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Principles of Mass Transfer1. General RemarksSome of the most typical chemical engineering problems lie in the field of mass transfer. A distinguishing mark of the chemical engineer is his ability to design and operate equipment in which reactants are prepared, chemical reactions take place, and separations of the resulting products are made. This ability rests largely on a proficiency in the science of mass transfer.Applications of the principles of momentum and heat transfer are common in many branches of engineering, but the application of mass transfer has traditionally been largely limited to chemical engineering. Other important applications occur in metallurgical processes, in problems of high-speed flight, and in waste treatment and pollution-control processes.By mass transfer is meant the tendency of a component in a mixture to travel from a region of high concentration to one of low concentration. For example, if an open test tube with some water in the bottom is placed in a room in which the air is relatively dry, water vapor will diffuse out through the column of air in the test tube. There is a mass transfer of water from a place where its concentration is high (just above the liquid surface) to a place where its concentration is low (at the outlet of the tube). If the gas mixture in the tube is stagnant, the transfer occurs by molecular diffusion. If there is a bulk mixing of the layers of gas in the tube by mechanical stirring or because of a density gradient, mass transfer occurs primarily by the mechanism of forced or natural convection. These mechanisms are analogous to the transfer of heat by conduction and by convection; there is, however, no counterpart in mass transfer for thermal radiation.The analogy between momentum and energy transfer has already been studied in some detail, and it is now possible to extend the analogy to include mass transfer.In discussing the fundamentals of mass transfer we shall consider mainly binary mixtures, although multicomponent mixtures are important in industrial applications. Some of these more complicated situations will be discussed after the basic principles have been illustrated in terms of binary mixtures,2. Molecular DiffusionMolecular diffusion occurs in a gas as a result of the random motion of the molecules. This motion is sometimes referred to as a random walk. Across a plane normal to the direction of the concentration gradient (or any other plane), there are fluxes of molecules in both directions. The direction of movement for any one molecule is independent of the concentration in dilute solutions. Consequently, in a system in which there is a concentration gradient, the fraction of molecules of a particular species (referred to as species A) which will move across a plane normal to the gradient is the same for both the high-and low-concentration sides of the plane. Because the total number of molecules of A on the high-concentration side is greater than on the low-concentration side, there is therefore a net movement of A in the direction in which the concentration of A is lower. If there are no counteracting effects, the concentrations throughout the mixture tend to become the same. In the analogous transfer of heat in a gas by conduction, the distribution of hotter molecules (those which have a higher degree of random molecular motion) tends to be evened out by random mixing on a molecular scale. Similarly, if there is a gradient of directed velocity (as distinguished from random velocity) across the plane, the velocity distribution tends toward uniformity as a result of the random molecular mixing. There is a transfer of momentum, which is proportional to the viscosity of the gas.The above remarks apply only in an approximate and qualitative way. The quantitative prediction of the diffusivity, thermal conductivity, and viscosity of a gas from a knowledge of molecular properties can be quite complicated. The consideration of such relations forms an important part of the subject of statistical mechanics.Molecular diffusion also occurs in liquids and solids. Crystals in an unsaturated solution dissolve, with subsequent diffusion away from the solid-liquid interface. Diffusion in solids is of importance in metallurgical operations. When iron which is unsaturated with respect to carbon is heated in a bed of coke, the concentration of the carbon near the surface is increased by inward diffusion of carbon atoms.3.Eddy DiffusionJust as momentum and energy can be transferred by the motion of finite parcels of fluid, so mass can be transferred. We have seen that the rate of these transfer operations, caused by bulk mixing in a fluid, can be expressed in terms of the eddy kinematics viscosity, the eddy thermal diffusivity, and the eddy diffusivity. This latter quantity can be related to a mixing length which is the same as that defined in connection with momentum and energy transfer. In fact, the analogy between heat and mass transfer is so straightforward that equations developed for the former are often found to apply to the latter by a mere change in the meaning of the symbols.Eddy diffusion is apparent in the dissipation of smoke from a smokestack. Turbulence causes mixing and transfer of the smoke to the surrounding atmosphere. In certain locations where atmospheric turbulence is lacking, smoke originating at the surface of the earth is dissipated largely by molecular diffusion. This causes serious pollution problems because mass is transferred less rapidly by molecular diffusion than by eddy diffusion.4.Convective Mass-Transfer CoefficientsIn the study of heat transfer we found that the solution of the differential energy balance was sometimes cumbersome or impossible, and it was convenient to express the rate of heat flow in terms of a convective heat-transfer coefficient by an equation likeThe analogous situation in mass transfer is handled by an equation of formThe mass flux NA is measured relative to a set of axes fixed in space. The driving force is the difference between the concentration at the phase boundary (a solid surface or a fluid interface) and the concentration at some arbitrarily defined point in the fluid medium. The convective coefficient kp may apply to forced or natural convection; there are no mass-transfer counterparts for boiling, condensation, or radiation heat-transfer coefficients. The value of kp is a function of the geometry of the system and the velocity and properties of the fluid, just as was the coefficient h.(Selected from* C. O. Bennett, and J. E. Myens, Momentum, Heat, and Mass Transfer, 2nd Edition, McGraw-Hill Inc. , 1974. )传质原理1. 概述一些典型的化学工程问题存在于传质领域。区分化学工程的一个重要标志,就是它是否有设计和操作设备的能力。在过程设备中,反应物被装着,化学反应既可发生,然后最终产物被分离开来。这种能力主要取决与他对传质学的熟练程度。动量原理和传热原理普遍应用在许多工程分支中广泛应用。但是,习惯上,传质的应用主要局限于化学工程领域中。其它重要的应用有冶金方面,高速飞行方面,废物处理及污染控制方面。传质就是混合物某种组分有从含量高的区域向含量低的区域扩散的趋势。例如,如果在一个相对干燥的房间里,放置一个底部带有水的开口试管中,水蒸气将通过试管中的空气柱扩散出来。这就是水的传质,水从高浓度地方(仅在液体表面之上)传递到低浓度地方(在管的出口处)。如果管中的气体混合物不流动,传递将以分子扩散的方式发生。如果有一个物体以机械搅拌的方式搅和管中的气体层。则这些机理就与通过传导和通过对流的热传递相类似;但是,在传质中没有热传质的对应物。在一些细节方面,我们已经详细地学习了动量和能量传递之间的类似之处,现在把这种类似性延伸到传质已成为可能。在讨论传质的基本原理时,我们将主要考虑双组分混合物。尽管多组分混合物在工业应用中很重要,但是,在讨论传质原理中,我们应该主要考虑双组分混合物。在以双组分混合物的方式阐明基本原理之后,我们将对部分这些更复杂的情况进行讨论。2. 分子扩散分子扩散运动是大量分子自由运动的结果。这种运动有时被称为自由运动。穿过垂直于浓度梯度方向的一个平面(或任何其它平面),在两个方向上都有分子扩散。在稀溶液中,每个分子的运动方向不受稀溶液的浓度限制。 因此,在一个存在浓度梯度的系统中,某一种类分子(把它当作种类A)的成分,对于平面的高浓度和低浓度两侧来说,是相同的,该种分子将运动穿过垂直于浓度梯度的平面。因为种类A的分子的总数目,在高浓度一侧比在低浓度一侧的大,所以就存在A在一个方向上的单方向运动,在该运动方向上A的浓度更低。如果没有抵消,则混合物的浓度将趋向相同。与气体中热量以传导方式的传递相类似,较热分子(那些分子具有自由分子运动的更高
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