Fluid motion, mass transfer/transport

Much of what I have to say will merely reinforce what has already been well said by L. G. Leal in his paper [1], In particular, I would emphasize that chemical engineers, indeed many other engineers also, are more concerned with transport processes than with fluid mechanics as such. It is true that in many processes the convective motions dominate, but their effect is largely a kinematic and not a dynamical one. Chemical engineers study dynamics as a means to an end relatively infrequently are the absolute stresses caused by fluid motion their prime interest. More often, issues in heat and mass transfer are most important. 

The second set of simulations is oriented towards the analysis of the simultaneous heat and mass transfer when two fluids are separated by a porous wall (membrane). The interest here is to couple the species transport through a wall associated with the heat transfer and to consider that the wall heat conduction is higher than the heat transported by the species motion. The process takes place through a cylindrical membrane and we assume the velocity to be quite slow in the inner compartment of the membrane. The process is described schematically in Fig. 3.65. The transformation of the above general model in order to correspond to this new description gives the following set of dimensionless equations ... 

Distinction should be made between mass transfer and the hulk fluid motion (or fluid flow) that occurs on a macroscopic level as a fluid is transported from one location to another, Mass transfer requires the presence of two regions at different chemical compositions, and mass transfer refers to the movement of a chemical species from a high concentration region toward a lower conccii-tralion one. The primary driving force for fluid flow is the pressure difference, whereas for mass transfer it is the concentration difference. 

During mass transfer in a moving medium, chemical species are transported both by molecular diffusion and by the bulk fluid motion, and the velocities of lire species are expressed as... 

The chemical reactions responsible for the production of deposits that accumulate on heat transfer surfaces may take place on the surface itself The deposit precursors migrate to the surface from the bulk fluid across the boundary layers by simple diffusion or diffusion brought about by the eddy motion in the fluid stream. An alternative route to the production of deposits from chemical reaction is that the reaction takes place in the bulk and particulate solid products are transported to the surface by mass transfer mechanisms. 

We are concerned in this book primarily with a description of the motion of fluids under the action of some applied force and with convective heat transfer in moving fluids that are not isothermal. We also consider a few analogous mass transfer problems involving the convective transport of a single solute in a solvent. 

At low Re, the viscous effects dominate inertial effects and a completely laminar flow occurs. In the laminar flow system, fluid streams flow parallel to each other and the velocity at any location within the fluid stream is invariant with time when boundary conditions are constant. This implies that convective mass transfer occurs only in the direction of the fluid flow, and mixing can be achieved only by molecular diffusion [37]. By contrast, at high Re the opposite is true. The flow is dominated by inertial forces and characterized by a turbulent flow. In a turbulent flow, the fluid exhibits motion that is random in both space and time, and there are convective mass transports in all directions [38]. 

Tha transport mechanisms of molecular diffusion and mass carried by eddy motion are again assumed edditive although the contribution of the molecular diffusivity term is quite small except in the region nenr a wall where eddy motion is limited. The eddy diffusivity is directly applicable to problems snch as the dispersion of particles or species (pollutants) from a souree into a homogeneously turbulent air stream in which there is little shear stress. The theories developed by Taylor.36 which have been confirmed by a number of experimental investigations, can describe these phenomena. Of more interest in chemical engineering applications is mass transfer from a turbolent fluid to a surface or an interface. In this instance, turbulent motion may he damped oni as the interface is approached aed the contributions of both molecolar and eddy diffusion processes must he considered. To accomplish this. 9ome description of the velocity profile as the interface is approached must be available. 

Mass transfer can be definnd simply as the movement of any identifiable species from one spatial location to another. Tha mechanism of movement can be macroscopic as in the flow of a fluid in a pipe (convection) or in the mechanical transport of solids by a conveyor belt. In addition, the transport of a panicolar species may be the result of madom molecular motion (molecular diffusion) or randum microscopic fluid motion (eddy or turbulent diffusion) in the presence of a composition gradient within a phase. This chapter is concerned primarily with mass transfer owing to molecular or microscopic processes. 

Use of symbolic drag coefficients (Section I1,C,2) and symbolic heat-and mass-transfer coefficients (Section IV, A) furnishes a unique method for describing the intrinsic, interphase transport properties of particles for a wide variety of boundary conditions. Here, the particle resistance is characterized by a partial differential operator that represents its intrinsic resistance to vector or scalar transfer, independently of the physical properties of the fluid, the state of motion of the particle, or of the unperturbed velocity or temperature fields at infinity. Though restricted as yet in applicability, the general ideas underlying the existence of these operators appear capable of extension in a variety of ways. 

Effect of Flow Regime on the Dimensionless Mass Transfer Correlation. For creeping flow of an incompressible Newtonian fluid around a stationary solid sphere, the tangential velocity gradient at the interface [i.e., g 9) = sin6>] is independent of (he Reynolds number. This is reasonable because contributions from accumulation and convective momentum transport on the left side of the equation of motion are neglected to obtain creeping flow solutions in the limit where Re 0. Under these conditions. 

Chapter 5 considers the stabiUty of fluid interfaces, a subject pertinent both to the formation of emulsions and aerosols and to thdr destruction by coalescence of drops. The closely related topic of wave motion is also diseussed, along with its implications for mass transfer. In both cases, boundary eonditions applicable at an interface are derived—a significant matter because it is through boundary conditions that interfacial phenomena influence solutions to the governing equations of flow and transport in fluid systems. 

The study of momentum transfer, or fluid mechanics as it is often called, can be divided into two branches fluid statics, or fluids at rest, and fluid dynamics, or fluids in motion. In Section 2.2 we treat fluid statics in the remaining sections of Chapter 2 and in Chapter 3, fluid dynamics. Since in fluid dynamics momentum is being transferred, the term momentum transfer or transport is usually used. In Section 2.3 momentum transfer is related to heat and mass transfer. 

In studying transport phenomena one is guaranteed to encounter situations involving fluid-solid or gas-liquid interfaces. These problems usually become more complex when fluid motion is involved. Traditionally, such complex problems are analyzed with the aid of the concept of a boundary layer. The boundary layer equations are well established for fluid flow, heat transfer, and mass transfer [8,9-13]. This set of equations is a convenient starting point for the scaling of the independent and dependent variables. However, before we begin it is helpful to briefly review descriptions of the three types of boundary layers. 

---