Capillaries heated

Thermospray interface. Provides liquid chromatographic effluent continuously through a heated capillary vaporizer tube to the mass spectrometer. Solvent molecules evaporate away from the partially vaporized liquid, and analyte ions are transmitted to the mass spectrometer s ion optics. The ionization technique must be specified, e.g., preexisting ions, salt buffer, filament, or electrical discharge. 

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... 

Chapter 10 deals with laminar flow in heated capillaries where the meniscus position and the liquid velocity at the inlet are unknown in advance. The approach to calculate the general parameters of such flow is considered in detail. A brief discussion of the effect of operating parameters on the rate of vaporization, the position of the meniscus, and the regimes of flow, is also presented. 

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. 

Hetsroni G, Gurevich M, Mosyak A, Rozenblit R (2003) Surface temperature measurement of a heated capillary tube by means of an infrared technique. Meas Sci Technol 14 807-814 Hetsroni G, Gurevich M, Mosyak A, RozenbUt R (2004) Drag reduction and heat transfer of surfactants flowing in a capillary tube. Int J Heat Mass Transfer 47 3797-3809 Hetsroni G, Mosyak A, Pogrebnyak E, Yaiin LP (2005) Eluid flow in micro-channels Int J Heat Mass Transfer 48 1982-1998... 

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. 

For a while now, the problem of flow and heat transfer in heated capillaries has attracted attention from a number of research groups, with several applications to engineering. The knowledge of the thermohydrodynamic characteristics of capillary flow with evaporative meniscus allows one to elucidate the mechanism of heat and mass transfer in porous media, to evaluate the efficiency of cooling system of electronic devices with high power density, as well as to optimize MEMS. 

The flow in a heated capillary depends on a number of parameters including the channel geometry, physical properties of the liquid and the heat flux. An immediate consequence of the liquid heating and evaporation is convective motion of both phases. The latter leads to a velocity and temperature field fransformation and a change in fhe meniscus shape. 

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). 

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. 

Chapter 8 consists of the following in Sect. 8.2 the physical model of the process is described. The governing equations and conditions of the interface surface are considered in Sects. 8.3 and 8.4. In Sect. 8.5 we present the equations transformations. In Sect. 8.6 we display equations for the average parameters. The quasi-one-dimensional model is described in Sect. 8.7. Parameter distribution in characteristic zones of the heated capillary is considered in Sect. 8.8. The results of a parametrical study on flow in a heated capillary are presented in Sect. 8.9. 

A capillary system is said to be in a steady-state equilibrium position when the capillary forces are equal to the hydrostatic pressure force (Levich 1962). The heating of the capillary walls leads to a disturbance of the equilibrium and to a displacement of the meniscus, causing the liquid-vapor interface location to change as compared to an unheated wall. This process causes pressure differences due to capillarity and the hydrostatic pressures exiting the flow, which in turn causes the meniscus to return to the initial position. In order to realize the above-mentioned process in a continuous manner it is necessary to carry out continual heat transfer from the capillary walls to the liquid. In this case the position of the interface surface is invariable and the fluid flow is stationary. From the thermodynamical point of view the process in a heated capillary is similar to a process in a heat engine, which transforms heat into mechanical energy. 

As already mentioned, the system ofEqs. (8.1-8.5) is supplemented by the Clausius-Clapeyron equation, as well as by the correlation that determines the dependence of enthalpy on temperature and describes the thermohydrodynamical characteristics of flow in a heated capillary. It is advantageous to analyze parameters of such flow to transform the system of governing equations to the form that is convenient for significant simplification of the problem. 

From the frame of the quasi-one-dimensional model it is possible to determine the hydrodynamic and thermal characteristics of the flow in a heated capillary, accounting for the influence of the capillary force. 

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. 

The velocity, pressure and temperature distribution in a heated capillary with evaporative interface surface are determined by the following parameters ac-... 

The vapor pressure, density and temperature practically do not change along the evaporation region in physieally realistic systems. The latter allows one to simplify the system of governing equations and reduce the problem to a successive solution of the shortened system of equations to determine the velocity, liquid pressure and gaseous phases as well as the interface shape in a heated capillary. 

Carey VP (1992) Liquid-vapour phase-change phenomena. Hemisphere, Washington, DC Collier SP (1981) Convective boiling and condensation. McGraw-Hill, New York Ha JM, Peterson GP (1998) Capillary performance of evaporation flow in micro grooves an analytical approach for very small tilt angles. ASME J Heat Transfer 120 452 57 Hetsroni G, Yarin LP, Pogrebnyak E (2004) Onset of flow instability in a heated capillary tube. Int J Multiphase Flow 30 1424-1449... 

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. 

Fig. 9.2 The velocity, temperature and pressure distributions along the axis of a heated capillary (A = w, T, P), G and L correspond to vapor and liquid domains, respectively. Solid line indicates the liquid domain, and dotted line indicates the vapor domain (concave meniscus). Reprinted from Peles et al. (2001) with permission...

Taking into account the above-mentioned factors it is possible to present the stationary flow in a heated capillary as a flow of liquid and its vapor divided by an infinitely thin evaporation front. The parameters of these flows are related to each other by the condition of mass, momentum and energy conservation at the evaporation front. 

To describe the flow in a horizontal heated capillary we use the mass, momentum and energy balance equations. At moderate velocity, the effects due to compressibility of liquid and vapor, as well as energy dissipation in gaseous and liquid phases are negligible. Assuming that thermal conductivity and viscosity of the vapor and the liquid are independent of temperature and pressure, we arrive at the following system of equations ... 

Equation (9.62) contains seven dimensionless parameters accounting for the hydrodynamic and thermal effects. The regimes in which stable flows in a heated capillary are possible correspond to the following interval of the length Zp 0 < Zp < 1. The latter allows us to use Eq. (9.62) to define the domains of the existence of stable and unstable flow regimes. In the multi-dimensional parametric space (Z, i9p Pep Ja Ts ki. c < pL.g) the limiting values of these parameters corre-... 

Consider some particular cases, which are of interest to the understanding of the general flow properties in a heated capillary. First, we examine a simple case when the Peclet number is much less than unity. Since Zl < 1, the assumption Pcl 1 corresponds to the condition Pcl l C 1. In this case Eq. (9.62) reduces to... 

The domain of the stable flow is located to the right of the boundary PeL(i ) (the shaded region in the graph). To the left of this curve is the domain in which stable flows in a heated capillary cannot occur. From the relation between the parameters and Ja, the parametric plane Pep — may be subdivided into two domains (1) < Ja, and (2) > Ja. Within the first of these the stable flows cannot occur... 

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... 

The experimental investigation of the flow in a heated capillary shows that, depending on the value of the Peclet number, various types of the process occurred. At small Pcl, the dominant role is the bubble formation at the channel wall, whereas for Pcl > 1, liquid evaporation leads to formation of an evaporation front. 

Fig. 9.14 Unsteady flow in a heated capillary Dl = 0.3, Ja = 1.83, PeL = 598. Reprinted from Peles et al. (2001) with permission...

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... 

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