Laminar mixing characterization

Hessel, V., Hardt, S Lowe, H., ScHONEELD, F., Laminar mixing in different interdigital micromixers - Part I Experimental characterization, AIChE... 

Hessel V, Hardt S, Lowe H, Schonfeld F (2003) Laminar mixing in different interdigital micromixers I. Experimental characterization. AIChE J 49(3) 566-577... 

Although the model, as well as the analytical techniques, were conceived particularly for the problem of the diffusion flame, it was clear that they would encompass both the case of slow chemistry in a vortex field and the diffusive mixing problem in general. The following work uses the vortex distortion model to study in detail the mixing of two liquids, their rapid chemical reaction and their slow chemical reaction, exhibiting those fluid mechanical features that characterize laminar mixing processes,... 

A long-standing issue in mixing theory (not only in the context of laminar mixing) has been how to characterize the state of a mixture. A largely debated issue is exactly what to measure and how to measure it. Resolving this problem is not a trivial task. 

The real power of using stretching computations to characterize chaotic flows lies in the fact that stretching is the link between the macro- and micromixing intensities in laminar mixing flows. In this section we describe the method for computing striation thickness distribution in our 3D example, the Kenics mixer. 

For laminar mixing other impellers are used, some laminar impellers are sketched in Fig. 7.4. To bring the fluid in the entire tank in motion, the diameter of these impellers usually approach the tank diameter since the laminar bulk flow is otherwise relatively low. Laminar impellers with diameter approaching the tank diameter are also called close-clearance impellers. Laminar mixers often have complex geometries, characterized by geometrical variables as the impeller diameter D, the blade width W, the pitch p, the impeller wall clearance C, and the off-bottom clearance Cb- In most applications, baffles are not needed and can in fact cause poor mixing behavior [87], Examples of laminar impellers are helical ribbons, screws, helical ribbon screws and anchor impellers. 

Impeller Reynolds Number a dimensionless number used to characterize the flow regime of a mixing system and which is given by the relation Re = pNDV/r where p = fluid density, N = impeller rotational speed, D = impeller diameter, and /r = fluid viscosity. The flow is normally laminar for Re <10, and turbulent for Re >3000. 

For an incompressible viscous fluid (such as the atmosphere) there are two types of flow behaviour 1) Laminar, in which the flow is uniform and regular, and 2) Turbulent, which is characterized by dynamic mixing with random subflows referred to as turbulent eddies. Which of these two flow types occurs depends on the ratio of the strengths of two types of forces governing the motion lossless inertial forces and dissipative viscous forces. The ratio is characterized by the dimensionless Reynolds number Re. 

The dimensionless variance has been used extensively, perhaps excessively, to characterize mixing. For piston flow, a = 0 and for a CSTR, a = l. Most turbulent flow systems have dimensionless variances that lie between zero and 1, and cr can then be used to fit a variety of residence time models as will be discussed in Section 15.2. The dimensionless variance is generally unsatisfactory for characterizing laminar flows where > 1 is normal in liquid systems. 

Laminar flow (LF) is also a form of tubular flow, and is the flow model for an LFR. It is described in Section 2.5. LF occurs at low Reynolds numbers, and is characterized by a lack of mixing in both axial and radial directions. As a consequence, fluid properties vary in both directions. There is a distribution of residence times, since the fluid velocity varies as a parabolic function of radial position. 

The bended micro channels had a width of 180 pm and a depth of 25 pm and a reduced length (25 mm) compared with the mini channels [151]. The flow in such channels was characterized at two very low Re (1.0 and 0.1) and compared with the flow in straight channels under some hydrodynamic conditions. In all four cases, undisturbed laminar flow was found. Mixing was only detectable at Re = 0.1 owing to diffusion mixing at a much prolonged residence time. At Re = 1, no mixing could be detected. 

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