Laminar flows continued tubes

This regime is characterized by the presence of two continuous fluid phases and an interface which can easily be described. The term separated flows is frequently employed to describe these situations in both horizontal and vertical systems. Some flow patterns in Regime I are advantageous for transferring heat between the tube wall and the fluid mixture or for carrying out two-phase reactions. The special case of laminar-laminar flow is included in this regime, and two studies seem to be of interest, Byers and King (B7) and Bentwich and Sideman (B3). 

Show how the Hagen-Poiseuille equation for the steady laminar flow of a Newtonian fluid in a uniform cylindrical tube can be derived starting from the general microscopic equations of motion (e.g., the continuity and momentum equations). 

Another variety of the continuous-coupling technique operates by transporting the coupling component suspension as a laminar flow upwards inside a vertical reaction tube. Portions of the diazonium compound, dissolved in an acidic aqueous medium, are added through appropriately located inlets in the walls of the reaction tube. The concentration of the added solution decreases as the reaction mixture flows upward and is designed to synchronize the uppermost inlet for the diazonium salt solution with the stoichiometric end point of the coupling reaction. 

Example 2-6 Consider the situation where the reactants at constant density are fed continuously into a pipe of length L instead of a tank of volume V as in the batch reactor. The reactants react as they flow down the tube with a speed u, and we assume that they flow as a plug without mixing or developing the laminar flow profile. Show that the conversion of the reactants is exactly the same in these very different reactor configurations. 

Polystyrene can be easily prepared by emulsion or suspension techniques. Harkins (1 ), Smith and Ewart(2) and Garden ( ) have described the mechanisms of emulsTon polymerization in batch reactors, and the results have been extended to a series of continuous stirred tank reactors (CSTR)( o Much information on continuous emulsion reactors Ts documented in the patent literature, with such innovations as use of a seed latex (5), use of pulsatile flow to reduce plugging of the tube ( ), and turbulent flow to reduce plugging (7 ). Feldon (8) discusses the tubular polymerization of SBR rubber wTth laminar flow (at Reynolds numbers of 660). There have been recent studies on continuous stirred tank reactors utilizing Smith-Ewart kinetics in a single CSTR ( ) as well as predictions of particle size distribution (10). Continuous tubular reactors have been examined for non-polymeric reactions (1 1 ) and polymeric reactions (12.1 31 The objective of this study was to develop a model for the continuous emulsion polymerization of styrene in a tubular reactor, and to verify the model with experimental data. 

The film is laminar, but waves are on the surface. If laminar flow m this wavy regime (30[Pg.1225]

The opportunity to measure the dilute polymer solution viscosity in GPC came with the continuous capillary-type viscometers (single capillary or differential multicapillary detectors) coupled to the traditional chromatographic system before or after a concentration detector in series (see the entry Viscometric Detection in GPC-SEC). Because liquid continuously flows through the capillary tube, the detected pressure drop across the capillary provides the measure for the fluid viscosity according to the Poiseuille s equation for laminar flow of incompressible liquids [1], Most commercial on-line viscometers provide either relative or specific viscosities measured continuously across the entire polymer peak. These measurements produce a viscometry elution profile (chromatogram). Combined with a concentration-detector chromatogram (the concentration versus retention volume elution curve), this profile allows one to calculate the instantaneous intrinsic viscosity [17] of a polymer solution at each data point i (time slice) of a polymer distribution. Thus, if the differential refractometer is used as a concentration detector, then for each sample slice i. 

Nusselt [35] also analyzed this problem, assuming that the condensate drained from an npper tube at bottom dead center as a continuous sheet, falling on the next lower tube and flowing down and around that tube in undisturbed laminar flow. Under these highly idealized conditions, the average coefficient for a row of tnbes N tubes high is... 

In laminar flow, heat transfer occurs only by conduction, as there are no eddies to carry heat by convection across an isothermal surface. The problem is amenable to mathematical analysis based on the partial differential equations for continuity, momentum, and energy. Such treatments are beyond the scope of this book and are given in standard treatises on heat transfer, Mathematical solutions depend on the boundary conditions established to define the conditions of fluid flow and heat transfer. When the fluid approaches the heating surface, it may have an already completed hydrodynamic boundary layer or a partially developed one. Or the fluid may approach the heating surface at a uniform velocity, and both boimdary layers may be initiated at the same time. A simple flow situation where the velocity is assumed constant in all cross sections and tube lengths is called... 

It consists of a cylinder through which a liquid is pumped upwards (cf. Fig. 5.24). In order to ensure a laminar flow field, the liquid first passes through a conical tube having a small slope. After the liquid has reached the cylinder, it is allowed to flow over the top rim. This flow causes the circular liquid surface to be expanded continuously in a radial way. After a steady... 

Laminar-flow tubular reactors are occasionally used for bulk, continuous polymerizations. A monomer or monomer mixture is introduced at one end of the tube and, if all goes well, a high molecular weight polymer emerges at the other end. Practical problems arise from three types of instability ... 

Kinetics belongs to the domain of non-equilibrium thermodynamics. If the deviation from the state of equilibrium is relatively small, linearized non-equilibrium thermodynamics applies. An example in physics is the laminar flow of a liquid through a tube under the influence of a small pressure gradient. The outstanding example of a chemical system described by linear thermodynamics is a flow reactor working under steady-state conditions. This is an open system continuously fed with reactants. The potential function which describes the reaction system is the entropy production, a = dS/dt, As derived in Section 2.3, systems which are forced... 

Consider now the steady, laminar flow of an incompressible Newtonian liquid through a uniform cylindrical tube, of internal radius a and length L. Let the axis of the tube be in the z direction. If is the liquid velocity component in the direction of the axis, then, assuming that there is no radial liquid flow, the equation of continuity gives du ldz = 0 and, further, the pressure is constant over any cross-section. Since the flow is steady bu /bt = 0 and this, with bu jbz = 0, ensures that Dw /Df is zero and the solution obtained is a creeping solution. 

One is that the end of the vortex is an axisymmetric phenomenon, that the end represents a sort of recirculating gas bubble . Such a vortex end is observed in the research field of vortex breakdown in vortex tubes , tubes in which a flowing liquid is caused to swirl with swirl vanes. A difference between a vortex tube and a cyclone or swirl tube is that the flow reverses in the latter, while in the vortex tube it continues past the vortex end, and discharges from the bottom of the tube. Another difference is that this type of experiment is usually (but not always, see Sarpkaya, 1995) performed under laminar flow conditions, while the flow in a cyclone is turbulent. 

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