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13.Princiles of Mass Transfer

(2009-01-03 13:29:12)
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13.Princiles of Mass Transfer

1.General Remarks

Some 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 products 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 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.Moleculay Diffusion

Molecular 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 diffusion

Just 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 cause serious pollution problems because mass is transferred less rapidly by molecular diffusion than by eddy diffusion.

4. Convective Mass-Transfer Coefficients

In 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 like

The analogous situation in mass transfer is handled by an equation of form

The mass flux NA is measured relative to a set of axes fixed in place. The driving force is the difference between the concentration at the phase boundary (a solid surface or a fluid interface) and the concentration at the 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 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

     

 

13.传质原理

1. 总述

化学工程中一些最典型的问题在于传质领域。化学工程师的一个显著特点就是他设计和操作设备的能力。这设备通常用于准备反应物,发生化学反应以及对最终产物进行分离。这种能力主要得益于对传质这门学科的熟练。动量传递和传热原理的运用在工程学的许多分支上是非常普遍的。但对于传质原理的运用却被传统性地限制在化工领域内。而在其它领域则主要运用于冶金过程、高速飞行问题以及废物处理和污染控制的过程中。

   传质意味着一个混合物中的某组分从高浓度层向低浓度的趋势。例如,当一支底部有水的开口试管被放置在一间空气相对干燥的房间里,水蒸气就会通过试管中的空气柱散布出来。这就进行了一次水的传质,是从水蒸气浓度高的地方(仅在液体的表面处)向(在试管的出口处)水蒸气浓度低的地方进行的。如果管中的混合气体是不流动的,那么传递就通过分子扩散来进行。如果是受到机械式的搅拌或者是密度梯度发生了变化而使得管中有大量的分层的气体,那么传递就主要通过强制对流或自然对流而发生。这些情况类似于通传导或对流产生传热那样;然而,在质量传递的过程中没有产生热辐射的补充物。

   动量传递和能量传递的相似之处在某些细节上已作了研究,而且现在此相似之处也可以扩大为包括传质在内了。

   尽管多元混合物在工业中的运用十分重要,但在讨论传质的基本原理时,我们应首先考虑二元混合物。一些相关的更加复杂的情况将在说明完二元混合物的基本原理后再做讨论。

2.分子扩散

   气体中的分子扩散是由分子的不规则运动产生的。这种运动有时被说成是分子的“不规则走动”。在一个倾向于浓度梯度方向的平面(或是其它任意平面)上,分子同时在两个方向中波动。而任何一个分子的运动方向都与稀释溶液的浓度无关。自然而然地,在一个倾向于浓度梯度的系体中,一些物质(称为A物质)的分子就会在梯度平面内移动,但无论是在平面内高浓度或是低浓度的一边,A物质分子份数都是一样的。由于A的分子总数在高浓度处比低浓度处要多,因此,A的分子在朝着低浓度方向那边形成一个运动网。如果没有中和的作用,那么整个混合物的浓度会趋向一致。类似于在气体中通过传导发生传热一样,那些比较活跃的分子(指更大幅度地做着不规则运动的分子)的分布就会在分子比例上由于随意混合而被平均掉。类似地,如果在平面中也有一个有方向的速度运动的梯度(与无方向的速度运动相区别),那么速度分布就会趋向一致,这是分子任意混合的结果。这里就存在着一种动量传递,它与气体的粘度成正比。

以上的陈述只适于用于性质大概相似的情况下。而扩散因素,导热系数以及气体的粘度在数量上的变化从分子的性能上说复杂多了。对这些关系的分析构成了统计力学这门学科的一个重要部分。

   分子扩散同样也会在液体和固体中发生。当晶体溶解在不饱和溶液中时,分子就会在固液界面处产生相应的扩散。固体分子的扩散在冶金过程中尤为重要。当一块含有不饱和碳的铁放在焦炭床上加热的时候,铁表面的碳含量就会由于内部碳原子的扩散而提高。

3.涡流扩散

   就像动量和能量通过在液体内部有限空间内动运而传递那样,质量也可以传递。我们已经知道,由于液体内大量的混合物运动而引起传递的速度可以用涡流动学粘度、涡流热扩散率和涡流扩散来表示。涡流扩散的数量与混合度有关,就像动量传递和能量传递所定义的那样。事实上,传热与传质两者相似之处是如此显而易见的。所以,由前者引伸出来的化学方程式通常也适用于后者,只不过符号的意思有所改变而已。

   从烟囱里冒出的烟消散中我们可以明显地看到涡流扩散。空气湍流使烟混合后又扩散到周围的空气中。在某些气体湍流缓慢的区域中,地球表面产生的烟雾很大一部分是通过分子扩散而消散的。这些引起了严重的污染问题,因为通过分子扩散的传质比涡流扩散的要慢。

4.质量传递的对流系数

   在对传热的学习中,我们发现不同的各种化学能的平衡,有时是难以达到的,甚至是不可实现的。如果用对流系数的方法来表达热流率,那将会十分方便。方程式如下:

 

同样我们可通过此方法来表达传质,方程是

 

我们通过固定在某一地方的两根数轴来测量钠(Na)的质流量。原动力就是在不同相界面上发生交换(一个固体表面或一个液体界面)与流质体中任意指定点的浓度两者之间的不同,对流系数Kp可适用于强制对流和自然对流。在达到沸点时没有类似的传质,传热的冷凝系数Kp的数值只是体系中几何形状和液体的速度及特征性能的一个函数,就像系数h那样。

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