The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constru...The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.展开更多
Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed...Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed and solved the governing equations using explicit finite difference method and the L1- algorithm as well as shifted Grunwald-Letnikov formula. The effects of fractional parameters, relaxation parameter, Reynolds number, and unsteadiness parameter on the velocity behavior and characteristics of boundary layer thickness and skin friction were analyzed. Results obtained indicate that the behavior of boundary layer of viscoelastic fluid strongly depends on time-space fractional parameters. Increases of time fractional derivative parameter and relaxation parameter cause a decrease of velocity while boundary layer thickness increase, but the space fractional derivative parameter and fractional Reynolds number have the opposite effects.展开更多
This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely d...This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.展开更多
Nowadays, Autonomous Underwater Vehicles(AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this ...Nowadays, Autonomous Underwater Vehicles(AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this paper, the hydrodynamic coefficients of an AUV in non-dimensional depths of 0.75, 1, 1.5, 2, and 4D are obtained for movement close to the free-surface. Reynolds Averaged Navier Stokes Equations(RANS) are discretized using the finite volume approach and the water-surface effects modeled using the Volume of Fraction(VOF) method. As the operating speeds of AUVs are usually low, the boundary layer over them is not fully laminar or fully turbulent, so the effect of boundary layer transition from laminar to turbulent flow was considered in the simulations. Two different turbulence/transition models were used: 1) a full-turbulence model, the k-ε model, and 2) a turbulence/transition model, Menter's Transition-SST model. The results show that the Menter's Transition-SST model has a better consistency with experimental results. In addition, the wave-making effects of these bodies are studied at different immersion depths in the sea-surface vicinity or at finite depths. It is observed that the relevant pitch moments and lift coefficients are non-zero for these axi-symmetric bodies when they move close to the sea-surface. This is not expected for greater depths.展开更多
The inner surface modification process by plasma-based low-energy ion implantation（PBLEII）with an electron cyclotron resonance（ECR）microwave plasma source located at the central axis of a cylindrical tube is model...The inner surface modification process by plasma-based low-energy ion implantation（PBLEII）with an electron cyclotron resonance（ECR）microwave plasma source located at the central axis of a cylindrical tube is modeled to optimize the low-energy ion implantation parameters for industrial applications.In this paper,a magnetized plasma diffusion fluid model has been established to describe the plasma nonuniformity caused by plasma diffusion under an axial magnetic field during the pulse-off time of low pulsed negative bias.Using this plasma density distribution as the initial condition,a sheath collisional fluid model is built up to describe the sheath evolution and ion implantation during the pulse-on time.The plasma nonuniformity at the end of the pulse-off time is more apparent along the radial direction compared with that in the axial direction due to the geometry of the linear plasma source in the center and the difference between perpendicular and parallel plasma diffusion coefficients with respect to the magnetic field.The normalized nitrogen plasma densities on the inner and outer surfaces of the tube are observed to be about 0.39 and 0.24,respectively,of which the value is 1 at the central plasma source.After a 5μs pulse-on time,in the area less than 2 cm from the end of the tube,the nitrogen ion implantation energy decreases from 1.5 keV to 1.3 keV and the ion implantation angle increases from several degrees to more than 40°;both variations reduce the nitrogen ion implantation depth.However,the nitrogen ion implantation dose peaks of about 2×10^（10）-7×10^（10）ions/cm^2 in this area are 2-4 times higher than that of 1.18×10^（10）ions/cm^2 and 1.63×10^（10）ions/cm^2 on the inner and outer surfaces of the tube.The sufficient ion implantation dose ensures an acceptable modification effect near the end of the tube under the low energy and large angle conditions for nitrogen ion implantation,because the modification effect is mainly determined by the ion implantation dose,just as the mass transfer process in PBLEII is dominated by low-energy ion implantation and thermal diffusion.Therefore,a comparatively uniform surface modification by the low-energy nitrogen ion implantation is achieved along the cylindrical tube on both the inner and outer surfaces.展开更多
We propose an experimental setup to measure the threshold pressure gradient （TPG） of microchannels with different wettability surfaces by the static method in microchannels with diameters from 20 μm to 320 μm, and...We propose an experimental setup to measure the threshold pressure gradient （TPG） of microchannels with different wettability surfaces by the static method in microchannels with diameters from 20 μm to 320 μm, and compare the TPG of microchannels with adsorption of cetyl trimethyl ammonium bromide （CTAB） with that without CTAB adsorption. The results show the existence of TPG in microchannels. The TPG of microchannels increases with decreasing hydrodynamic diameter, and the relation between TPG and diameter is in agreement with the single-log normalization. The TPG of a microchannel with CTAB adsorption decreases obviously as compared with the microchannel without CTAB adsorption. The TPG of microchannels with different wettabilities of boundary surface are different, and the resistance of liquid flow can be reduced by changing the wettability of boundary surfaces.展开更多
