The influence of nano-particle tracers on the slip length measurements by microPTV

Direct measurement of slip length is based on the measured fluid velocity near solid boundary. However, previous micro particle image velocimetry/particle tracking velocimetry （microPIV/PTV） measurements have reported surprisingly large measured near-wall velocities of pressure-driven flow in apparent contradiction with the no-slip hy-pothesis and experimental results from other techniques. To better interpret the measured results of the microPIV/PTV, we performed velocity profile measurements near a hy-drophilic wall （z = 0.25-1.5 μm） with two sizes of tracer particles （φ 50 nm and φ200 nm）. The experimental results indicate that, at less than 1 μm from the wall, the deviations between the measured velocities and no-slip theoretical values obviously decrease from 93% of φ200 nm particles to 48% of φ50 nm particles. The Boltzmann-like exponential measured particle concentrations near wall were found. Based on the non linear Boltzmann distribution of particle concentration and the effective focus plane thickness, we illustrated the reason of the apparent velocity increase near wall and proposed a method to correct the measured velocity profile. By this method, the deviations between the corrected measured velocities and the no-slip theoretical velocity decrease from 45.8% to 10%, and the measured slip length on hy-drophilic glass is revised from 75 nm to 16 nm. These results indicated that the particle size and the biased particle concentration distribution can significantly affect near wall velocity measurement via microPIV/PTV, and result in larger measured velocity and slip length close to wall.

Minimal Length Quantum Mechanics of Dirac Particles in Noncommutative Space

We study the two-dimensional harmonic oscillator in commutative and noncommutative space within the framework of minimal length quantum mechanics for spin-l^2 particles. The energy spectra and the eigenfunction are obtained in both cases. Special cases are also deduced.

Heat and mass transfer study in fluidized bed granulation-Prediction of entry length

Fluidized bed granulation is a process by which granules or coated particles are produced in a single piece of equipment by spraying a hinder as solution, suspension, or melt on the fluidized powder bed. Heat and mass transfer correlation useful for designing a granulator has been derived based on the equivalence of evaporation rate of the liquid to the heat transferred from hot gas to particles： （m/A）Dp^2λ/Lmf（1-εmf）（Tg-Tl）Kg=hDp/Kg.This equation is applied to data on granulation experiments by different workers to calculate Reynolds number and Nusselt number to obtain a relation between heat and mass transfer from gas to particles during granulation on a logarithmic scale from which the following empirical relation is obtained： Nu=0.0205Re^1.3876 which is comparable to Kothari＇s correlation Nu=0.03Re^1.3.By using the heat and mass transfer correlation obtained, the entry length, that is the length of granulator up to which effective heat transfer from gas to bed particles takes place, is estimated, which is also validated with experimental study. The correct estimation of entry length is useful in optimal design of a granulator.