Capillary limitation

A Viscous limit B Sonic limit C Capillary limit D Entrainment limit E Boiling limit (low T fluids) 

The capillary pressure at position jc along the heat pipe is the difference between vapor pressure and liquid pressure denoted as Pcix) = P ix) - Pi(x), where v is the vapor and / the liquid. The capillary pressure is established by the menisci that form at the interface. At the liquid-vapor interface, the Young-Laplace equation can be written as 

The capillary pressure difference at a liquid-vapor interface for most heat pipe applications is 

The values for can be found theoretically for simple geometries and experimentally for other geometries  

Cylindrical pore The capillary pressure for cylindrical pore is given as 

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In general, detectors in CE have to cope with problems of three types small mass (picogram levels) of analytes injected (due to the limitations in the volumes), which can be loaded into the capillary, limited peak volumes, and inadequately separated peaks. 

CZE is high voltage, free-solution electrophoresis carried out in a capillary. The capillary is filled with the running electrolyte (a buffer solution), and the ionic analytes are separated on the basis of the differences in their electrophoretic mobilities. The favorable ratio of surface area to volume allows the dissipation of the Joule heat from the capillary and the application of high electric fields with rapid and efficient separations. Also, the anticonvective characteristic of the capillary limits the process of zone diffusion, maintaining the efficiency of separation without the need of further anticonvective media such as gels. 

Figure 11. Capillary limit for the flat mHP with a copper sintered powder as a wick...

Figure 12.36 illustrates the relationship between the static liquid and static vapor pressures in an operating heat pipe. As shown, the capillary pressure gradient across a liquid-vapor interface is equal to the pressure difference between the liquid and vapor phases at any given axial position. For a heat pipe to function properly, the net capillary pressure difference between the wet and dry points, identified in Fig. 12.36, must be greater than the summation of all the pressure losses occurring throughout the liquid and vapor flow paths. This relationship, referred to as the capillary limitation, can be expressed mathematically as... 

Because the equations used to evaluate both the Reynolds number and the Mach number are functions of the heat transport capacity, it is necessary to first assume the conditions of the vapor flow. Using these assumptions, the maximum heat capacity qc m can be determined by substituting the values of the individual pressure drops into Eq. 12.1 and solving for qc m. Once the value of qc m is known, it can then be substituted into the expressions for the vapor Reynolds number and Mach number to determine the accuracy of the original assumption. Using this iterative approach, which is covered in more detail by Chi [9], accurate values for the capillary limitation as a function of the operating temperature can be determined in units of watt-m or watts for (qL)c m and qc m, respectively. 

Detection in CE has to face two challenging problems, namely, small amounts of analytes injected and tiny peak volumes. To the present, UV-vis detector is, by far, the most widely adopted despite the short internal diameter of the capillary limits the concentration sensitivity. Among the different modes of CE, CZE coupled with UV detection is the most widely found for the analysis of opium alkaloids in different matrices [107-111]. Nevertheless, to avoid the major disadvantage of CE related to its lack of sensitivity compared to HPLC, various approaches to this sensitivity limitation have been developed, mostly by the use of preconcentratiOTi procedures such as sweeping techniques [112, 113] or held-amplihed sample injection (FASl) [107,108]. 

Note also that a small drop vibrating in air has its wavelength necessarily fixed by its radius R, Since we are then in the capillary limit ( k), equation (5.54) enables us to deduce the dimensional form of the period r of oscillation. The result is r oc pR / y, For a millimeter-size drop, this period is of the order of a millisecond. 

Microheat pipes are subjected to the same operating limits as the conventional heat pipe. The capillary limitation is the most important operating limit of the microheat pipe. 

Capillary limit occurs when the capillary pressure is too low to provide enough liquid to the evaporator from the condenser. It leads to dryout in the evaporator. The dryout prevents continuation of thermodynamic cycle, and the heat pipe cannot function properly any more. 

Heat Pipe Failure - Failures of the heat pipes can occur from a variety of known modes, and unknown modes. The known failure scenarios for this application include micrometeoroids impacts leading to loss of fluid inventory, materials chemical stability including build up of non condensable gas and mass transport of corrosion products to the evaporator, and an over temperature (over power) leading to evaporator dry out from exceeding the heat pipes capillary limit. 

KAPL Letter SPP-SEC-0022, Evaluation of the Capillary Limit for the Northrop-Grumman Water Heat Pipe , dated July 20, 2005... 

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