Quiescent fluid

In a quiescent fluid, the dimensionless mass-transfer coefficient, or the Nusselt number, djkj for a sphere is two. In fluidized beds the Nusselt... 

Convective heat transfer is classified as forced convection and natural (or free) convection. The former results from the forced flow of fluid caused by an external means such as a pump, fan, blower, agitator, mixer, etc. In the natural convection, flow is caused by density difference resulting from a temperature gradient within the fluid. An example of the principle of natural convection is illustrated by a heated vertical plate in quiescent air. 

The static properties of an isolated chain constitute a good starting point to study polymer dynamics many of the features of the chain in a quiescent fluid could be extrapolated to the kinetics theories of molecular coil deformation. As a matter of fact, it has been pointed out that the equations of chain statistics and chain dynamics are intimately related through the simplest notions of graph theory [16]. 

In quiescent liquids and in bubble columns, buoyancy-driven coalescence is more important. Large fluid particles with a freely moving surface will also have a low-pressure region at the edge of the particle where the velocity is maximum. This low-pressure region will not only allow the bubble to stretch out and form a spherical cap but also allow other bubbles to move into that area and coalesce. Figure 15.14 shows an example of this phenomenon. 

As is well known, fluid dynamics is the study of motion and transport in liquids and gases. It is primarily concerned with macroscopic phenomena in nonequilibrium fluids and covers such behavior as diffusion in quiescent fluids, convection, laminar flows, and fully developed turbulence. 

Stone, H. A., and Leal, L. G., Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399-427 (1989). 

An alternative to the rotating disk method in a quiescent fluid is a stationary disk placed in a rotating fluid. This method, like the rotating disk, is based on fluid mechanics principles and has been studied using benzoic acid dissolving into water [30], Khoury et al. [31] applied the stationary disk method to the study of the mass transport of steroids into dilute polymer solutions. Since this method assumes that the rotating fluid near the disk obeys solid body rotation, the stirring device and the distance of the stirrer from the disk become important considerations when it is used. A similar device was developed by Braun and Parrott [32], who used stationary spherical tablets in a stirred liquid to study the effect of various parameters on the mass transport of benzoic acid. 

For liquids stored at their saturation vapor pressure, P = Ps, and Equation 4-91 is no longer valid. A much more detailed approach is required. Consider a fluid that is initially quiescent and is accelerated through the leak. Assume that kinetic energy is dominant and that potential energy effects are negligible. Then, from a mechanical energy balance (Equation 4-1), and realizing that the specific volume (with units of volume/mass) v = 1/p, we can write... 

Boundary Layer. There exists a quiescent boundary layer through which the organotin species must diffuse before being carried by the sea water flow past the surface of the coating. The boundary layer under laminar flow conditions and under turbulent flow conditions are quantitatively defined (9) the thickness of the layer (L) decreases as the fluid velocity increases. 

Particles subject to Brownian motion tend to adopt random orientations, and hence do not follow these rules. A particle without these symmetry properties may follow a spiral trajectory, and may also rotate or wobble. In general, the drag and torque on an arbitrary particle translating and rotating in an unbounded quiescent fluid are determined by three second-order tensors which depend on the shape of the body ... 

In addition to the effect of the walls on the drag on the particle, the particle alters the shear on the duct. Consider a particle settling through a quiescent fluid (Fig. 9.1 with Uq = 0). Brenner (B3) showed that, for low particle Re with the particle small by comparison with the distance between particle and wall (i.e., / 1 — where = b/R), there is an excess pressure drop, AP, between points far below and far above the particle given by... 

On the interface between quiescent fluids, interfacial motions may take the form of ripples (E4, 02) or of ordered cells (B5, L5, 02, S22). Slowly growing cells may exist for long periods of time (B5, 02), or the cells may oscillate and drift over the surface (L6, L7). When the phases are in relative motion, interfacial disturbances usually take the form of localized eruptions, often called interfacial turbulence (M3). This form of disturbance can also be observed at the interface of a drop (S8). A thorough review of interfacial phenomena, including a number of striking photographs, has been presented by Sawistowski (S7). 

The first serious attempt to predict the quantity of air entrained by a falling stream theoretically was that of Hemeon [1]. Hemeon modelled the air entrainment process as one whereby the drag force exerted by each solid particle was essentially equal to that of a single particle falling through a quiescent fluid. He deduced that the induced (entrained) air flow, Q[n, is given by (converted here to SI units) ... 

Heat Transfer of a Single Sphere in a Quiescent Fluid... 

For a quasi-steady-state heat conduction between an isothermal sphere and an infinitely large and quiescent fluid, the temperature distribution in the fluid phase is governed by... 

In the microfluid dynamics approaches the continuity and Navier-Stokes equation coupled with methodologies for tracking the disperse/continuous interface are used to describe the droplet formation in quiescent and crossflow continuous conditions. Ohta et al. [54] used a computational fluid dynamics (CFD) approach to analyze the single-droplet-formation process at an orifice under pressure pulse conditions (pulsed sieve-plate column). Abrahamse et al. [55] simulated the process of the droplet break-up in crossflow membrane emulsification using an equal computational fluid dynamics procedure. They calculated the minimum distance between two membrane pores as a function of crossflow velocity and pore size. This minimum distance is important to optimize the space between two pores on the membrane... 

FIG. 7 Aggregation kinetics of hematite (diameter = 70 nm) under favorable chemical conditions and in quiescent fluid, (a) First 30 min of aggregation showing the smallest size fractions, (b) full 150-min experiment showing the smallest size fractions, and (c) Complete data set. 

---