Rate of diffusion

By inserting the absolute values of R and N in equation (109) and by assuming a temperature of 300° absolute and an absolute viscosity of solvent of 0.01 (H2O at 20°) we obtain the very simple relation 

A precision method for determining D was devised by E. Cohen and Bruins it allows of measurements with a limit of error of a few thousandths and constitutes, at present, the most accurate and reliable method for systematic experiments in this field. 

as may often be the case in the examination of high polymeric siib-staiu es, precision measurements are not required, but merely an estimation of particle size, it is possible to use considerably simpler arrangements, for ( xample, those of Oeholm or of Northrop and Anson they have been used in the fi( ld of the cellulose dc rivatives, particularly by Herzog and his co-workers and by McBain and his school. The micro-method of Ftirth has however, attained great importance recently it eliminates 

Ulmann, Molekulgrossenhestinimung hochpolymerer Natvrstojfe. Dresden and Leipzig 1936, p. 80 et seep 

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Graham showed that the rate of diffusion of different gases through a porous diaphragm was inversely proportional to the square roots of their densities this is the basis of a method of separation of gases, and has been applied successfully to the separation of hydrogen and deuterium. 

A diffusion mechanism is also used in dialysis as a means of separating colloids from crystalloids. The rate of diffusion of molecules in gels is practically the same as in water, indicating the continuous nature of the aqueous phase. The diffusion of gases into a stream of vapour is of considerable importance in diffusion pumps. 

Fick s law of diffusion A law relating the rate of diffusion of a substance in a given direction to the gradient of its concentration. 

The rate of dissolving of a solid is determined by the rate of diffusion through a boundary layer of solution. Derive the equation for the net rate of dissolving. Take Co to be the saturation concentration and rf to be the effective thickness of the diffusion layer denote diffusion coefficient by . 

Diffusion may be defined as the movement of a species due to a concentration gradient, which seeks to maximize entropy by overcoming inhomogeneities within a system. The rate of diffusion of a species, the flux, at a given point in solution is dependent upon the concentration gradient at that particular point and was first described by Pick in 1855, who considered the simple case of linear difflision to a planar surface ... 

The molecular formula of ozone was determined by comparing its rate of diffusion with that of a known gas. The geometric structure... 

In the experiments using a i i mixture of nitric and sulphuric acids (table 4.1, eolumn (y)) reaetion oceurred under heterogeneous eonditions, about 50 cm of mixed aromatie eompounds and 25 em of mixed aeids being used. The results are therefore eomplicated by differenees in solubilities and rates of diffusion to the aeid layer. 

The flow of droplets is directed through a small orifice (Skimmer 1 Figure 12.1) and across a small region that is kept under vacuum by rotary pumps. In this region, approximately 90% of solvent and injected helium is removed from the incipient particle beam. Because the rate of diffusion of a substance is inversely proportional to its molecular mass, the lighter helium and solvent molecules diffuse away from the beam and are pumped away. The heavier solute molecules diffuse more slowly and pass through the first skimmer before they have time to leave the beam the solute is accompanied by residual solvent and helium. 

The efficiency of separation of solvent from solute varies with their nature and the rate of flow of liquid from the HPLC into the interface. Volatile solvents like hexane can be evaporated quickly and tend not to form large clusters, and therefore rates of flow of about 1 ml/min can be accepted from the HPLC apparatus. For less-volatile solvents like water, evaporation is slower, clusters are less easily broken down, and maximum flow rates are about 0.1-0.5 ml/min. Because separation of solvent from solute depends on relative volatilities and rates of diffusion, the greater the molecular mass difference between them, the better is the efficiency of separation. Generally, HPLC is used for substances that are nonvolatile or are thermally labile, as they would otherwise be analyzed by the practically simpler GC method the nonvolatile substances usually have molecular masses considerably larger than those of commonly used HPLC solvents, so separation is good. 

Cotton linters or wood pulp are nitrated using mixed acid followed by treatment with hot acidified water, pulping, neutralization, and washing. The finished product is blended for uniformity to a required nitrogen content. The controlling factors in the nitration process are the rates of diffusion of the acid into the fibers and of water out of the fibers, the composition of mixed acid, and the temperature (see Cellulose esters, inorganic esters). 

An alternative method known as slicing and scaling has been developed (23,24). In this, the rate of diffusion is determined on a thin specimen (6—10 mm thick) and a scaling factor S used to relate the results to a thick specimen. For a material satisfying the requirements of a constant diffusion and constant initial pressure,, the same ratio of time thickness provides the same values of p and %. Thus the thermal resistance of a specimen of thickness at time can be obtained by conditioning a specimen of thickness over a time given by... 