We report on a first observation of a floating- spherical Hg （density 13g/cm3） drop on top of a glycerin （density 1.26g/cm3） drop, the latter is hemispherical and about four times larger in volume. This observatio...We report on a first observation of a floating- spherical Hg （density 13g/cm3） drop on top of a glycerin （density 1.26g/cm3） drop, the latter is hemispherical and about four times larger in volume. This observation is clearly against nature＇s gravity law and has never been reported before. Here we present spectacular high resolution photos that clearly demonstrate this remarkable floating phenomenon. Using milli-Q water, the Hg drop would stay down adhered at the triple line. Instead, the coincidental use of tap water displays the same phenomenon. Increasing the volume of the supporting liquid to a certain value causes the Hg drop to sink. A 5-M NaCl aqueous solution is found enough to show the same floating phenomenon. This floating mercury as a phenomenon is puzzling. On this length scale it seems that surface tension and curvature dominate over gravity.展开更多
Several methods have been used to approximate free surface boundaries in finite difference numerical simulations. Each of these methods has its advantages and disadvantages. This paper presents a new technique for th...Several methods have been used to approximate free surface boundaries in finite difference numerical simulations. Each of these methods has its advantages and disadvantages. This paper presents a new technique for the numerical solution of transient incompressible free surface fluid flows. This powerful method, which is based on the concepts of “Buoy positioning” and “Buoy relaying\', successfully represents the free surface using a Lagrangian method on a Eulerian grid by directly solving the free surface evolution equation. The Eulerian finite\|difference forms of the full Navier\|Stokes equations are solved by the Successive over Relaxation (SOR) method with a set of buoys to keep track of the free surface. The capabilities of the analysis procedure are demonstrated through viscous free surface fluid flow examples. The method is simpler and more efficient than other methods especially in treating complicated free boundary configurations.展开更多
基金One of the authors(S.M.) was financially supported by UGC New Delhi,India through the Special Assistance Programme DSA Phase-1
文摘The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell （UCM） model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration （suction） and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration （suction） and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case.
基金supported by the National Natural Science Foundation of China (51476191 and 51406008)
文摘Fractional boundary layer flow of Maxwell fluid on an unsteady stretching surface was investigated. Time-space dependent fractional derivatives are introduced into the constitutive equations of the fluid. We developed and solved the governing equations using explicit finite difference method and the L1- algorithm as well as shifted Grunwald-Letnikov formula. The effects of fractional parameters, relaxation parameter, Reynolds number, and unsteadiness parameter on the velocity behavior and characteristics of boundary layer thickness and skin friction were analyzed. Results obtained indicate that the behavior of boundary layer of viscoelastic fluid strongly depends on time-space fractional parameters. Increases of time fractional derivative parameter and relaxation parameter cause a decrease of velocity while boundary layer thickness increase, but the space fractional derivative parameter and fractional Reynolds number have the opposite effects.
基金Supported by the DST Research Project No.SR/SY/MS:521/08and CSIR,New Delhi
文摘This paper is concerned with the generation of waves due to initial disturbances at the upper surface of a two-layer fluid, as the upper layer is covered by an inertial surface and the lower layer extends infinitely downwards. The inertial surface is composed of thin but uniform distribution of non-interacting material. In the mathematical analysis, the Fourier and Laplace transform techniques have been utilized to obtain the depressions of the inertial surface and the interface in the form of infinite integrals. For initial disturbances concentrated at a point, the inertial surface depression and the interface depression are evaluated asymptotically for large time and distance by using the method of stationary phase. They are also depicted graphically for two types of initial disturbances and appropriate conclusions are made.
文摘Nowadays, Autonomous Underwater Vehicles(AUVs) are frequently used for exploring the oceans. The hydrodynamics of AUVs moving in the vicinity of the water surface are significantly different at higher depths. In this paper, the hydrodynamic coefficients of an AUV in non-dimensional depths of 0.75, 1, 1.5, 2, and 4D are obtained for movement close to the free-surface. Reynolds Averaged Navier Stokes Equations(RANS) are discretized using the finite volume approach and the water-surface effects modeled using the Volume of Fraction(VOF) method. As the operating speeds of AUVs are usually low, the boundary layer over them is not fully laminar or fully turbulent, so the effect of boundary layer transition from laminar to turbulent flow was considered in the simulations. Two different turbulence/transition models were used: 1) a full-turbulence model, the k-ε model, and 2) a turbulence/transition model, Menter's Transition-SST model. The results show that the Menter's Transition-SST model has a better consistency with experimental results. In addition, the wave-making effects of these bodies are studied at different immersion depths in the sea-surface vicinity or at finite depths. It is observed that the relevant pitch moments and lift coefficients are non-zero for these axi-symmetric bodies when they move close to the sea-surface. This is not expected for greater depths.
