Reynolds number, characterization

The principal length and time scales, and Reynolds numbers characterizing a turbulent flow... 

Table 2.1. The principal length and time scales, and Reynolds numbers characterizing a fully developed turbulent flow defined in terms of the turbulent kinetic energy k, turbulent dissipation rate e, and the kinematic viscosity v. 

As mentioned earlier, Reynolds numbers determined for the bulk flow have to be discerned from Reynolds numbers characterizing a particle-liquid dissolution system. The latter were calculated for drug particles of different sizes using the Reynolds term according to the combination model. The kinematic viscosity of the dissolution medium at 37°C is about 7 x 10-03 cm2/sec. The fluid velocities (Ua) employing the paddle method at stirring rates of 50-150 rpm can be taken from the literature and may arbitrarily be used as the slip velocities at the particle surfaces. 

The Reynolds number characterizing laminar-turbulent transition for bulk flow in a pipe is about Re 2300 provided that the fluid moves unidirectionally, the pipe walls are even and behave in a hydraulically smooth manner, and the internal diameter remains constant. However, intestinal walls do not fulfill these hydraulic criteria due to the presence of curvatures, villi, and folds of mucous membrane, which are up to 8 mm in the duodenum, for instance (Fig. 18). Furthermore, the internal diameter of the small intestine is estimated to... 

The diameter of drug particles and hence the surface specific length L is much smaller than the pipe diameter. For this reason, particle-liquid Reynolds numbers characterizing the flow at the particle surface are considerably lower than the corresponding bulk Reynolds numbers. Particle-liquid Reynolds numbers for particle sizes below 250 pm were calculated to be below Re 1 for flow rates up to 100 mL/min. However, this circumstance does not limit the applicability of the boundary layer concept, since in aqueous hydrodynamic... 

Reynolds numbers calculated for the in vivo hydrodynamics are considerably lower than those of the corresponding in vitro numbers, both for bulk and particle-liquid Reynolds numbers. Remarkably, bulk Reynolds numbers in vivo appear to have about the same magnitude as particle-liquid Reynolds numbers characterizing the flow at the particle surface in vitro using the paddle apparatus. In other words, it appears that hydrodynamics per se play a relatively minor role in vivo compared to the in vitro dissolution. This can be attributed to physiological co-factors that greatly affect the overall dissolution in vivo but are not important in vitro (e.g., absorption and secretion processes, change of MMC phases,... 

The Reynolds number characterizes the flow conditions for a given geometrical arrangement on any scale. 

The Reynolds number characterizes the dynamics of the fluid flow. The Stanton number characterizes the dynamics of the heat flow. The Prandtl number characterizes the substance being heated as it flows. The Prandtl number varies from substance to substance and varies with temperature for water, Pr = 7.7 at 15°C and 1.5 at 100°C. 

The Reynolds number characterizes the relation between the inertial forces and the friction forces of the fluid flow. 

The Reynolds Number characterizes the flow properties (laminar or turbulent). L is the characteristic length length for a plate, diameter for cylinder or sphere. 

Due to the fact that the physical dimensions of the flow structures in microfluidic systems are in the micro-scale, the Reynolds numbers characterizing fluid-flow in microfluidic systems are well below the critical value for turbulence and the flow regime is, consequently, laminar (Pohar Plazl, 2008). Therefore, micromixers in microfluidic systems rely on molecular diffusion. In general, micromixers used for ionic liquid synthesis are designed in such a way that their internal flow geometries reduce diffusion distances. Some examples of micromixers used for ionic liquid synthesis are shown in Figure 3. 

The next two important parameters are the Reynolds munber and the capillary number. The Reynolds number characterizes the importance of inertial forces as compared with viscose forces. To dednce the relevant expression for the Reynolds number, let us consider the spreading of a two-dimensional droplet over a solid surface (gravity action is neglected). In this case, the Navier-Stokes equation with the incompressibihty condition takes the following form ... 

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