Hydrodynamics flow rate

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. 

Theoretical studies on FIA have been aimed at establishing an accurate relationship between the geometric (length and diameter) and hydrodynamic (flow rate) characteristics of a FIA system and the parameters defining the profile obtained (travel time, co-ordinates of the peak maximum and peak width). 

Two introduction methods are commonly employed in capillary electrophoresis. Hydrodynamic injection is based on siphoning, or gravity feeding the sample into the anodic end of the capillary. The anodic end is removed from the buffer reservoir and placed in the sample solution. The capillary end is then raised so that the liquid level in the sample vial is at a height Ah above the level of the cathodic buffer, and is held in this position for a fixed time t. This process has been automated for reproducibility, and the hydrodynamic flow rate has been shown to obey Eq. 12.9 ... 

Apparently, it is possible to modify the biorelevant media and also the involved hydrodynamics, flow rate so as to achieve IVIVC in this particular situation. However, more studies with different BCS class II compounds are needed. 

The duration of the response results primarily from the rate of elution of the sample, and not on any inherent limitation in the response time of the electrode. This is a characteristic of ion-selective electrodes, but amperometric responses depend not only on the duration of elution but also on flow rate because of the hydrodynamic effects discussed previously. 

Fouling is the term used to describe the loss of throughput of a membrane device as it becomes chemically or physically changed by the process fluid (often by a minor component or a contaminant). A manifestation of fouling in cross-flow UF is that the membrane becomes unresponsive to the hydrodynamic mass transfer which is rate-controlling for most UF. Fouling is different from concentration polarization. Both reduce output, and their resistances are additive. Raising the flow rate in a cross-flow UF will increase flux, as in Eq. 

Calibration curves for PS and PMMA are shown in Figs. 15.3-15.5. The slight differences in courses of calibration curves for PS in THF, chloroform, and toluene, as well as the curve for PMMA in THF (Fig. 15.3), can be explained by the flow rate variations for different pumping systems and by the hydrodynamic volume effects, respectively. The calibration curves for PMMA in mixed eluents THF/toluene are shown in Fig. 15.4. Three percent of THF in toluene assured a reasonable SEC elution of PMMA. However, more chloroform was needed to obtain a good SEC elution of PMMA in mixed eluent chloroform/toluene... 

The larger macromolecules can be separated using larger particle size columns. However, the flow rate should be watched carefully. As the effective hydrodynamic size of the macromolecules may be reduced due to the deformation by shear (23). Figure 22.8 shows that the effective hydrodynamic size of a 12-15 X 10 MW polyacrylamide sample will not reach its maximum, or the size without shear, unless the flow rate is reduced to 0.01 ml/min. A... 

The basics observed in molded products are always the same only the extent of the features varies depending on the process variables, material properties, and cavity contour. That is the inherent hydrodynamic skin-core structure characteristic of all IM products. However, the ratio of skin thickness to core thickness will vary basically with process conditions and material characteristics, flow rate, and melt-mold temperature difference. These inherent features have given rise to an increase in novel commercial products and applications via coinjection, gas-assisted, low pressure, fusible-core, in-mold decorating, etc. 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

Well-defined hydrodynamic conditions, with high rate of mass transport, are essential for successful use of electrochemical detectors. Based on the Nemst approximate approach, the thickness of the diffusion layer (<5) is empirically related to the solution flow rate (U) via... 

Equation (8.64) allows the shape of the velocity profile to be calculated (e.g., substitute ytr = constant and see what happens), but the magnitude of the velocity depends on the yet unknown value for dPjdz. As is often the case in hydrodynamic calculations, pressure drops are determined through the use of a continuity equation. Here, the continuity equation takes the form of a constant mass flow rate down the tube ... 

Under realistic conditions a balance is secured during current flow because of additional mechanisms of mass transport in the electrolyte diffusion and convection. The initial inbalance between the rates of migration and reaction brings about a change in component concentrations next to the electrode surfaces, and thus gives rise to concentration gradients. As a result, a diffusion flux develops for each component. Moreover, in liquid electrolytes, hydrodynamic flows bringing about convective fluxes Ji j of the dissolved reaction components will almost always arise. 

The presence of a gas in the suspension results in an increase of the stirrer speed required to establish the state of complete suspension. The propeller usually requires a higher speed than the turbine. Furthermore, a critical volume gas flow exists above which drastic sedimentation of particles occurs. Hence, homogenisation of the suspension requires an increase of the rotational speed and/or a decrease of the gas flow rate. The hydrodynamics of suspensions with a solid fraction exceeding 0.25-0.3 becomes very complex because such suspensions behave like non-Newtonian liquids. This produces problems in the scale-up of operations. Hydrodynamics, gas hold-up, mass-transfer coefficients, etc. have been widely studied and many correlations can be found in literature (see e.g. Shah, 1991). 

Eredictions. A rotating cyhnder within a cyhnder electrode test system as been developed that operates under a defined hydrodynamics relationship (Figs. 25-15 and 25-16). The assumption is that if the rotating electrode operates at a shear stress comparable to that in plant geometry, the mechanism in the plant geometty may be modeled in the laboratory. Once the mechanism is defined, the appropriate relationship between fluid flow rate and corrosion rate in the plant equipment as defined by the mechanism can be used to predict the expected corrosion... 

Under changing flow conditions, it can be important to include some consideration of the hydrodynamic changes within the column (Fig. 3.53), as manifested by changes in the fractional dispersed phase holdup, h , and the phase flow rates, Ln and G . which, under dynamic conditions, can vary from stage to stage. Such variations can have a considerable effect on the overall dynamic characteristics of an extraction column, since variations in hn also... 

Since the vapour phase dynamics are negligible, the vapour flow rate through the column is constant from plate to plate, at the rate of V, k mol/s. The liquid flow rates Ln, and the liquid holdup on the plate, however, will vary, under changing hydrodynamic conditions in the column. The corresponding notation, for any plate n in the column, is as indicated in Fig. 3.58. 

The flow domain of TCP can be described by two dimensionless hydrodynamic parameters, corresponding to the rotational speed of the inner cylinder and the imposed axial flow rate the Taylor number, To, and the axial Reynolds number, Re, respectively ... 

This section focuses on steady and unsteady hydrodynamic modes that emerge as the rotational speed of the inner cylinder (expressed by Ta) and pressure-driven axial flow rate (scaled by Re) are varied, while the outer cylinder is kept fixed. These modes constitute primary, secondary and higher order bifurcations, which break the symmetry of the base helical Couette-Poiseuille (CP) flow and represent drastic changes in flow structure. Figure 4.4.2 presents a map of observed hydrodynamic modes in the (Ta, Re) space, and marks the domain where all of the hydrodynamic modes that interest us appear. We will return to this figure shortly. 

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