scholarly journals Lagrangian Solution for an Irrotational Progressive Water Wave Propagating on a Uniform Current

2013 ◽  
Vol 30 (4) ◽  
pp. 825-845 ◽  
Author(s):  
Yang-Yih Chen ◽  
Hsuan-Shan Chen ◽  
Chu-Yu Lin ◽  
Meng-Syue Li
Keyword(s):  
Particle Velocity ◽  
Particle Motion ◽  
Particle Transport ◽  
Water Wave ◽  
Particle Trajectory ◽  
Lagrangian Solution ◽  
Transport Velocity ◽  
Motion Period ◽  
Fifth Order ◽  
Horizontal Particle

Abstract Experiments are conducted to measure the motion properties of water particle for the progressive water wave propagation in the presence of following and adverse uniform currents. The experimental data are used to validate the fifth-order Lagrangian solution from Chen and Chen. The experimental results show that the measured data of the particle motion properties such as the b line (denoted as the line connecting the positions of consecutive particles of the same b label), the particle velocity, the particle transport velocity (drift velocity), the particle trajectory, the particle motion period, and the Lagrangian mean level are in close agreement with those of the fifth-order Lagrangian solution. The study also shows that the particle label could adopt the position coordinates of the particle as if it were in still water. The motion of the b line oscillates like wave motion: its wavelength is equal to the progressive wavelength and its wave velocity obeys the Doppler effect so the sum of the velocities of the progressive wave and current, the particle motion period, the Lagrangian mean level, and the particle transport velocity less current velocity are the same as for the case of pure progressive waves. For following currents, the shape of particle trajectory depends on the horizontal particle velocity at the trajectory trough. For adverse currents, the shape of particle trajectory depends on the horizontal particle velocity at the trajectory crest. For a description of the flow motion, the Lagrangian solution could be more effective and precise than the Eulerian solution.

3D Measurements of Nano-Particle Transport in Complex 2.5D Micro-Models

2015 ◽  
Author(s):  
Jagannath Upadhyay ◽  
Daniel S. Park ◽  
Karsten E. Thompson ◽  
Dimitris E. Nikitopoulos
Keyword(s):  
Particle Velocity ◽  
Particle Transport ◽  
Three Dimensional ◽  
Laser Scanning Microscopy ◽  
Nano Particles ◽  
Confocal Laser ◽  
Nano Particle ◽  
Micro Model ◽  
Micro Particle Image Velocimetry

A confocal Micro-Particle Image Velocimetry (C-μPIV) technique along with associated post image processing algorithms is established to quantify three dimensional distributions of nano-particle velocity and concentration at the micro-scale (pore-scale) in 2.5D porous media designed from a Boise rock sample. In addition, an in-situ, non-destructive method for measuring the geometry of the micro-model, including its depth, is described and demonstrated. The particle experiments use 900 nm fluorescence labeled polystyrene particles at a flow rate of 10 nLmin−1 and confocal laser scanning microscopy (CLSM), while in-situ geometry measurements use regular microscope along with Rhodamine dye and a depth-to-fluorescence-intensity calibration. Image post-processing techniques include elimination of background noise and signal from adsorbed nano-particle on the inner surfaces of the micro-model. In addition, a minimization of depth of focus technique demonstrates a capability of optically thin slice allowing us to measure depth wise velocity in 2.5D micro-model. The mean planar components of the particle velocity of the steady-state flow and particle concentration distributions were measured in three dimensions. Particle velocities range from 0.01 to 122 μm s−1 and concentrations from 2.18 × 103 to 1.79 × 104 particles mm−2. Depth-wise results show that mean velocity closer to the top wall is comparatively higher than bottom walls, because of higher planar porosity and smooth pathway for the nano-particles closer to the top wall. The three dimensional micro-model geometry reconstructed from the fluorescence data can be used to conduct numerical simulations of the flow in the as-tested micro-model for future comparisons to experimental results after incorporating particle transport and particle-wall interaction models.

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

Exact Solitary-wave Solutions for the General Fifth-order Shallow Water-wave Models

1999 ◽  
Vol 54 (3-4) ◽  
pp. 272-274
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Solitary Wave ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Model Parameters ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Special Cases ◽  
Wave Models ◽  
Fifth Order

We perform a computerized symbolic computation to find some general solitonic solutions for the general fifth-order shal-low water-wave models. Applying the tanh-typed method, we have found certain new exact solitary wave solutions. The pre-viously published solutions turn out to be special cases with restricted model parameters.

