Fluid lamella

Figure 2.43 Model geometry for the CFD calculations on flow in curved micro channels (above) and time evolution of two initially vertical fluid lamellae over a cross-section of the channel (below), taken from [139].The secondary flow is visualized by streamlines projected on to the cross-sectional area of the channel. The upper row shows results for fC = 150 and the lower row for K = 300.

Adjacent fluid lamellae lose their boundaries and interfere with each other, causing laminar flow to change to transitional or turbulent flow. Energy dissipation increases dramatically under these circumstances. 

Ohtsuru et al. (25) have recently investigated the behavior of phosphatidylcholine in a model system that simulated soy milk. They used spin-labelled phosphatidylcholine (PC ) synthesized from egg lysolecithin and 12-nitroxide stearic acid anhydride. The ESR spectrum of a mixture of PC (250 yg) and native soy protein (20 mg) homogenized in water by sonication resembled that observed for PC alone before sonication. However, when PC (250 yg) was sonicated in the presence of heat-denatured soy protein (20 mg), splitting of the ESR signal occurred. On this basis, they postulated the existence of two phases PC making up a fluid lamella phase and PC immobilized probably due to the hydrophobic interaction with the denatured protein. In a study of a soy-milk model, Ohtsuru et al. (25) reported that a ternary protein-oil-PC complex occurred when the three materials were subjected to sonication under the proper condition. Based on data from the ESR study, a schematic model has been proposed for the reversible formation-deformation of the ternary complex in soy milk (Figure 2). 

Figure 1.1 Skctdi of a partJlolopipod (i.e., the fluid lamella) on which various stresses are acting. The quantity Tc,g6Ap is the o-component of the force exerted on the /3-directed face of the parallelepiped. Its direction is represented by the ai rows. For the sake of clarity, only those stresses acting on the front faces are displayed.

Figure 1.4 Sketch of a fluid lamella (shaded area) whose faces in x-, y-, eind -direction can be moved independently in the direction of the double arrows. As an example we show states of the lamella differing in strain in the x-direction such that the right plot shows an expanded lamella (relative to the plot on the left side) of different width in that direction.

Figure 1.5 Sketch of a fluid lamella (shaded area) sheared in the x-direction, where a shear strsdn of osxo/2 is applied to the upper and lower substrate, respectively.

Reducing the solution of the convection-diffusion equation for the concentration field to a ID problem in the comoving frame-of-reference clearly reaches its limits if the fluid lamellae get deformed and are no longer arranged in parallel. Such a situation may occur if the channel depth is not small compared to its width and the design comprises a sudden expansion or contraction of the flow... 

Although the accurate computation of liquid-phase reactions remains difficult due to numerical issues, Aold et al. [82] performed simulations of various model reaction systems, allowing relative comparisons. In particular, they studied the effects of the width of the fluid lamellae and the rate constants on reactant conversion and product selectivity. Qualitatively, the results reveal a strong dependence of the product selectivity on the lamellar width. From these CFD simulations, a model was developed that relates lamellar width, rate constants and product selectivity for various multiple reactions and reaction conditions. 

Figure 19.5 Construction and mode of operation of the standard slit interdigital micromixer, (a) Left, upper housing with two inlets and the outlet slit in the middle center, inlay with interdigital mixing structure right, lower housing with cutout for the inlay, (b) Mixing principle fluids to be mixed flow into mixing channels, formation of a fluid lamellae and disintegration into droplets [53].

Experiments show that during collisions at high Weber numbers extremely thin fluid lamellae appear. A rupture of the lamella is not observed in binary droplet collisions at least for Weber numbers up to 2800, cf. [2, 12, 23, 30]. In contrast to this physical behavior, simulations in the literature predict the rupture of the lamella see, e.g., [18, 21, 29]. One main reason for this rupture is a low mesh resolution for the lamella. As a result, the part containing the rim remains, while the lamella breaks into many fragments see Fig. 1.1. 

Figure 7.3.21(a)). It is as if fluid lamellae (laminae) of each species located at different distances from the wall (y = 0) travel at different velocities therefore they arrive at different times at the channel end. (For a comparison, in elution chromatography (Section 7.1.5.1) different species also arrive at different times at the end of the column however, each species exists throughout the column cross section as the species peak travels. Similarly, in capillary electrophoresis (Section 6.3.1.2) species arriving at the end of the capillary at different times exist throughout the capiUaiy cross section.) This technique was first proposed hy Giddings (1966). 

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