Reynolds number solvent

Chain degradation in turbulent flow has been frequently reported in conjunction with drag reduction and in simple shear flow at high Reynolds numbers [187], Using poly(decyl methacrylate) under conditions of turbulent flow in a capillary tube, Muller and Klein observed that the hydrodynamic volume, [r ] M, is the determining factor for the degradation rate in various solvents and at various polymer concentrations [188], The initial MWD of the polymers used in their experiments are, however, too broad (Mw/Iiln = 5 ) to allow for a precise... 

Fig. 3.7a,b Friction coefficients as function of solvent Reynolds number Rewat in (n) adiabatic flow, and (b) diabatic flow. Reprinted from Hetsroni et al. (2004) with permission... 

For flow of some kind of surfactant solutions (Habon G solutions at concentration 530 and 1,060 ppm) in the tube of d = 1.07 mm in the range of Reynolds number based on solvent viscosity Re = 10-450, the increase of pressure drop in adiabatic and diabatic conditions was observed compared to that of pure water. 

Figure 6-5 Drag reduction data for polyacrylamide solutions (A/Re,s is the Reynolds number based on the solvent properties.) MDR is Virks maximum drag reduction assymptote (Virk, 1985). (From Darby and Chang, 1984).

The model for turbulent drag reduction developed by Darby and Chang (1984) and later modified by Darby and Pivsa-Art (1991) shows that for smooth tubes the friction factor versus Reynolds number relationship for Newtonian fluids (e.g., the Colebrook or Churchill equation) may also be used for drag-reducing flows, provided (1) the Reynolds number is defined with respect to the properties (e.g., viscosity) of the Newtonian solvent and (3) the Fanning friction factor is modified as follows ... 

ARe>s is the Reynolds number based on the solvent properties, /zs is the solvent viscosity, D is the pipe diameter, F is the velocity in the pipe, and A is the fluid time constant (from the Carreau model fit of the viscosity curve). 

Solution. We first calculate the Reynolds number for the solvent (water) under the given flow conditions, using a viscosity of 0.01 poise and a density of 1 g/cm3. 

The rate of agitation, stirring, or flow of solvent, if the dissolution is transport-controlled, but not when the dissolution is reaction-con-trolled. Increasing the agitation rate corresponds to an increased hydrodynamic flow rate and to an increased Reynolds number [104, 117] and results in a reduction in the thickness of the diffusion layer in Eqs. (43), (45), (46), (49), and (50) for transport control. Therefore, an increased agitation rate will increase the dissolution rate, if the dissolution is transport-controlled (Eqs. (41 16,49,51,52), but will have no effect if the dissolution is reaction-controlled. Turbulent flow (which occurs at Reynolds numbers exceeding 1000 to 2000 and which is a chaotic phenomenon) may cause irreproducible and/or unpredictable dissolution rates [104,117] and should therefore be avoided. 

If a gas such as ammonia or CO2 (phase 1) is absorbing into a liquid solvent (phase 2), the resistance R2 is relatively important in controlling the rate of adsorption. This is also true of the desorption of a gas from solution into the gas phase. Usually R2 is of the order 10 or 10 sec. cm. h though the exact value is a function of the hydrodynamics of the system consequently various hydrodynamic conditions give a variety of equations relating R2 to the Reynolds number and other physical variables in the system. For the simplest system where the liquid is infinite in extent and completely stagnant, one can solve the diffusion equation... 

Here, the particle Reynolds number is based on the slip velocity. If terminal velocity is used, then the above correlation gives the minimum value for the mass transfer coefficient. Minimum mass transfer coefficients further depend on the density difference between solid particles and solvent. For the typical case of water, the approximate values presented in Table 3.7 can be used (Harriot, 1962). 

Once the vessel type has been selected and the rate expression established for the cleaning process, the design engineer must decide which variables are significant for the scaling process. Mathematical tools in the form of dimensionless variables are useful for determining these variables. Every chemical or physical process can be defined by a set of dimensionless ratios or variables intrinsic to the process. An example is the Reynolds number, which is defined for a process with internal flow through a tube by solvent properties, flow rate of the solvent, and the diameter of the tube. l... 

Reynolds number p = density of the solvent p = dynamic viscosity of the solvent... 

The impeller Reynolds number is proportional to the standard Reynolds number and is arrived at by assuming that the velocity of the solvent flow through the chamber is proportional to the speed of the impeller and the area through which it acts. The impeller Froude number is arrived at in a similar manner. 

Working with porous clay plates impregnated with phosphatide-free soybean oil and with tetrachloroethylene as a solvent. Boucher et al. (125) found that experimentally determined extraction rates checked closely with theory. A typical theoretical extraction curve is shown (curve A) in Figure 18. A lack of correspondence between extraction rates and Reynolds number of the flowing solvent, over a... 

We have already noted that mass transfer in a liquid is almost always characterized by large values of the Peclet number (the Peclet number for mass transfer involves the product of the Schmidt number and Reynolds number instead of the Prandtl number and Reynolds number) and that the dimensionless form of the convection-diffusion equation governing transport of a single solute through a solvent is still (9-7), with 6 now being a dimensionless solute concentration. For transfer of a solute from a bubble or drop into a liquid that previously contained no solute, the concentration 6 at large distances from the bubble or drop will satisfy the condition... 

We saw in Chapter 10 that the boundary-layer structure, which arises naturally in flows past bodies at large Reynolds numbers, provides a basis for approximate analysis of the flow. In this chapter, we consider heat transfer (or mass transfer for a single solute in a solvent) in the same high-Reynolds-number limit for problems in which the velocity field takes the boundary-layer form. We saw previously that the thermal energy equation in the absence of significant dissipation, and at steady state, takes the dimensionless form... 

In Chap. 9, we considered the solution of this equation in the limit Re 1, where the velocity distribution could be approximated by means of solutions of the creeping-flow equations. When Pe 1, we found that the fluid was heated (or cooled) significantly in only a very thin thermal boundary layer of 0(Pe l/3) in thickness, immediately adjacent to the surface of a no-slip body, or () Pe l/2) in thickness if the surface were a slip surface with finite interfacial velocities. We may recall that the governing convection di ffusion equation for mass transfer of a single solute in a solvent takes the same form as (111) except that 6 now stands for a dimensionless solute concentration, and the Peclet number is now the product of Reynolds number and Schmidt number,... 

Re, Reynolds number based on the solvent viscosity, pUdh/r s... 

N p particle Reynolds number based on apparent viscosity NRes solvent Reynolds number... 

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