Reynolds numbers emulsion

Figure 10. Monomer conversion rates as a function of emulsion Reynolds number for straight and helical tubular reactors...

Figure 12, Molecular weight vs. emulsion Reynolds number at conversion rates...

A summary of the nine batch reactor emulsion polymerizations and fifteen tubular reactor emulsion polymerizations are presented in Tables III IV. Also, many tubular reactor pressure drop measurements were performed at different Reynolds numbers using distilled water to determined the laminar-turbulent transitional flow regime. 

Reynolds number based on emulsion properties prior to polymerization, dimensionless... 

Figure 49. Flux as a function of Reynolds number for crossflow electrofiltration of oil-water emulsions at several voltages (23)...

The Froude number, = vP Lg, is similar to it is a measure of the inertial stress to the gravitational force per unit area acting on a fluid. Its inclusion in Eq. (11) is justified when density differences are encountered in the absence of substantive differences in density, e.g., for emulsions more so than for suspensions, the Froude term can be neglected. Dimensionless mixing time is independent of the Reynolds number for both laminar and turbulent flow regimes, as in-... 

The performance of a fluidized bed combustor is strongly influenced by the fluid mechanics and heat transfer in the bed, consideration of which must be part of any attempt to realistically model bed performance. The fluid mechanics and heat transfer in an AFBC must, however, be distinguished from those in fluidized catalytic reactors such as fluidized catalytic crackers (FCCs) because the particle size in an AFBC, typically about 1 mm in diameter, is more than an order of magnitude larger than that utilized in FCC s, typically about 50 ym. The consequences of this difference in particle size is illustrated in Table 1. Particle Reynolds number in an FCC is much smaller than unity so that viscous forces dominate whereas for an AFBC the particle Reynolds number is of order unity and the effect of inertial forces become noticeable. Minimum velocity of fluidization (u ) in an FCC is so low that the bubble-rise velocity exceeds the gas velocity in the dense phase (umf/cmf) over a bed s depth the FCC s operate in the so-called fast bubble regime to be elaborated on later. By contrast- the bubble-rise velocity in an AFBC may be slower or faster than the gas-phase velocity in the emulsion... 

Reynolds number based on velocity emulsion phase... 

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 flowing emulsion was assumed homogeneous, so that the continuity equations could be used. Additional assumptions were the fluid is an incompressible Newtonian with constant properties the flow is laminar at the maximum experimental Reynolds number of 210 and less there is negligible viscous heating flow is at steady... 

To describe emulsion formation two main factors must be considered, namely hydrodynamics and interfacial science. In hydrodynamics, consideration must be given to the type of flow, whether laminar or turbulent, and this depends on the Reynolds number (as wiU be discussed later). 

When deposition of emulsion drops is investigated, sedimentation can be neglected so that the first term in Eq. (10.27) dominates even at strong retardation. Retardation of the surface becomes less efficient with increasing bubble dimensions and, respectively, Reynolds number. Therefore, the experimental verification of the hypothesis of incomplete retardation of the surface at intermediate Reynolds numbers is of interest. A maximum removal of impurities fi om the water used is important in such experiments. 

For a similar system, the shear viscosity was found to follow the power law model with yield (Pal et al. 1986). Owing to the presence of yield stress, the flow of concentrated emulsion was found to be facilitated by superposition of 10 Hz oscillation on the steady-state shear flow - up to 40 % energy saving was reported (Jezequel et al. 1985). More recently, the relative viscosity of emulsions was described in terms of scaling parameters (Pal 1997). Ten principal variables were incorporated into six dimensionless groups X, k, reduced time, h = t/(r n,dV8 kB T), relative density, = pd/pm> Peclet number, Pe = ti yd /SkeT, and Reynolds number. Re = p yd /4rin,. For the steady-state flow of well-stabilized emulsions, it was argued that the relative viscosity of emulsions should depend only on two... 

O.JS/cj). If a percentage porosity as low as 10% is substituted, it would only give a maximum Reynolds number of 7.8 which is well within the range of 1 to 10 for the transition from laminar to turbulent flow in sands and sandstones. Although the porous media used in the present study are composed of different materials, the order of magnitude of the maximum Reynolds number is quite within reasonable limits, should be sufficient for the applicability of Darcy s law. It should be noted that the viscosities of emulsions are, in most cases, much higher than that of water. Consequently, Reynolds numbers would go even below 1. This condition would rule out the possibility of a change from laminar to turbulent flow in the present studies. 

The data used to illustrate emulsion polymerization at low Reynolds numbers were obtained by emulsion polymerization of styrene for 5 hours at 70 in a 500-ml reactor equipped with a 1.5-inch pitched-blade impeller under conditions where 500stirring rate. Although there are only three points, they form a straight line that extrapolates to a point close to the origin. 

The data used to illustrate emulsion polymerization at high Reynolds numbers were those of Ruben (17) 65 35 vinyl chloride-ethyl acrylate copolymers were prepared using a 40-50 60-50 monomer water ratios, 9.2% hydrocarbon sulfonate and 2.3% polyoxyethylated phenol emulsifiers, 0.57% ammonium persulfate initiator, and 0.40% sodium acetate buffer. The polymerizations were carried out in a 2-gallon jacketed stainless steel reactor equipped with a 2-, 3-, or 4-inch flat-blade impeller at pressures less than 110 psi, for 4 hours at 52°, 2 hours at 54°, and 3 hours at 60°. Figure 11 shows... 

Emulsions of the types SE (O/W) and DE (W/O/W) with different initial secondary mean drop sizes were passed through differently sized nozzles (liquid caps, diameters 0.5, 0.7, 1.0, 2.5 mm) at GLR = 0 (no gas flow). From this, X503 Nozzie/J so,3, iniaai was plotted versus the related nozzle Reynolds number / ei,Nozzie or secondary drop Reynolds number Reix>rop [(23.5) and (23.6)] with Rei,Drop = / ij ozzie (x5o,3/dn) and denoting the nozzle diameter as demonstrated in Fig. 23.15 (top). 

Two-dimensional (2D) microfluidic systems that can produce highly monodisperse emulsion droplets have been intensively studied in various fields [59-63]. Confined microfluidic channels such as T-junctions [64-68], cross-junctions [69-71], flow-focusing geometries [72-79] and other co-flow geometries [67, 80, 81] are generally used. Under the conditions of low Reynolds and capillary numbers [66], highly monodisperse emulsion droplets are reproducibly formed in the channels, typically... 

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