Dielectrophoresis velocities response on tapered electrode profile: simulation and experimental

2019 ◽  
Vol 36 (2) ◽  
pp. 45-53
Author(s):  
Muhammad Izzuddin Abd Samad ◽  
Muhamad Ramdzan Buyong ◽  
Shyong Siow Kim ◽  
Burhanuddin Yeop Majlis
Keyword(s):  
Electric Field ◽  
Field Intensity ◽  
Particle Velocity ◽  
Applied Voltage ◽  
Electric Field Intensity ◽  
Particle Trajectory ◽  
Numerical Study ◽  
Time Interval ◽  
Content Type ◽  
Field Density

Purpose The purpose of this paper is to use a particle velocity measurement technique on a tapered microelectrode device via changes of an applied voltage, which is an enhancement of the electric field density in influencing the dipole moment particles. Polystyrene microbeads (PM) have used to determine the responses of the dielectrophoresis (DEP) voltage based on the particle velocity technique. Design/methodology/approach Analytical modelling was used to simulate the particles’ polarization and their velocity based on the Clausius–Mossotti Factor (CMF) equation. The electric field intensity and DEP forces were simulated through the COMSOL numerical study of the variation of applied voltages such as 5 V p-p, 7 V p-p and 10 V p-p. Experimentally, the particle velocity on a tapered DEP response was quantified via the particle travelling distance over a time interval through a high-speed camera adapted to a high-precision non-contact depth measuring microscope. Findings The result of the particle velocity was found to increase, and the applied voltage has enhanced the particle trajectory on the tapered microelectrode, which confirmed its dependency on the electric field intensity at the top and bottom edges of the electrode. A higher magnitude of particle levitation was recorded with the highest particle velocity of 11.19 ± 4.43 µm/s at 1 MHz on 10 V p-p, compared to the lowest particle velocity with 0.62 ± 0.11 µm/s at 10 kHz on 7 V p-p. Practical implications This research can be applied for high throughout sensitivity and selectivity of particle manipulation in isolating and concentrating biological fluid for biomedical implications. Originality/value The comprehensive manipulation method based on the changes of the electrical potential of the tapered electrode was able to quantify the magnitude of the particle trajectory in accordance with the strong electric field density.

Solid-particle motion in two-dimensional peristaltic flows

1976 ◽  
Vol 73 (1) ◽  
pp. 77-96 ◽  
Author(s):  
Tin-Kan Hung ◽  
Thomas D. Brown
Keyword(s):  
Reynolds Number ◽  
Solid Particle ◽  
Particle Motion ◽  
Particle Transport ◽  
Particle Displacement ◽  
Two Dimensional ◽  
Single Bolus ◽  
Highly Nonlinear ◽  
Neutrally Buoyant ◽  
Gap Width

Some insight into the mechanism of solid-particle transport by peristalsis is sought experimentally through a two-dimensional model study (§ 2). The peristaltic wave is characterized by a single bolus sweeping by the particle, resulting in oscillatory motion of the particle. Because of fluid-particle interaction and the significant curvature in the wall wave, the peristaltic flow is highly nonlinear and time dependent.For a neutrally buoyant particle propelled along the axis of the channel by a single bolus, the net particle displacement can be either positive or negative. The instantaneous force acting upon the particle and the resultant particle trajectory are sensitive to the Reynolds number of the flow (§ 3 and 4). The net forward movement of the particle increases slightly with the particle size but decreases rapidly as the gap width of the bolus increases. The combined dynamic effects of the gap width and Reynolds number on the particle displacement are studied (§ 5). Changes in both the amplitude and the form of the wave have significant effects on particle motion. A decrease in wave amplitude along with an increase in wave speed may lead to a net retrograde particle motion (§ 6). For a non-neutrally buoyant particle, the gravitational effects on particle transport are modelled according to the ratio of the Froude number to the Reynolds number. The interaction of the particle with the wall for this case is also explored (§ 7).When the centre of the particle is off the longitudinal axis, the particle will undergo rotation as well as translation. Lateral migration of the particle is found to occur in the curvilinear flow region of the bolus, leading to a reduction in the net longitudinal transport (§ 8). The interaction of the curvilinear flow field with the particle is further discussed through comparison of flow patterns around a particle with the corresponding cases without a particle (§ 9).

