Fluidic density

The specificity of DFT treated for BEC implies functionals of the couple [p(r),T (r)] in terms of the overall super-fluidic density p(r) and of the order parameter T (r), both defined through the 7V-particles ensemble statistical average (Vetter, 1997 Putz, 2011b-c, 2012c)... 

A similar situation is observed in the case of the cation-radical derived from dimethylhexa-phenyl diphosphafnlveninm dication as a resnlt of redaction of the latter by the sodinm salt of the naphthalene anion-radical (Biaso et al. 2006). According to ESR, x-ray experimental data, and results of DFT calculations, the diphosphafnlveninm cation-radical detains the excess electron density within the exocyclic double bond (see Scheme 3.41). Stabilization is gained by conjngation with the two pentavalent phosphorus atoms. Biaso et al. (2006) rationalize the electronic strnctnre throngh two valence-isomeric fluidic forms of the distonic type. 

Conversely, in a piezoelectric inkjet (PIJ) head, the deflection of a membrane drives ink through each nozzle — schematics of the various configurations used in PIJ heads can be found elsewhere. The timescale for PIJ drop ejection is similar to that in a TIJ head (Fig. 1), thus, both are capable of firing 10000 to 30000 drops from a nozzle each second. Typical nozzle diameters d = 10—50 fxm), ink viscosities ( 7 = 1—5 centipoise), ink surface tensions (a = 20—50dyne/cm), and ink densities (p = 0.9—l.lg/ml) are fairly similar for the TIJ and PIJ printers for office and home use. The resulting key fluidic parameters for such print heads are summarized in Table 2. 

High-Density Plates, Microarrays, Micro fluidics 217... 

Fortunately, it is found possible also to apply the methods of microelectronics to, for example, mechanics, optics, fluidics, and, finally, chemistiy or biochemistiy. Systems may thus be designed with extreme functional density and powered at costs which do decrease by orders of magnitude year by year. The recognition of this prospect was the main reason why methods of manufacturing micro-patterns were devised, and these micro-patterns were combined in micro-systems. Thus, one may state that microelectronics should be considered as the source from wliich micro-systems engineering sprung. From the start it was clear that, even though a... 

Structure, channel surface, and fluidic property, which could affect the focusing process. In this respect, Lee et al. [99] proposed a similar model in which the effect of the density of the different fluids is taken into account. Moreover, Wu and Nguyen [100] presented a more complex method that considered the effect of the different viscosities of the sample stream and sheath streams. 

Microfluidics handles and analyzes fluids in structures of micrometer scale. At the microscale, different forces become dominant over those experienced in everyday life [161], Inertia means nothing on these small sizes the viscosity rears its head and becomes a very important player. The random and chaotic behavior of flows is reduced to much more smooth (laminar) flow in the smaller device. Typically, a fluid can be defined as a material that deforms continuously under shear stress. In other words, a fluid flows without three-dimensional structure. Three important parameters characterizing a fluid are its density, p, the pressure, P, and its viscosity, r. Since the pressure in a fluid is dependent only on the depth, pressure difference of a few pm to a few hundred pm in a microsystem can be neglected. However, any pressure difference induced externally at the openings of a microsystem is transmitted to every point in the fluid. Generally, the effects that become dominant in microfluidics include laminar flow, diffusion, fluidic resistance, surface area to volume ratio, and surface tension [162]. 

Any feature of the fluidic network whose internal volume changes with pressure acts as a fluidic capacitor, because those volume changes imply that additional mass will be stored inside the feature. This behavior can be exploited to alter the characteristic timing of flow inside a fluidic circuit (e.g., [41]). Assuming density changes are negligible, the mass flow rate can be written as... 

A solution to the problem of high throughput has been found in using the principles of fluidics - or, more importantly, microfluidics with its extreme volumetric density of internal cavities for the samples. Fluidics can accelerate the processes - in particular the insertion of the samples and reagents into the individually addressable positions - because the fluid (and also the objects the fluid carries, like living cells in... 

Consider a fluidic system with surface tension effects. The characteristic scales for length and velocity are L and U. The physical parameters are density p, viscosity v, gravity g, and surface tension y. By using the Buckingham n theorem, one can obtain three independent nondimensional groups from these six variables. An option for a set of three independent nondimensional numbers is... 

Heuberger, M., and M. Zach. 2003. Nano-fluidics structural forces, density anomalies and the pivotal role of nano-particles. Langmuir. 19 1943-1947. 

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