Capillary flows Stability

The onset of flow instability in a heated capillary with vaporizing meniscus is considered in Chap 11. The behavior of a vapor/liquid system undergoing small perturbations is analyzed by linear approximation, in the frame work of a onedimensional model of capillary flow with a distinct interface. The effect of the physical properties of both phases, the wall heat flux and the capillary sizes on the flow stability is studied. A scenario of a possible process at small and moderate Peclet number is considered. The boundaries of stability separating the domains of stable and unstable flow are outlined and the values of the geometrical and operating parameters corresponding to the transition are estimated. 

The capillary flow with distinct evaporative meniscus is described in the frame of the quasi-dimensional model. The effect of heat flux and capillary pressure oscillations on the stability of laminar flow at small and moderate Peclet number is estimated. It is shown that the stable stationary flow with fixed meniscus position occurs at low wall heat fluxes (Pe -Cl), whereas at high wall heat fluxes Pe > 1, the exponential increase of small disturbances takes place. The latter leads to the transition from stable stationary to an unstable regime of flow with oscillating meniscus. 

Chapter 11 consists of following Sect. 11.2 deals with the pattern of capillary flow in a heated micro-channel with phase change at the meniscus. The perturbed equations and conditions on the interface are presented in Sect. 11.3. Section 11.4 contains the results of the investigation on the stability of capillary flow at a very small Peclet number. The effect of capillary pressure and heat flux oscillations on the stability of the flow is considered in Sect. 11.5. Section 11.6 deals with the study of capillary flow at a moderate Peclet number. 

For the study of flow stability in a heated capillary tube it is expedient to present the parameters P and q as a function of the Peclet number defined as Pe = (uLd) /ocl. We notice that the Peclet number in capillary flow, which results from liquid evaporation, is an unknown parameter, and is determined by solving the stationary problem (Yarin et al. 2002). Employing the Peclet number as a generalized parameter of the problem allows one to estimate the effect of physical properties of phases, micro-channel geometry, as well as wall heat flux, on the characteristics of the flow, in particular, its stability. 

It will be noted that applying the present approximation for the analysis of the stability of capillary flow at high heat fluxes corresponding to the domain 0 < Xf < x[ is purely symbolic, since the general assumption that Pol < 1 is not valid at... 

Because the benzene derivative and nitric acid are immiscible, the impact of mixing/ distribution on slug formation was investigated. Uniform slugs of the aromatic compound/nitric acid were formed in a Y-piece [22]. The capillary attached has a stabilizing effect on the slug flow. The deviation of slug size distribution is very small (about 5%). Hence, interfacial area is nearly constant for this type of capillary flow. 

Further, the enzyme MIA was adapted to a capillary flow-injection format [55,56] as described in Section IV.C. The IC50 for 2,4-D using this approach was reduced to about 0.5 ngmL , while the cross-reactivities of interferents were again <1% (Table 5). The improvement obtained with the capillary-based assay is dramatic and promising, although long-term stability of the MIP in the capillary and reproducibility are issues that remain. 

Fig. 1 Scheme of apparatus for adsorption measurement. (1) Electromagnetic valve (2) flow stabilizer (3) needle valve (4), (6), (12) injector (5), (7) sorption pipe (8) thermal conductivity detector (9), (11) six-port valve (10) fteezing capillary (13) chromatography column (14) flame ionization detector (15) amplifier (16) electrometer (17) analog-to-digital converter (18) computer. 

The above considerations assume the absence of hydrodynamic flow. However, hydrodynamic flow may contribute to the migration of solutes. Hydrodynamic flow can be introduced unintentionally (e.g., by erroneous positioning of inlet and outlet reservoirs) or intentionally (e.g., by applying pressurized gas to the inlet or underpressurized atmosphere to the outlet) to improve flow stability, repeatability, and transfer to an off-capillary detector. The existence of additional hydrodynamic flow in the CE column cannot be ignored in some CE-MS systems. 

Other investigators have shown that extrudate irregularities also appear to occur as a result of capillary flow behavior. For example, Howells and nbow [15], who extruded molten polymer directly from tubes without an inlet region, found that irregularities occurred. Others have attributed the phenomenon to boundary slip [16]. Attempts have also been made to try to explain the phenomenon on the basis of stability theory [17] and the compressibility of the polymer melt [17]. 

Lyngaae-Jrrgensen. J. (1981) Domain stability during capillary flow of well dispersed two phases polymer blends. ACS. Org. Coat. Plast. Chem. 15. 174... 

The collapse of foam is attributed to (a) the diffusion of gas molecules from a small bubble with higher internal pressure to a large one with lower internal pressure or into the bulk gas phase surrounding the foam system, (b) coalescence of bubbles due to capillary flow that results in rupture of the lamellar film between the adjacent bubbles (usually slower than (a) and occurring even in stabilized foam system), and (c) rapid hydrodynamic drainage of liquid between bubbles that leads to rapid collapse of bubbles [35], In most nonrigid foam systems, all three mechanisms are operative simultaneously to some extent during the foam collapse process. 

We deal here with the stability of flow in a heated capillary tube when liquid is evaporating on the meniscus. The capillary, as shown in Fig. 11.1, is a straight vertical pipe with diameter d and length 1. The wall heat flux is uniform = const. The thermal conditions on the capillary inlet and outlet are ... 

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