Theoretical Effects of Contaminant Particles on the Lubrication Considering Particle Rotation

2008 ◽  
Author(s):  
Haiyan Han ◽  
Youyun Zhang ◽  
Zhenyuan Zhong
Keyword(s):  
High Pressure ◽  
Particle Velocity ◽  
Particle Motion ◽  
Particle Rotation ◽  
Film Pressure ◽  
Minimum Film Thickness ◽  
Contaminant Particle ◽  
Lubrication Characteristics ◽  
Short Time ◽  
The Continuum

The model of a lubrication problem involving a Newtonian fluid with the contaminant particle smaller than the minimum film thickness is developed. The interaction of fluid and particle is considered in the model. The behavior of a particle in the lube oil is also studied. The lube oil is regarded as the continuum phase, and the lubrication problem is solved by the modified Reynolds equation to determine the film pressure and velocity. The dynamics of a particle in the lubricant are studied using Newton’s second law to determine the particle velocity, angular velocity and displacement. The effects of the particle motion including translation and rotation on lubrication characteristics are analyzed. The effect of relative velocity between particle and oil on the pressure is also discussed. The results indicate that the particle motion has a significant effect on the film pressure distribution. When the particle velocity is lower than the film velocity, the motion of particle causes a significant pressure increase. This high pressure only lasts a short time if the particle rotation is neglected. However, when considering the particle rotation, the high pressure will last a much longer time.

On the effect of gravitational and hydrodynamic forces on particle motion in a quiescent fluid at high particle Reynolds numbers

2008 ◽  
Vol 86 (6) ◽  
pp. 791-799
Author(s):  
M Rostami ◽  
A Ardeshir ◽  
G Ahmadi ◽  
P J Thomas
Keyword(s):  
Particle Velocity ◽  
Particle Motion ◽  
Particle Diameter ◽  
Time History ◽  
Reynolds Numbers ◽  
Added Mass ◽  
High Particle ◽  
Starting Point ◽  
History Force ◽  
The Impact

Trajectories of 5 and 10 mm metallic and plastic particles in a quiescent liquid during their sedimentation toward a plate were studied using experimental and numerical means, and the influence of gravity, drag, added mass, and history forces were evaluated. Variations of particle diameter and density allowed measurements at Reynolds numbers, based on the impact velocity, in the range of 1 000 to 13 000. A computer model was developed and the Lagrangian equation of particle motion was solved. The results showed that the combination of gravity, drag, and added mass forces are important for the simulation of the motion of small particles for the duration of their flight from the starting point to the wall impact, in the range of particle Reynolds numbers between 1000 and 5000. Comparison of the simulation results with the data showed that the predicted trajectories underestimated the experimental observations by about 1% to 4.3%. When the history force was included in the governing equation, however, excellent agreement between the measured and predicted particle trajectory was obtained. Experimental results for the motion of large particles showed oscillations in the time history of particle velocity when the particle Reynolds number was in the range of 3 000 to 13 000. Repeating the experiment, and averaging the data of a large number of experiments, yielded averaged curves for the particle velocity that did not show oscillatory values. In this case, good agreement between numerical and experimental data was observed. The study also shows that at high particle Reynolds numbers, the effect of the history force becomes negligibly small.PACS No.: 47.55kf

On the decrease of velocity with depth in an irrotational water wave

1953 ◽  
Vol 49 (3) ◽  
pp. 552-560 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Periodic Motion ◽  
Water Wave ◽  
Pressure Fluctuations ◽  
Periodic Wave ◽  
Finite Amplitude ◽  
Transport Velocity ◽  
Mean Pressure ◽  
Mass Transport Velocity ◽  
The Mean ◽  
The Waves

ABSTRACTThe following theorems are proved for irrotational surface waves of finite amplitude in a uniform, incompressible fluid:(a) In any space-periodic motion (progressive or otherwise) in uniform depth, the mean square of the velocity is a decreasing function of the mean depth z below the surface. Hence the fluctuations in the mean pressure increase with z.(b) In any space-periodic motion in infinite depth, the particle motion tends to zero exponentially as z tends to infinity. The pressure fluctuations at great depths are therefore simultaneous, but they do not in general tend to zero.(c) In a progressive periodic wave in uniform depth the mass-transport velocity is a decreasing function of the mean depth of a particle below the free surface, and the tangent to the velocity profile is vertical at the bottom. This result conflicts with observations in wave tanks, and shows that the waves cannot be wholly irrotational.(d) Analogous results are proved for the solitary wave.

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