Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.

Kinetic-theory-based investigation of electronegative plasma–wall transition with two populations of electrons

Kinetic theory has been employed to investigate the magnetized plasma-sheath structure and its characteristics in the presence of more than one species of negatively charged particles:hot electrons,cold electrons,and negative ions.The cold electrons and negative ions are considered to obey a Maxwellian distribution,whereas the hot electrons follow a truncated Maxwellian distribution.The Bohm sheath condition has been extended for the case of more than one species of negatively charged particles,in which the concentration of hot electrons has a crucial role in achieving the Bohm velocity.The thermal motion of hot electrons is much higher compared to cold electrons and negative ions,such that the variation of hot electron concentrations and the temperature ratio of hot to cold electrons play a key role in the determination of the plasma-sheath parameters:particle densities,electrostatic potential,the flow of positive ions towards the wall,and sheath thickness.We have estimated the deviation of the resultant drift velocity of positive ions on the plane perpendicular to the wall from the parallel component at the presheath–sheath interface.It is found that the deviation between the two velocity components increases with an increase in the obliqueness of the magnetic field.Furthermore,the results obtained from the kinetic trajectory simulation model are compared with the results obtained using a fluid model;the results are qualitatively similar,although the potential varies by less than 4%in terms of the magnitude at the wall.

AXIAL HEAT CONDUCTION MODEL TO PREDICT MAXIMUM HEAT REMOVE OF MINIATURE HEAT PIPE BASED ON GREY MODEL THEORY

Computer chip is always accompanied by the increase of heat dissipation and miniaturization. The miniature heat pipes are widely used in notebook computer to resolve the heat dissipation problems. Maximum heat removed model of miniature heat pipes building by grey model is presented. In order to know the foundation for modeling, the smooth grade of error examination is inquired and the accuracy of grey relational grade is verified. The model can be used to select a suitable heat pipes to solve electric heat problems in the future. Final results show that the grey model only needs four experiment data and its error value is less than 10%, further, it is better than computational fluid dynamics （CFD） model.

Experimental Investigation on Constrained Abrasive Fluid Polishing for Optical Glass

To find a cost effective,high-precision and environmental friendly way of polishing for optical glass,a series of experiments were focused on about constrained abrasive fluid polishing. Since abrasive particles can repeatedly impact the workpiece in a multidirectional way with high energy, the constrained abrasive fluid polishing method for optical glass has been proposed based on the abrasive fluid machining theory and elastic emission machining theory. A constrained abrasive fluid polishing system was designed and developed to polish K9 glass samples. Results show that K9 glass obtains a high accuracy with less fluid. Experiments indicate that,in a more effective,high-precision and environmental friendly way,constrained abrasive fluid polishing is possible to improve the quality of workpiece surface compared with free abrasive fluid polishing. In the process of removing materials of constrained abrasive fluid polishing,it gives priority to removing the materials of high spot and the high frequency error of smooth local zone can be modified. The abrasive particles can repeatedly impact the workpiece in a multidirectional way,and there are certain relationship among surface quality,material removal rate, and parameters such as speed,clearance, angle, time and particle size. In the process of constrained abrasive fluid polishing, it shows a high material removal rate,and it needn't to clamp workpieces. As a result,it could improve the processing efficiency significantly. The research on constrained abrasive fluid polishing has a practical significance and practical value in industrial production.

Interacting two-fluid viscous dark energy models in a non-flat universe

We study the evolution of the dark energy parameter within the scope of a spatially non-fiat and isotropic Friedmann-Robertson-Walker model filled with barotropic fluid and bulk viscous stresses. We have obtained cosmological solutions that do not have a Big Rip singularity, and concluded that in both non-interacting and interacting cases the non-fiat open Universe crosses the phantom region. We find that during the evolution of the Universe, the equation of state for dark energy ωD changes from ωDeff 〉 - 1 to ωDeff 〈 - 1, which is consistent with recent observations.

An Obliquely Propagating Electromagnetic Lower-Hybrid-Drift Instability in Plasmas with Negative Ions

In this study, by employing a local fluid theory for warm plasma containing negative ions, an obliquely propagating electromagnetic instability in the lower hybrid frequency range driven by cross-field currents or relative drifts between electrons and ions was investigated. It is found that the growth rate of the lower-hybrid-drift instability （LHDI） can be controlled by appropriate selection of the propagation direction, the wave number and the relative population of the negative ions.

