Interface laminar flow

Below we consider a quasi-one-dimensional model of flow and heat transfer in a heated capillary, with hydrodynamic, thermal and capillarity effects. We estimate the influence of heat transfer on steady-state laminar flow in a heated capillary, on the shape of the interface surface and the velocity and temperature distribution along the capillary axis. 

Laminar Flow in a Heated Capillary with a Distinct Interface... 

The developed theory of two-phase laminar flow with a distinct interface which is based on a one-dimensional approximation, takes into account the major features of the process the inertia, gravity, surface tension and friction forces and leads to the physically realistic pattern of a laminar flow in a heated micro-channel. This allows one to use the present theory to study the regimes of flow as well as optimizing a cooling system of electronic devices with high power densities. 

We first explain the setting of reactors for all CFD simulations. We used Fluent 6.2 as a CFD code. Each reactant fluid is split into laminated fluid segments at the reactor inlet. The flow in reactors was assumed to be laminar flow. Thus, the reactants mix only by molecular diffusion, and reactions take place fi om the interface between each reactant fluid. The reaction formulas and the rate equations of multiple reactions proceeding in reactors were as follows A + B R, ri = A iCaCb B + R S, t2 = CbCr, where R was the desired product and S was the by-product. The other assumptions were as follows the diffusion coefficient of every component was 10" m /s the reactants reacted isothermally, that is, k was fixed at... 

A significant advance in this area was recently made by Li and coworkers [30,31], who developed a laminar flow technique, that allowed the direct contact of two liquids with better-defined mass transport compared to the Lewis cell. Laminar flow of the two phases parallel to the interface was produced through the use of flow deflectors. By forcing flow parallel to, rather than towards, the interface, it was proposed that the interface was less likely to be disrupted. Reactions were followed by sampling changes in bulk solution concentrations. 

A schematic of the apparatus developed is shown in Fig. 3. Stirrers mix and push the lighter and heavier phases in each compartment, with the maximum rotation speed governed by the need to maintain the interface steady. Flow deflectors ensure that the phases are circulated in each chamber and that flow near the interface is laminar. The interfacial plate (thickness 2 mm) is rectangular with a hole at its center. The distance from the interface to the flow deflectors is less than 6 mm. The two phases are analyzed by withdrawing small volumes via sampling holes. 

Of the methodologies considered, the Lewis cell, employs direct contact of the two liquids, but does not have well-defined hydrodynamics. The constant interface cell with laminar flow has better-defined hydrodynamics, but the interfacial flux is not measured... 

The modeling of mass transport from the bulk fluid to the interface in capillary flow typically applies an empirical mass transfer coefficient approach. The mass transfer coefficient is defined in terms of the flux and driving force J = kc(cbuik-c). For non-reactive steady state laminar flow in a square conduit with constant molecular diffusion D, the mass balance in the fluid takes the form... 

This regime is characterized by the presence of two continuous fluid phases and an interface which can easily be described. The term separated flows is frequently employed to describe these situations in both horizontal and vertical systems. Some flow patterns in Regime I are advantageous for transferring heat between the tube wall and the fluid mixture or for carrying out two-phase reactions. The special case of laminar-laminar flow is included in this regime, and two studies seem to be of interest, Byers and King (B7) and Bentwich and Sideman (B3). 

Chapter 3 Diffusion Coefficients. This chapter demonstrates how to estimate the diffusion coefficients of dilute chemical concentrations in water and air. The chapter is important any time that diffusion cannot be ignored in an application of chemical transport and fate. Some of these cases would be in laminar flows, in sediment, in groundwater transport, and close to an interface in turbulent flows. 

Figure 3.3. Various features of diffusion and convection associated with crystal growth in solution (a) in a beaker and (b) around a crystal. The crystal is denoted by the shaded area. Shown are the diffusion boundary layer (db) the bulk diffusion (D) the convection due to thermal or gravity difference (T) Marangoni convection (M) buoyancy-driven convection (B) laminar flow, turbulent flow (F) Berg effect (be) smooth interface (S) rough interface (R) growth unit (g). The attachment and detachment of the solute (solid line) and the solvent (open line) are illustrated in (b).

Third, turbulent transport is represented as a succession of simple laminar flows. If the boundary is a solid wall, then one considers that elements of liquid proceed short distances along the wall in laminar motion, after which they dissolve into the bulk and are replaced by other elements, and so on. The path length and initial velocity in the laminar motion are determined by dimensional scaling. For a liquid-fluid interface, a roll cell model is employed for turbulent motion as well as for interfacial turbulence. 

When transport is not able to do its job adequately and there is a change in the interfacial concentrations of electron acceptors and donors from the bulk values, there is a variation of concentration with distance from the interface toward the bulk of the solution. What matters, however, as far as the charge-transfer reaction is concerned, is the gradient of concentration at the interface because it is this gradient that drives the diffusion flux Jjy Even when there is convection with a laminar flow of electrolyte, the transport in the (assumed) stagnant layer adjacent to the electrode is by diffusion... 

Semenov (S6) considered generally the effects of a gas drag at the film interface for all the cases listed above for smooth laminar film flow (see Section III, F, 2), and later experimental work confirmed these results (K20, K10, S7) for the case when the film thickness is very small, with no waves present on the film surface, and at moderate gas flow rates. The early treatment by Nusselt (N6, N7) also gave results in agreement with the experimental data obtained under these restricted conditions. Brauer s treatment of the problem (Section III, F, 2) (Bl8) also assumed laminar flow of the film and absence of surface waves. The experimental work of Feind (F2), which refers to countercurrent gas/film flow in a vertical tube, showed that, although such a treatment was useful in predicting the qualitative effects of the gas stream on the film thickness and other properties, the Reynolds number range in which it applied strictly was very limited. 

The rate at which ions can diffuse to the interface, and therefore. (i,n. is inversely proportional to S (the thickness of the convection free, laminar flow, diffusion layer). The latter is typically reduced by... 

The profiles in Figure 3.37B represent the situation in which a potential is applied that requires equal concentrations of O and R at the electrode surface to satisfy the Nernst equation (i.e., E = Eq R). To fulfill this requirement, the electrode electrolyzes O to R at the rate required to maintain equal concentrations of O and R at the surface. If this potential is maintained, a continuous electrolysis of O to R is necessary to maintain surface concentrations because R diffuses away from the interface across the stagnant layer and is then swept away by the laminar flow. 

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