Laminar power density

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. 

The intensity in turbulent flow is expressed by the power density e (the amount of energy dissipated per unit volume per unit time) for laminar flow. 

Hence the smaller the eddies, the shorter their lifetime. Moreover, smaller eddies have a higher local power density. Inside a small eddy, Re is small, hence the flow is laminar, and in laminar flow e equals >1 T2 local / will equal u (lc)/lcxl/r(lc). Eddies below a certain size cannot be formed, since the local value of e would be so high that the kinetic energy would be fully dissipated as heat. 

The dispersing effect of HP systems is related to the intense turhulence in and behind the accelerating zone, as well as to cavitation (mainly for radial difiusers and nozzles) and laminar elongation at the entrance to the dispersion unit (especially for nozzles and counter-jet dispersers). The computation of the turhulent flow field in the dispersion unit commonly requires numerical tools, in particular when the effect of cavitation is to be adequately considered. Nonetheless, it is possible to provide simple estimates for the hydrodynamic stress on the particles because the power density Py can be approximated by that of a pipe flow ... 

The power density Py is the characteristic quantity of turbulent flow. It determines the size of the smallest eddies and the intensity of microturbulence. In addition, it is a measure of the shear intensity in laminar flows or the intensity of cavitation in ultrasonic fields (see above). The power input P in the dispersion zone can be derived from the pressure drop (e.g. in pipes and nozzles) or can be measured caloricafly (e.g. for rotor-stator systems and ultrasonication Pohl 2005 Kuntzsch 2004). Additionally, P can be roughly approximated by the electric power consumption of the dispersion machine (e.g. for ultrasonication Mandzy et al. 2005 Sauter et al. 2008), even though the real values may be lower by a factor of 2 to 5. A further source of uncertainty is the volume of the dispersion zone (Vdisp). since the stress intensities are not uniformly distributed in dispersion apparatuses. In particular, this applies to agitated vessels, where the highest dissipation rates are obtained in the vicinity of the stirring instmment (Henzler and Biedermann 1996),... 

Overall, the performance of microfluidic cells in terms of power density has already reached or even exceeded the levels of comparable technologies. Performance benchmarks aside, other critical metrics related to utility also need to be addressed in order for this technology to become commercially viable, namely the efflciency/fuel utilization, co-laminar interface stability, and the stacking/scale-up solutions. Although nearly 100 % fuel utilization has been achieved [16], matching this level of efficiency with high power density is a major challenge that has not been realized to date. Further research on recirculation may potentially lead to a... 

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