【Daily Question】Chemical Engineering Principles 105: Double-Membrane Theory (July 10)

Between the gas and liquid fluids in contact with each other, there is a stable phase interface; on each side of this interface lies a very thin layer of effective laminar flow. The solute diffuses through this layer in the form of molecules； At the phase interface, the gas and liquid phases reach phase equilibrium ； In the central region outside the film layers, due to thorough turbulence of the fluid, the concentration of the solute is uniform; that is, the concentration gradient in the central region of the two phases is 0, with all concentration variations concentrated within the two effective laminar film layers.

Gas absorption is the process by which the absorbent in the gas phase is transferred across the phase boundary to the liquid phase. When a gas comes into contact with a liquid, even if turbulence exists in the main body of the fluid, stable gas stagnation layers (gas films) and liquid stagnation layers (liquid films) exist on either side of the gas-liquid interface. The absorption process involves molecules of the substance to be absorbed moving from the gas phase to the surface of the gas film, then passing through this gas film by molecular diffusion to reach the gas-liquid interface; at this interface, the substance dissolves into the liquid phase, and from there it enters the liquid phase via molecular diffusion through the liquid film. Regarding the gas absorption mass transfer process, the basic principles of the double-membrane theory are as follows: 1. There is a stable phase interface between the gas and liquid phases in contact; on each side of this interface there is a very thin stagnant layer. All the mass transfer resistance on both sides of the interface is concentrated within these two stagnant layers, and the absorbent substance passes from the gas phase into the liquid phase through these two membrane layers by molecular diffusion ； 2. At the phase interface, the gas and liquid phases can reach equilibrium instantaneously; there is no mass transfer resistance at the interface, and the compositions of the solute in the two phases at the interface are in equilibrium, meaning that the required driving force for mass transfer is zero or the gas and liquid phases are in equilibrium. 3. In the gas-liquid two-phase main body outside the two stagnant membranes, due to thorough fluid turbulence, there is no concentration gradient, and the material composition is uniform. The mass transfer resistance of the solute in each phase is concentrated within a virtual stagnant film.

Between the gas and liquid phases in contact with each other, there exists a stable phase interface. On each side of this interface there is a very thin layer of stagnant fluid, and all the mass transfer resistance on either side of the interface is concentrated within these two layers of stagnant fluid. The solute passes from the gas phase into the liquid phase through these two layers by molecular diffusion； At the phase interface, the gas and liquid phases can reach equilibrium instantaneously; there is no mass transfer resistance at the interface, and the compositions of the solute in the two phases at the interface are in equilibrium, meaning that the required driving force for mass transfer is zero or the gas and liquid phases are in equilibrium. In the gas-liquid two-phase main body outside the two stagnant membranes, due to thorough fluid turbulence, there is no concentration gradient and the material composition is uniform. The mass transfer resistance of the solute in each phase is concentrated within a virtual stagnant film.

1. There is a stable phase interface between the gas and liquid phases in contact with each other; on each side of the interface there is a very thin stagnant layer. All the mass transfer resistance on both sides of the phase interface is concentrated within these two stagnant layers, and the solute passes from the gas phase into the liquid phase through these layers by molecular diffusion； 2. At the phase interface, the gas and liquid phases can reach equilibrium instantaneously; there is no mass transfer resistance at the interface, and a balance exists between the compositions of the solute in the two phases at that interface, meaning that the required driving force for mass transfer is zero or the gas and liquid phases are in equilibrium ； 3. In the gas-liquid phase region outside the two stagnant films, due to thorough turbulence of the fluid, there is no concentration gradient and the material composition is uniform. The mass transfer resistance of the solute in each phase is concentrated within the virtual stagnant films.

1. There is a stable phase interface between the gas and liquid phases in contact with each other; on each side of the interface there is a very thin stagnant layer. All the mass transfer resistance on both sides of the phase interface is concentrated within these two stagnant layers, and the solute passes from the gas phase into the liquid phase through these two layers by molecular diffusion. 2. At the phase interface, the gas and liquid phases can reach equilibrium instantaneously; there is no mass transfer resistance at the interface, and the compositions of the solute in the two phases at the interface are in equilibrium, meaning that the required driving force for mass transfer is zero or the gas and liquid phases are in equilibrium. 3. In the gas-liquid two-phase main body outside the two stagnant membranes, due to thorough fluid turbulence, there is no concentration gradient, and the material composition is uniform. The mass transfer resistance of the solute in each phase is concentrated within a virtual stagnant film.