In the oxidation process, a layer of dopant is apphed to the surface of sihcon and patterned sihcon dioxide for subsequent thermal diffusion into the sihcon. The masking property of the Si02 is based on differences in rates of diffusion. Diffusion of dopant into the oxide is much slower than the diffusion into the sihcon. Thus, the dopants reach only the sihcon substrate. Oxide masks are usually 0.5—0.7 p.m thick. 

The rate of diffusion of the carbon atoms is given by Fick s laws of diffusion. In one dimension,... 

The phases present in products can differ from those predicted from equilibrium diagrams. Nonequilibrium metastable phases form at solidification rates experienced in commercial ingots. Because of the low rate of diffusion of iron in alurninum, equilibrium conditions can only be established by long heat treatments and are very slowly approached at temperatures below about 550 °C. Small additions of other elements, particularly manganese, can also modify the phase relations. 

Work in the area of simultaneous heat and mass transfer has centered on the solution of equations such as 1—18 for cases where the stmcture and properties of a soHd phase must also be considered, as in drying (qv) or adsorption (qv), or where a chemical reaction takes place. Drying simulation (45—47) and drying of foods (48,49) have been particularly active subjects. In the adsorption area the separation of multicomponent fluid mixtures is influenced by comparative rates of diffusion and by interface temperatures (50,51). In the area of reactor studies there has been much interest in monolithic and honeycomb catalytic reactions (52,53) (see Exhaust control, industrial). Eor these kinds of appHcations psychrometric charts for systems other than air—water would be useful. The constmction of such has been considered (54). 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

Most theories of droplet combustion assume a spherical, symmetrical droplet surrounded by a spherical flame, for which the radii of the droplet and the flame are denoted by and respectively. The flame is supported by the fuel diffusing from the droplet surface and the oxidant from the outside. The heat produced in the combustion zone ensures evaporation of the droplet and consequently the fuel supply. Other assumptions that further restrict the model include (/) the rate of chemical reaction is much higher than the rate of diffusion and hence the reaction is completed in a flame front of infinitesimal thickness (2) the droplet is made up of pure Hquid fuel (J) the composition of the ambient atmosphere far away from the droplet is constant and does not depend on the combustion process (4) combustion occurs under steady-state conditions (5) the surface temperature of the droplet is close or equal to the boiling point of the Hquid and (6) the effects of radiation, thermodiffusion, and radial pressure changes are negligible. 

The stmcture of residual char particles after devolatilization depends on the nature of the coal and the pyrolysis conditions such as heating rate, peak temperature, soak time at the peak temperature, gaseous environment, and the pressure of the system (72). The oxidation rate of the chat is primarily influenced by the physical and chemical nature of the chat, the rate of diffusion and the nature of the reactant and product gases, and the temperature and pressure of the operating system. The physical and chemical characteristics that influence the rate of oxidation ate chemical stmctural variations, such as the... 

Chemical modification of the cotton fiber must be achieved within the physical framework of this rather compHcated architecture. Uniformity of reaction and distribution of reaction products are iaevitably iafiuenced by rates of diffusion, swelling and shrinking of the whole fiber, and by distension or contraction of the fiber s iadividual stmctural elements duting finishing processes. 

A number of special processes have been developed for difficult separations, such as the separation of the stable isotopes of uranium and those of other elements (see Nuclear reactors Uraniumand uranium compounds). Two of these processes, gaseous diffusion and gas centrifugation, are used by several nations on a multibillion doUar scale to separate partially the uranium isotopes and to produce a much more valuable fuel for nuclear power reactors. Because separation in these special processes depends upon the different rates of diffusion of the components, the processes are often referred to collectively as diffusion separation methods. There is also a thermal diffusion process used on a modest scale for the separation of heflum-group gases (qv) and on a laboratory scale for the separation of various other materials. Thermal diffusion is not discussed herein. 

Rate of Diffusion. Diffusion is the process by which molecules are transported from one part of a system to another as a result of random molecular motion. This eventually leads to an equalization of chemical potential and concentration throughout the system, and in the case of dyeing an equihbrium between dye in the fiber and dye in the dyebath. In dyeing there are three stages to diffusion diffusion of dye through the bulk solution of the dyebath to the fiber surface, diffusion through this surface, and diffusion of dye from the surface into the body of the fiber to allow for more dye to diffuse through the surface layer. These processes have been summarized elsewhere (9). 

The insoluble, hydrophobic disperse dyes readily dye nylon, and because their mode of attraction is completely nonionic they are completely insensitive to chemical variations and pH. Small molecular-sized disperse dyes (ca mol wt 400) show very high rates of diffusion and excellent migration properties and they are insensitive to physical variations in the nylon. As the molecular size of disperse dyes increases they show increasing sensitivity to physical variation. 

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