Electrophoresis of a Cylinder in a Cylindrical Tube

2017 ◽  
Vol 22 (4) ◽  
pp. 1101-1122 ◽  
Author(s):  
Huicheng Feng ◽  
Teck Neng Wong
Keyword(s):  
Zeta Potential ◽  
Electric Double Layer ◽  
Tube Wall ◽  
Cylindrical Tube ◽  
Mixing Enhancement ◽  
Tube Radius ◽  
Bipolar Coordinates ◽  
Velocity Scale ◽  
Scale Ratio ◽  
Cylinder Rotation

AbstractElectrophoresis of a cylinder suspended in a cylindrical tube is analytically studied in the limit of thin electric double layer approximation. The electric and fluid flow fields within the annulus, and the cylinder velocities are analytically obtained in bipolar coordinates. The results are analyzed with various values of dimensionless parameters: eccentricity, cylinder-to-tube radius ratio and tube-to-cylinder zeta potential ratio (i.e., tube-to-cylinder velocity scale ratio). The analysis shows that microvortices are generated within the annulus. By changing the parameters, different flow patterns can be created, which shows potential for mixing enhancement in micro/nanofluidics. Moreover, the cylinder not only translates but also rotates when the cylinder and tube are eccentric. The cylinder rotation might be utilized as a micromotor or an electric field detector. The cylinder trajectories show that the cylinder may approach the tube wall or rest within the tube depending on the zeta potential ratio.

Physical basis of the dependence of blood viscosity on tube radius

1960 ◽  
Vol 198 (6) ◽  
pp. 1193-1200 ◽  
Author(s):  
Robert H. Haynes
Keyword(s):  
Flow Rate ◽  
Blood Viscosity ◽  
Apparent Viscosity ◽  
Hind Limb ◽  
Marginal Zone ◽  
Tube Wall ◽  
Effective Diameter ◽  
Tube Radius ◽  
Vascular Bed ◽  
A Cell

Two theories are applied to measurements of the decrease in apparent viscosity of blood in narrow tubes (Fahraeus-Lindqvist effect). First, the effect may be attributed to the presence of unsheared laminae in the fluid (sigma phenomenon), and it was found that the thickness of such laminae must vary between 3.5 µ at 10% hematocrit and 34 µ at 80%. Alternatively, the effect may be caused by a cell-free marginal zone adjacent to the tube wall, which would have to be 6 µ thick at 10% hematocrit and 1.5 µ at 80%. There is a slight suggestion in the data that the effect may be reversed as the flow rate approaches zero (i.e. the apparent viscosity rises in small tubes). Finally, a method is proposed for calculating the effective diameter of a vascular bed, and it was found to be 55 µ for a dog's hind limb.

Numerical Simulation of Heavy Particle Dispersion—Scale Ratio and Flow Decay Considerations

1994 ◽  
Vol 116 (1) ◽  
pp. 154-163 ◽  
Author(s):  
Lian-Ping Wang ◽  
David E. Stock
Keyword(s):  
Numerical Simulation ◽  
Time Scale ◽  
Dispersion Coefficient ◽  
Fluid Velocity ◽  
Heavy Particle ◽  
Particle Dispersion ◽  
Heavy Particles ◽  
Velocity Scale ◽  
Scale Ratio ◽  
Diffusivity Ratio

Lagrangian statistical quantities related to the dispersion of heavy particles were studied numerically by following particle trajectories in a random flow generated by Fourier modes. An experimental fluid velocity correlation was incorporated into the flow. Numerical simulation was performed with the use of nonlinear drag. The simulation results for glass beads in a nondecaying turbulent air showed a difference between the horizontal dispersion coefficient and vertical dispersion coefficient. This difference was related to the differences of both the velocity scale and the time scale between the two direction. It was shown that for relatively small particle sizes the particle time scale ratio dominates the value of the diffusivity ratio. For large particles, the velocity scale ratio reaches a value of 1/2 and thus fully determines the diffusivity ratio. Qualitative explanation was provided to support the numerical findings. The dispersion data for heavy particles in grid-generated turbulences were successfully predicted by the simulation when flow decay was considered. As a result of the reduction in effective inertia and the increase in effective drift caused by the flow decay, the particle dispersion coefficient in decaying flow decreases with downstream location. The particle rms fluctuation velocity has a slower decay rate than the fluid rms velocity if the drift parameter is large. It was also found that the drift may substantially reduce the particle rms velocity.