基金supported by National Natural Science Foundation of China(Nos.50725519,51271048,51321004)
文摘The inner surface modification process by plasma-based low-energy ion implantation（PBLEII）with an electron cyclotron resonance（ECR）microwave plasma source located at the central axis of a cylindrical tube is modeled to optimize the low-energy ion implantation parameters for industrial applications.In this paper,a magnetized plasma diffusion fluid model has been established to describe the plasma nonuniformity caused by plasma diffusion under an axial magnetic field during the pulse-off time of low pulsed negative bias.Using this plasma density distribution as the initial condition,a sheath collisional fluid model is built up to describe the sheath evolution and ion implantation during the pulse-on time.The plasma nonuniformity at the end of the pulse-off time is more apparent along the radial direction compared with that in the axial direction due to the geometry of the linear plasma source in the center and the difference between perpendicular and parallel plasma diffusion coefficients with respect to the magnetic field.The normalized nitrogen plasma densities on the inner and outer surfaces of the tube are observed to be about 0.39 and 0.24,respectively,of which the value is 1 at the central plasma source.After a 5μs pulse-on time,in the area less than 2 cm from the end of the tube,the nitrogen ion implantation energy decreases from 1.5 keV to 1.3 keV and the ion implantation angle increases from several degrees to more than 40°;both variations reduce the nitrogen ion implantation depth.However,the nitrogen ion implantation dose peaks of about 2×10^（10）-7×10^（10）ions/cm^2 in this area are 2-4 times higher than that of 1.18×10^（10）ions/cm^2 and 1.63×10^（10）ions/cm^2 on the inner and outer surfaces of the tube.The sufficient ion implantation dose ensures an acceptable modification effect near the end of the tube under the low energy and large angle conditions for nitrogen ion implantation,because the modification effect is mainly determined by the ion implantation dose,just as the mass transfer process in PBLEII is dominated by low-energy ion implantation and thermal diffusion.Therefore,a comparatively uniform surface modification by the low-energy nitrogen ion implantation is achieved along the cylindrical tube on both the inner and outer surfaces.
基金Supported by the National Natural Science Foundation of China under Grant No 10972199, and the Natural Science Foundation of Zhejiang Province under Grant No Y607425.
文摘We propose an experimental setup to measure the threshold pressure gradient （TPG） of microchannels with different wettability surfaces by the static method in microchannels with diameters from 20 μm to 320 μm, and compare the TPG of microchannels with adsorption of cetyl trimethyl ammonium bromide （CTAB） with that without CTAB adsorption. The results show the existence of TPG in microchannels. The TPG of microchannels increases with decreasing hydrodynamic diameter, and the relation between TPG and diameter is in agreement with the single-log normalization. The TPG of a microchannel with CTAB adsorption decreases obviously as compared with the microchannel without CTAB adsorption. The TPG of microchannels with different wettabilities of boundary surface are different, and the resistance of liquid flow can be reduced by changing the wettability of boundary surfaces.
文摘We report on a first observation of a floating- spherical Hg （density 13g/cm3） drop on top of a glycerin （density 1.26g/cm3） drop, the latter is hemispherical and about four times larger in volume. This observation is clearly against nature＇s gravity law and has never been reported before. Here we present spectacular high resolution photos that clearly demonstrate this remarkable floating phenomenon. Using milli-Q water, the Hg drop would stay down adhered at the triple line. Instead, the coincidental use of tap water displays the same phenomenon. Increasing the volume of the supporting liquid to a certain value causes the Hg drop to sink. A 5-M NaCl aqueous solution is found enough to show the same floating phenomenon. This floating mercury as a phenomenon is puzzling. On this length scale it seems that surface tension and curvature dominate over gravity.
文摘Several methods have been used to approximate free surface boundaries in finite difference numerical simulations. Each of these methods has its advantages and disadvantages. This paper presents a new technique for the numerical solution of transient incompressible free surface fluid flows. This powerful method, which is based on the concepts of “Buoy positioning” and “Buoy relaying\', successfully represents the free surface using a Lagrangian method on a Eulerian grid by directly solving the free surface evolution equation. The Eulerian finite\|difference forms of the full Navier\|Stokes equations are solved by the Successive over Relaxation (SOR) method with a set of buoys to keep track of the free surface. The capabilities of the analysis procedure are demonstrated through viscous free surface fluid flow examples. The method is simpler and more efficient than other methods especially in treating complicated free boundary configurations.
