Two-phase capillary flow

The quasi-one-dimensional model of laminar flow in a heated capillary is presented. In the frame of this model the effect of channel size, initial temperature of the working fluid, wall heat flux and gravity on two-phase capillary flow is studied. It is shown that hydrodynamical and thermal characteristics of laminar flow in a heated capillary are determined by the physical properties of the liquid and its vapor, as well as the heat flux on the wall. 

The quasi-one-dimensional model of flow in a heated micro-channel makes it possible to describe the fundamental features of two-phase capillary flow due to the heating and evaporation of the liquid. The approach developed allows one to estimate the effects of capillary, inertia, frictional and gravity forces on the shape of the interface surface, as well as the on velocity and temperature distributions. The results of the numerical solution of the system of one-dimensional mass, momentum, and energy conservation equations, and a detailed analysis of the hydrodynamic and thermal characteristic of the flow in heated capillary with evaporative interface surface have been carried out. 

Peles el al. (2000) elaborated on a quasi-one-dimensional model of two-phase laminar flow in a heated capillary slot due to liquid evaporation from the meniscus. Subsequently this model was used for analysis of steady and unsteady flow in heated micro-channels (Peles et al. 2001 Yarin et al. 2002), as well as the study of the onset of flow instability in heated capillary flow (Hetsroni et al. 2004). 

Weislogel MM, Lichter S (1998) Capillary flow in an interior corner. 1 Eluid Mech 373 349-378 Wu PY, Little WA (1984) Measurement of the heat transfer characteristics of gas flow a fine channels heat exchangers used for microminiature refrigerators. Cryogenics 24 415 20 Xu X, Carey VP (1990) Film evaporation from a micro-grooved surface an approximate heat transfer model and its comparison with experimental data. J Thermophys 4(4) 512-520 Yarin LP, Ekelchik LA, Hetsroni G (2002) Two-phase laminar flow in a heated micro-channels. Int J Multiphase Flow 28 1589-1616... 

Figure 4.51 Liquid/liquid two-phase plug-flow with plugs of nitrating agent (dark) and organic phase (white) in a capillary micro reactor [94].

From the beginning of the 1980s, some effective experimental approaches based on new principles have been invented for the study of interfacial reactions in solvent extraction chemistry. Recently, some methods were developed from our laboratory, the highspeed stirring (HSS) method [4,5], the two-phase stopped flow method [6], the capillary plate method [7], the reflection spectrometry [8], and the centrifugal liquid membrane (CLM) method [9]. 

Recently, the micro-two-phase sheath flow method (Figure 10.3) has been invented. Fast interfaeial reactions, which proceeded in less than 1 millisecond, were measured using this method, coupled with fluorescence microspectroscopy. An inner organic micro-flow was generated in the aqueous phase flowing from the tip of a capillary (i.d.. 

The measurement of fast interfacial reactions is very difficult, since the reaction has started just after contact of the two phases. The HSS method could measure a reaction several seconds after the contact, and the two-phase stopped-flow method could measure the reaction in the range from a few tenths of a millisecond to several hundred milliseconds. The micro two-phase sheath flow method can measure reactions as fast as < 1 ms [10]. A schematic drawing of the laser-induced fluorescence measurement in the sheath flow system is shown in Fig. 3. An inner organic phase and an outer aqueous phase flow with the same line velocity. The fluorescence at the interface is observed as a function of the distance from the end of the fused-silica capillary. The distance is converted into time. 

Payers, F.J., and Sheldon, J.W., The Effect of Capillary Pressure and Gravity on Two-Phase Fluid Flow in a Porous Medium, Petroleum Transactions, AIME, Vol. 216, 1959, pp. 147-155. 

Vapor Pressure. The Shiley Infusaid implantable infusion pump utilizes energy stored in a two-phase fluorinated hydrocarbon fluid. The pump consists of a refillable chamber that holds the dmg and a chamber that holds the fluid. The equiUbrium vapor pressure of the fluid, a constant 60 kPa (450 mm Hg), compresses the bellows, pumping the dmg through a bacterial filter, a capillary flow restrictor, and an infusion cannula to the target body site (56,116). 

