Micro laminar flow mixing

M 39] [P 37] Using an azo-type competitive reaction, the mixing efficiency could be determined via the selectivity [41]. Using a P-type micro mixer, laminar flow mixing could be investigated (see Figure 1.104). The selectivities measured are far from the ideal behavior of a tubular reactor. 

Separation layer mixers use either a miscible or non-miscible layer between the reacting solutions, in the first case most often identical with the solvent used [48]. By this measure, mixing is postponed to a further stage of process equipment. Accordingly, reactants are only fed to the reaction device, but in a defined, e.g. multi-lamination-pattem like, fluid-compartment architecture. A separation layer technique inevitably demands micro mixers, as it is only feasible in a laminar flow regime, otherwise turbulent convective flow will result in plugging close to the entrance of the mixer chamber. 

P 24] Computer simulations were carried out using the software Fluent 6 [68], A 3-D solid model of the T-channel micro mixer was built and named in Gambit The simulations were made solely for the zone of the T-junction, since for all other zones, including the downstream section of the mixing channel, laminar flow was assumed. Thus, a fine mesh of 173 000 brick elements could be used for the solid model. 

The separation-layer technique benefits from the unique feature of micro mixers, such as to operate in a laminar flow regime [135], By the absence of convective recirculation patterns, at least close to the inlet, the separation layer remains as a barrier between the solution to be mixed, as long as it is not passed by molecules owing to diffusive transport. 

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. 

In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. 

The basic unit operation on the pressure driven laminar flow platform is the contacting of at least two liquid streams at a microfluidic channel junction (see Fig. 7). This leads to controlled difflisional mixing at the phase interface, e g. for initiation of a (bio-) chemical reaction [105]. It can also be applied for the lateral focusing of micro-objects like particles or cells in the channel [95]. The required flow focusing channel network consists of one central and two S5munetric side channels, connected at a junction to form a common outlet channel. By varying the ratio of the flow rates, the lateral width of the central streamline within the common outlet channel can be adjusted very accurately. Consequently, micro-objects suspended in the liquid flowing... 

In a vortex-free laminar flow, there is no concentration gradient in the direction of the flow, so the convection term in this equation is zero. The introducing of the vortex in the micro flow is able to enhance mixing by inducing convection mixing (Fig. 6). This application has been proved and utilized in many research and literatures [4, 5]. 

N. Kockmann, S. Dreher, P. Woias, Unsteady laminar flow regimes and mixing in T-shaped micromixers. Technical Paper, ASME 5th International Conjerence on Nano-, Micro- and Minichannels, Puebla, Mexico, 2007, ICNMM2007-30041. 

It is well known that the flow within micro-channels is restricted to diffusive mixing under laminar flow conditions. Based on Pick s law, the relationship between the travel distance (L) of a molecule by diffusion and time (t) can be simplified as L = (2D tf where D is the diffusion coefficient. 

Mixing is a crucial process in many micro- and nanofluidic systems. Despite the small length scales involved, molecular diffusion alone is often insufficient to rapidly produce a uniform mixture. The small length scales also make it inpractical to produce turbulent flow, which is typically used to mix rapidly in macroscale systems. Special consideration has thus been given to the design of smaU-scale devices that rapidly mix fluid under laminar flow conditions. A key requirement of this development is the ability to consistently quantify the degree to which fluid is mixed in a device by a given protocol. 

Sometimes micro mixing in the continuous phase is important. This also acts on the intermediate scale eddies or "striations" (in laminar flow) with significant concentration differences will usually have a "thickness" that is also on the order of 10 to 10 m. 

Under laminar conditions all mixing processes are much slower, but relatively speaking, the micro- mixing is slowed down most, since there is no turbulence (mechanism c is absent). /Jso in laminar flow, the mixing of the feed with the reactor contents usually is the critical factor. It is customary to indicate both mixing processes with die term micro-mixing. 

As was pointed out on p. 60, micro- and meso-mixing are not really different processes in laminar flow. We will consider them as one. 

Micro-mixing is often a relatively slow process in the diffusion equation the characteristic path length is the average striation thickness 8 in the laminar flow, so that the diffusion time should be (see eq. (4.8)) ... 

Note the similarity between eq. (4.18) and eq. (4.12), for the meso-mixing time in turbulent flow. In laminar flow, meso- and micro-mixing are identical. So we see that the ratio of meso-mixing times in laminar and turbulent flow in the same stirred vessel with the same power input can be estimated from... 

The micro-mixing time may be equal to the diffusion time needed to equalize concentrations on the scale of the smallest eddies (in turbulent flow) or the striations (in laminar flow), see s. (4.8) and (4.16). However, with sufficiently intense turbulence, or in vigorously stirred viscous media, the micro-mixing times may be completely determined by rapid deformation of small liquid elements. The micro-mixing time may then be equal to the "engulfment time" in turbulent flow, or the "deformation time" in laminar flow see equations (4.10 and (4.19). Micro-mixing times in turbulent flow are generally on the order of 10 to 1 s, and in laminar flow they can be anywhere between 10 and 10 s. 

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