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A lump of sugar added to a cup f black coffee eventually dissolves and then diffuses uniformly throughout the coffee. Perfume presents a pleasant fragrance which is imparted throughout the surrounding atmosphere. These are examples of mass transfer. Mass transfer plays a very important role in many industrial processes: the removal of pollutants from plant discharge streams by absorption, the striping of gases from wastewater, neutron diffusion within nuclear reactors, the diffusion of adsorbed substances within the pores of activated carbon, the rate of catcalled chemical and biological reactions, and air conditioning are typical examples.
Mass transfer takes place in either gas phase or liquid phase or in both cases simultaneously. When a liquid evaporates into a still gas, vapor is transferred from the surface to the bulk of gas as a result of the concentration gradient. This process continues until the gas is saturated and the concentration gradient is reduced to zero.
In a still fluid or in a fluid flowing under streamline conditions in a direction of right angles to the concentration gradient, the transfer is affected by random motion of the molecules.
Molecular diffusion or molecular transport can be defined as the transfer or movement of individual molecules wrought a fluid by means of the random, individual movements of the molecules. Whenever a particular molecule of this mixture diffuses, it must diffuse through other molecules; consequently, in almost every practical example there are at least two components present and possibly more.
The molecular diffusion process is shown schematically in the below figure.
A random path that molecule A might take in diffusing through B molecules from point (1) to (2) is shown. If there are a greater number of A molecules near point (1) than at (2), then, since molecules diffuse randomly in direction, more A molecules will diffuse from (1) o (2) than from (2) to (1). The net diffusion of A is from high-to-low concentration regions. Molecule A Molecule B Diffusion is explained in this experiment through the First Pick’s Law.
The first Pick’s Law states that the molar diffusion flux of A in B at a certain direction (say Z), is proportional to the negative of the concentration gradient of A in that direction: [pica Molar diffusion flux is defined as the molar diffusion flow rate (nab) per cross sectional area unit of diffusion (L): [pica First Pick’s law is turned to an equation by introducing a coefficient named effusion coefficient of Main B or diffusivity of A in B, DAB: [pica] (1) where [pica is the molar flux of A in the z is the diffusion coefficient of A in B.
Its dimension is LET-1 and thus the unit is mm/s, and [pica]is the concentration gradient in z direction. Equation (1) is applicable for only general cases. If the diffusion occurs for either one kind of molecules into a gas composed of molecules of the same mass velocity and free paths, the equation is incomplete. Since the rate of transfer of A in a mixture of two components, A and B, will be determined not only by the rate of diffusion of A, but also by the behavior of B, Pick’s Law can be presented in another form.
The molar flow rate A per unit cross sectional area, due to molecular motion is given by: [pica (2) where AN is the molar rate of diffusion of A per unit area, DAB is the diffusion coefficient of A in B, CA is the molar concentration of A, y is the distance in the direction of diffusion. The corresponding rate of diffusion of B is given by: If the total pressure and the total molar concentration is constant, [pica and[pica] must be equal and opposite and therefore A and B tend to diffuse in opposite directions. In many processes B will neither remain stationary nor effuse at an equal and opposite molar rate of A.
Exact calculations relating to this type of problems are difficult. If turbulent flow of fluid occurs, eddy diffusion takes place in addition to molecular diffusion and the rate of diffusion is increased as denoted below: [pica(4) where DE is eddy diffusivity. Its’ value increases if turbulence increases and is more difficult to evaluate than the molecular diffusivity. In the case where diffusion takes place in a stationary gas the rates of diffusion of A and B are given by: Applying the ideal gas law does this: where P is the system’s pressure
T is the system’s temperature R is molar gas constant [pica (8) as concentration of substance, C is also equal to the ratio of mole, n of the substance to its’ volume, V . If a surface is introduced on which A is absorbed but B is not absorbed, a partial pressure gradient will be set up, causing A to diffuse towards and B away from the surface. Given this process to continue for a short interval, A will be absorbed at the surface and B will tend to diffuse away. Thus a total pressure gradient will be produced causing a bulk motion of A and B towards the surface, in addition to the transfer by diffusion.
Since there is no net motion of B, the bulk rate or flow must exactly balance its transfer by diffusion. Thus the bulk rate of flow of B The bulk flow of B is accompanied by a bulk flow of A as below: Bulk flow of A = [pica The total rate of transfer of A is obtained by summing the transfers by diffusion and bulk flow. By adding equation (5) and (9), the total transfer, AN’ is given by: AN’ = [pica(5) + (9) = [pica] (10) This relation shown by equation (10) is known as Stefan Law.
Integration of equation (10) between two positions denoted by suffixes 1 and 2 gives us the results as below: [pica] AN’ = (11) (12) 13) where the suffix m denotes the logarithmic mean value of the quantity at the positions 1 and 2. There are several ways by which the diffusion coefficient, D can be determined. In Winkle method, the liquid contained in a narrow diameter vertical tube which is maintained at a constant temperature and a vapor free gas, is passed through the top of the tube rapidly enough to ensure that the partial pressure of the vapor remains approximately zero (Figure 1).
Gas Stream (Figure 1) The rate of mass transfer is given by: AN’= [pica Where CA = the saturation concentration at the interface and L is the effective stance through which mass transfer is taking place. But considering the evaporation of the liquid. AN’ = [pica Where (L = the density of the liquid. Thus, Integrating and putting L = LO at t = 0, evaporation of the liquid, AN’= [pica] [pica] Finally, the following equation is obtained: A graph of Chip] versus L-LO yields a straight line with gradient ,s= (pica and intercept of 0 3. METHODOLOGY When performing the experiment, the Gaseous Diffusion Apparatus is referred. 1 . Capillary tube, R is washed with detergent that is provided and cleansed with distilled water. Then, it is rinsed with a little of acetone liquid. The cleaning process is done with a syringe. 2. With another syringe, acetone is filled into the capillary tube, R until it reaches the height of 35. Mm. This is done carefully to ensure that no air bubble is trapped inside the tube. 3. The tube is inserted into the metal nut, N until the top part of the tube hangs on the nut. 4.
Slowly, the tube is screwed into the upper plat, with its T part perpendicular to the microscope, M. 5. Vacuum tube, V is inserted at one end of the ‘T’ part of capillary tube, R. 6. The vertical height of microscope, M is adjusted until the capillary tube, R can be seen in the microscope, M. The distance of the object lens to the tank is adjusted. 7. When the meniscus level is determined, the fernier scale is aligned to the unmovable scale. 8. When the lens is adjusted, the air pump, P and heater are switched on. 9. The temperature controller is adjusted to maintain the temperature at ICC.