the measurement of hydrodynamic permeability, thermo-osmotic permeability and thermo-osmotic pressure difference is shown in Eig. 3.3. The membrane was fixed with araldite between two ground-glass joints. Thermocouples were inserted through the adjoining tubes so that the junctions touched the membrane. 

According to the above equation, thermo-osmotic pressure difference (AP/AT)j f should be a constant quantity. This is found to be so in Fig. 3.8 where AP has been plotted against AT. 

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... 

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. 

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. 

In Chapters 3 and 4, it has been pointed out that on application of force in the form of temperature difference, potential difference or pressure difference, the development of steady thermo-osmotic pressure, electro-osmotic pressure or streaming potential takes some time. Similar situation occurs when these forces are withdrawn, resulting in the decay of steady state. Build-up and decay in the case of electro-kinetic phenomena have been found to be exponential (Section 4.6). Detailed analysis of the relaxation phenomena and co-relations between the relaxation time and membrane composition have been reported. 

The thermodynamic preliminaries and concepts needed for defining osmotic pressure are discussed in Sections 3.2a-c. The nonideality of colloidal solutions can be appreciable since the solvent and solute particles are so different in size. Classical thermo-... 

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. 

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