ANALYTICAL SOLUTION OF FILLING AND EXHAUSTING PROCESS IN PNEUMATIC SYSTEM

The filling and exhausting processes in a pneumatic system are involved with many factors, and numerical solutions of many partial differential equations are always adapted in the study of those processes, which have been proved to be troublesome and less intuitive. Analytical solutions based on loss-less tube model and average friction tube model are found respectively by using fluid net theory, and they fit the experimental results well. The research work shows that： Fluid net theory can be used to solve the analytical solution of filling and exhausting processes of pneumatic system, and the result of loss-less tube model is close to that of average friction model, so loss-less tube model is recommended since it is simpler, and the difference between filling time and exhausting time is determined by initial and final pressures, the volume of container and the section area of tube, and has nothing to do with the length of the tube.

Application of binding theory for seepage of viscoelastic fluid in a variable diameter capillary

The polymer solution for polymer flooding is a viscoelastic fluid. There exist both shear flow and elongational flow when the polymer solution flows in a porous medium, where an additional dissipation is involved. The additional dissipation caused by elongational deformation is often ignored while studying the flow of the fluid in a porous medium. For a complex polymer solution, the generated elongational pressure drop cannot be ignored. In a capillary of fixed diameter, the polymer solution is only impacted by the shear force, and its rheological property is pseudoplastic. Therefore the variable diameter capillary and the converging-diverging flow model with different cross sections are required to describe the flow characteristics of the polymer solution in porous media more accurately. When the polymer solution flows through the port, we have the elongational flow and the polymer molecules undergo elongational deformation elastically. By using the mechanical energy balance principle and the minimum energy principle, a mathematical model of non-Newtonian fluid inlet flow was established by Binding. On the basis of the Binding theory, with the application of the theory of viscoelastic fluid flow in the circular capillary and the contraction-expansion tube, the relations between the viscoelastic fluid flow rate and the pressure drop are obtained.

The bulk viscous string cosmology in an anisotropic universe with late time acceleration

A model of a cloud formed by massive strings is used as a source of Bianchi type II cases. We assume that the expansion （θ） in the model is proportional to the shear （σ）. To get an exact solution, we consider the equation of state of the fluid to be in the stiff form. It is found that the bulk viscosity played a very important role in the history of the universe. In the presence of bulk viscosity the particles dominate over strings whereas in the absence of it, strings dominate over the particles, which is not consistent with recent observations. Also we observe that the viscosity causes the expansion of the universe to be accelerating. Our models are evolving from an early decelerating phase to a late time accelerating phase. The physical and geometrical behaviors of these models are discussed.

Phase Equilibrium Calculation of Mixtures: Use of the SAFT-BACK Equation of State for Binary Systems under Elevated Pressure

The statistical associating fluid theory (SAFT) Boublík Alder Chen Kreglewshi(BACK) equation of state is employed to correlate vapor liquid equilibria of 16 binary mixtures composed of supercritical fluids with other fluids at elevated pressures. The van der Waals mixing rules are used and the binary parameters are adjusted to experimental data. The SAFT BACK equation of state provides a better correlation of vapor liquid equilibrium than the original BACK equation. Consequently, the binary parameters computed from the data sets can be used to accurately predict the saturated densities of the vapor and liquid phases.

Phase Equilibrium Calculation of Mixtures: Comparison of SAFT, Modified SAFT, and BACK EOS for Supercritical CO_2-C_2H_5OH System

Three calculational models, statistical associating fluid theory (SAFT), modified SAFT, and Boublík Alder Chen Kreglewshi (BACK) are compared for supercritical CO 2 C 2H 5OH using a set of van der Waals type mixing rules for both the BACK equation of state (EOS) and the SAFT EOS. Equations are presented for the residual Helmholtz free energy, residual chemical potentials, and compressibilty factor for mixtures. A comparison with experimental vapor liquid equilibrium (VLE) data reveals that the BACK EOS together with the suggested mixing rules provides more accurate prediction of the binary system than the SAFT or the modified SAFT model with no adjustable binary parameters. The correlation results are improved with an adjustable parameter.

An Analytic Equation of State Based on SAFT-CP for Binary Non-Polar Alkane Mixtures Across the Critical Point

The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.