It is clear that the separation ratio is simply the ratio of the distribution coefficients of the two solutes, which only depend on the operating temperature and the nature of the two phases. More importantly, they are independent of the mobile phase flow rate and the phase ratio of the column. This means, for example, that the same separation ratios will be obtained for two solutes chromatographed on either a packed column or a capillary column, providing the temperature is the same and the same phase system is employed. This does, however, assume that there are no exclusion effects from the support or stationary phase. If the support or stationary phase is porous, as, for example, silica gel or silica gel based materials, and a pair of solutes differ in size, then the stationary phase available to one solute may not be available to the other. In which case, unless both stationary phases have exactly the same pore distribution, if separated on another column, the separation ratios may not be the same, even if the same phase system and temperature are employed. This will become more evident when the measurement of dead volume is discussed and the importance of pore distribution is considered. 

The quasi-one-dimensional model of two-phase flow in a heated capillary slot, driven by liquid vaporization from the interface, is described in Chap. 8. It takes... 

Serizawa et al. (2002) studied experimentally, through visualization, the two-phase flow patterns in air-water two-phase flows in round tubes. The test section for air-water experiments consisted of a transparent silica or quartz capillary tube with circular cross-section positioned horizontally. The two-phase flow was realized through a mixer with different designs, as shown in Figs. 5.4 and 5.5. The air was injected into the mixer co-axially while water was introduced peripherally. 

As demonstrated in Fig. 5.7, the result indicates that two-phase flow patterns observed in a 100 pm quartz tube are almost similar to those observed in a 25 pm silica capillary tube with several exceptions. One such exceptions is that in slug flow encountered at low velocities, small liquid droplets in a gas slug stick to the tube wall (Fig. 5.8). This fact is evidence that no liquid film exisfs befween fhe gas slug and the tube wall. 

Two-phase flow characteristics of capillaries are known to be significantly different from the characteristics of larger channels, and consequently the existing vast literature associated with the phenomenology of change-of-phase heat transfer and two-phase flow hydrodynamic processes generally do not apply to capillaries. 

Barajas AM, Panton RL (1993) The effect of contact angle on two-phase flow in capillary tubes. Int J Multiphase Flow 19 337-346... 

Fukano T, Kariyasaki A (1993) Characteristics of gas-liquid two-phase flow in a capillary. Nucl Eng Des 141 59-68... 

Morris SJS (2003) The evaporating meniscus in the channel. J Fluid Mech 494 297-317 Peles YP, Yarin LP, Hetsroni G (2000) Thermohydrodynamic characteristics of two-phase flow in a heated capillary. Int J Multiphase Flow 26 1063-1093 Peles YP, Yarin LP, Hetsroni G (2001) Steady and unsteady flow in a heated capfllary. Int J Multiphase Flow 27 577-598... 

Chapter 9 consists of the following in Sect. 9.2 the physical model of two-phase flow with evaporating meniscus is described. The calculation of the parameters distribution along the micro-channel is presented in Sect. 9.3. The stationary flow regimes are considered in Sect. 9.4. The data from the experimental facility and results related to two-phase flow in a heated capillary are described in Sect. 9.5. 

The development of the two-phase flow in a heated capillary at different Peclet number is illustrated in Fig. 9.13. It shows that different mechanisms of two-phase flow formation may occur depending on the value of Peu. At small Pcl the fine bubble formation (on the micro-channel wall) plays a dominant role. Growth of these bubbles leads to a blockage of the micro-channel, to a sharp change of the hydraulic... 

Peles YP, Yaiin LP, Hetsroni G (1998) Heat transfer of two phase flow in a heated capillary, Heat Transfer 1998. In Proceedings of the 11th International Heat Transfer Conference, Kyongju, Korea, 23-28 August 1998, vol 2... 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

In a steady state two-phase flow in a heated capillary, there is the balance of forces, which act on the liquid and its vapor. The analysis of this balance shows that there are two stable states of the flow. They correspond to the different locations of the meniscus, which separates the liquid and the vapor. The existence of such states... 

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