What are the arguments in favor of the double-membrane theory? Gas absorption is the process by which the absorbent in the gas phase is transferred across the phase boundary to the liquid phase. When a gas comes into contact with a liquid, even if turbulence exists in the main body of the fluid, stable gas stagnation layers (gas films) and liquid stagnation layers (liquid films) exist on either side of the gas-liquid interface. The absorption process involves molecules of the substance to be absorbed moving from the gas phase to the surface of the gas film, then passing through this gas film by molecular diffusion to reach the gas-liquid interface; at this interface, the substance dissolves into the liquid phase, and from there it enters the liquid phase via molecular diffusion through the liquid film.

Between the gas and liquid phases in contact with each other, there exists a stable phase interface. On each side of this interface, there is a very thin layer of stagnant fluid. All the mass transfer resistance on both sides of the phase interface is concentrated within these two layers of stagnant fluid; the solute passes from the gas phase into the liquid phase through molecular diffusion across these two layers； 2. At the phase interface, the gas and liquid phases can reach equilibrium instantaneously; there is no mass transfer resistance at the interface, and a balance exists between the compositions of the solute in the two phases at that interface, meaning that the required driving force for mass transfer is zero or the gas and liquid phases are in equilibrium ； 3. In the gas-liquid phase region outside the two stagnant films, due to thorough turbulence of the fluid, there is no concentration gradient and the material composition is uniform. The mass transfer resistance of the solute in each phase is concentrated within the virtual stagnant films.

The two-film theory is a classic theory of mass transfer mechanism, proposed in 1923 by W.G. Whitman and L.K. Lewis. As a theory of interfacial mass transfer kinetics, it provides a good explanation for the process by which liquid absorbents absorb gaseous solutes.

In two fluids, gas and liquid, in mutual contact, there is a stable phase interface, with a very thin effective laminar layer on each side of the interface. The solute diffuses through this membrane layer in the direction toward the molecules. At the phase interface, the gas and liquid phases reach phase equilibrium. In the central region outside the membrane layer, due to thorough mixing of the fluid, the concentration of the solute is uniform; thus, the concentration gradient in that central region is zero. All concentration variations are confined within the two effective laminar flow membrane layers.

What are the arguments in favor of the double-membrane theory? Gas absorption is the process by which the absorbent in the gas phase is transferred across the phase boundary to the liquid phase. When a gas comes into contact with a liquid, even if turbulence exists in the main body of the fluid, stable gas stagnant layers (gas films) and liquid stagnant layers (liquid films) exist on either side of the gas-liquid interface. The absorption process involves molecules of the solute moving from the gas phase to the surface of the gas film, then passing through this gas film via molecular diffusion to reach the gas-liquid interface; at this interface, the solute dissolves into the liquid phase, and from there it enters the liquid phase main body through the liquid film via molecular diffusion. Regarding the gas absorption mass transfer process, the basic principles of the double-membrane theory are as follows: Diagram of the double-membrane theory. 1. There is a stable phase interface between the gas and liquid phases in contact with each other; on each side of this interface there is a very thin stagnant layer. All the mass transfer resistance on both sides of the interface lies within these two stagnant layers. The solute passes through these layers by molecular diffusion, moving from the gas phase to the liquid phase. 2. At the phase interface, the gas and liquid phases reach equilibrium instantaneously; there is no mass transfer resistance at this interface. The compositions of the solute in the two phases are in equilibrium, meaning that the required driving force for mass transfer is zero, or the gas and liquid phases are in equilibrium. 3. In the gas-liquid two-phase main body outside the two stagnant membranes, due to thorough fluid turbulence, there is no concentration gradient, and the material composition is uniform. The mass transfer resistance of the solute in each phase is concentrated within a virtual stagnant film. According to the double-membrane theory, the concentration distribution near the gas-liquid interface is as shown in the figure on the right.