Poiseuille gas flow in the transition regime I. Formulation of the general theory

A theoretical treatment is given of gas flow along a tube of circular cross-section for arbitrary ratio of intermolecular collision mean free path to tube radius. A general solution is obtained of the Boltzmann equation which is valid for any intermolecular collision operator. The spatial variation of this solution is exhibited explicitly and its velocity dependence is given in terms of the solution of certain integral equations.

The general formulae given in the previous paper are investigated in detail using a simple relaxation-time approximation for the collision operator, and numerical results are obtained for the total gas flow through a capillary tube at various values of the ratio of tube radius to collision mean free path. For all values of this ratio, the results obtained agree with experiment to within about 2%.


A theoretical treatment is given of heat flow at low temperatures in liquid helium, contained in a tube of circular cross-section. Results are obtained for arbitrary ratio of phonon–phonon collision mean free path to tube radius, and agree with experiment to within a few parts per cent.


2006 ◽  
Vol 963 ◽  
Author(s):  
Goutam Koley ◽  
Zhihua Cai

ABSTRACTGaN nanostructure synthesis was done in a quartz tube furnace using ammonia and liquid Ga as precursors, and hydrogen as the carrier gas. Ni nanoparticles formed due to annealing, has been used as the catalyst layer, facilitating vapor-liquid-solid growth of the nanostructures. The growth process resulted in the formation of two types of structures, straight nanowires, and irregular growth sometimes resulting in nanospirals. Growth using uniform distribution of catalyst over the entire surface resulted in growth of straight nanowires, while growth performed on catalyst patterned surface resulted in growth of nanospirals. The diameter of the nanowires varied from 20 – 100 nm, while for spirals the cross-sectional diameters were found to be in the range of 100 nm – 1 micron, and spiral diameters in the range of several microns. Using the present growth system and gas flow set-up, it was possible to synthesize ultra-long nanowires and spirals, with overall lengths exceeding 70 microns. The regular straight nanowires were found to have a smooth circular cross-section, while the irregular wires and nanospirals were found to have a very rough surface with approximate hexagonal or triangular cross-sections. Some of the spirals changed into straight nanowires with uniform triangular cross-sections. While more investigations are required to fully establish their structures, based on preliminary characterization and past studies, we conclude that the nanowires with circular cross-sections grow along the c-direction [0001], while the spirals and consequent triangular cross-section nanowires grow along one of the non-polar directions. The formation of spirals themselves may be related to the polarization properties of GaN, similar to those predicted for ZnO nanosprings and nanoribbons.


1982 ◽  
Vol 116 ◽  
pp. 393-409 ◽  
Author(s):  
D. Weihs ◽  
I. Frankel

The cross-section shape and stability of a liquid cylinder moving perpendicularly to its axis in a gaseous medium is studied. Such liquid cylinders are formed during the break-up process of thin, rapidly moving liquid sheets, appearing in spray and atomization processes. The equilibrium shape is affected mainly by two factors: the dynamic-pressure distribution in the gas flow and the surface tension on the liquid boundary. The former tends to distort the liquid cross-section into an oval shape while the latter tends to restore the circular cross-section.A series expansion for the shape of the cylinder cross-section was determined by assuming incompressible potential flow, neglecting the effects of body forces and internal circulation in the liquid.The stability analysis shows that in the range of low Weber numbers the cylinder break-up is due to the divergence of varicose perturbations. The wavenumber of the most rapidly growing perturbation, its rate of growth and the maximal wavenumber for which varicose instability occurs, are all found to decrease as the Weber number grows, owing to a pressure distribution caused by the varicose distortion, which tends to reduce these perturbations.


1973 ◽  
Vol 95 (1) ◽  
pp. 52-58
Author(s):  
W. G. Rieder ◽  
D. R. Haworth

A generalized approach based on a model of the Boltzmann equation is suggested for predicting velocity profiles and gas flow rates through trapezoidal microgaps. Sample results are given for selected trapezoidal, rectangular, square, and circular cross section passages for Knudsen numbers ranging from 0.1 to about 10. Comparison of predicted flow rates for rectangular passages with available empirical data seems to indicate that where passage size is characterized by a single dimension, a simple across-channel measurement is inappropriate. While relative velocity profiles are independent of this value, flow rates are not. Accuracy of predictions may be enhanced by matching with analytical or empirical results for similar geometries of larger size. A flow rate from the low Knudsen number end of the transition regime is matched with one from the overlapping region of the slip-flow regime and an arbitrary adjustment is made in the characterization of passage size. This adjustment can then be incorporated into the results throughout the transition regime.


Energetika ◽  
2018 ◽  
Vol 64 (2) ◽  
Author(s):  
Igor Kuzmenko ◽  
Alexandre Gourjii

The problem of the axisymmetric laminar flow of a two-phase (liquid-gas) flow inside the infinite system of coaxial tubes with a circular cross-section located vertically is considered. Analysis of the analytical solution showed that increase in velocity of the gas flow leads to the appearance of the hold-up regime (then the velocity of media at the interface is zero) and flooding regime (when volume flow of liquid is zero). It is discovered that these regimes occur at lower values of the velocity of the gas flow for the heated medium in comparison with the cold medium.


AIChE Journal ◽  
2016 ◽  
Vol 62 (8) ◽  
pp. 2893-2901 ◽  
Author(s):  
Wenxi Ren ◽  
Gensheng Li ◽  
Shouceng Tian ◽  
Mao Sheng ◽  
Xin Fan

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner


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