Motion of an array of drops through a cylindrical tube

1998 ◽  
Vol 358 ◽  
pp. 1-28 ◽  
Author(s):  
C. COULLIETTE ◽  
C. POZRIKIDIS
Keyword(s):  
Stokes Flow ◽  
Apparent Viscosity ◽  
Numerical Solutions ◽  
Initial Period ◽  
Mathematical Formulation ◽  
Axisymmetric Flow ◽  
Circular Cross Section ◽  
Cylindrical Tube ◽  
Boundary Integral ◽  
Tube Radius

We study the pressure-driven transient motion of a periodic file of deformable liquid drops through a cylindrical tube with circular cross-section, at vanishing Reynolds number. The investigations are based on numerical solutions of the equations of Stokes flow obtained by the boundary-integral method. It is assumed that the viscosity and density of the drops are equal to those of the suspending fluid, and the interfaces have constant tension. The mathematical formulation uses the periodic Green's function of the equations of Stokes flow in a domain that is bounded externally by a cylindrical tube, which is computed by tabulation and interpolation. The surface of each drop is discretized into quadratic triangular elements that form an unstructured interfacial grid, and the tangential velocity of the grid-points is adjusted so that the mesh remains regular for an extended but limited period of time. The results illustrate the nature of drop motion and deformation, and thereby extend previous studies for axisymmetric flow and small-drop small-deformation theories. It is found that when the capillary number is sufficiently small, the drops start deforming from a spherical shape, and then reach slowly evolving quasi-steady shapes. In all cases, the drops migrate radially toward the centreline after an initial period of rapid deformation. The apparent viscosity of the periodic suspension is expressed in terms of the effective pressure gradient necessary to drive the flow at constant flow rate. For a fixed period of separation, the apparent viscosity of a non-axisymmetric file is found to be higher than that of an axisymmetric file. In the case of non-axisymmetric motion, the apparent viscosity reaches a minimum at a certain ratio of the drop separation to tube radius. Drops with large effective radii to tube radius ratios develop slipper shapes, similar to those assumed by red blood cells in flow through capillaries, but only for capillary numbers in excess of a critical value.

Study of the Creep Deformation of Sanicro 25 Austenitic Steel by Computer Simulations

2019 ◽  
Vol 961 ◽  
pp. 156-162
Author(s):  
Tri Widodo Besar Riyadi ◽  
Fakhri Hasamulhaq Ahmad ◽  
Ibham Veza ◽  
Agung Setyo Darmawan ◽  
Agus Dwi Anggono ◽  
...  
Keyword(s):  
Experimental Data ◽  
Austenitic Steel ◽  
Power Law ◽  
Tube Wall ◽  
Cylindrical Tube ◽  
Stress And Strain ◽  
Uniform Temperature ◽  
Material Parameters ◽  
Simulation Input ◽  
Abaqus Software

The Abaqus software was used to simulate the creep behavior of a cylindrical tube of Sanicro-25 austenitic steel under an internal pressure of 11.3 MPa at a uniform temperature at 750 °C. The data used for the simulation input were obtained from the experimental data of a previous work. The hidden information of material parameters was estimated from the shape of creep strain versus time plots obtained from the experimental data. The validated results between the simulation and the experimental data produced the material parameter of the creep power law which were set at 2.6 x 10-22 for the power law constant and 9 for the stress exponent. The parameters were further used to explore the stress and strain inside and outside of the tube wall and the thickness changes of the tube wall.

Modeling of Electroosmotic Nanoflows With Overlapped Double Layer

2011 ◽  
Author(s):  
Reza Nosrati ◽  
Mehrdad Raisee ◽  
Ahmad Nourbakhsh
Keyword(s):  
Zeta Potential ◽  
Double Layer ◽  
Electric Double Layer ◽  
Potential Distribution ◽  
Present Model ◽  
Ionic Concentration ◽  
Channel Height ◽  
Parabolic Profile ◽  
Poisson Boltzmann ◽  
Volume Method

In the present paper a new model is proposed for electric double layer (EDL) overlapped in nanochannels. The model aimed to obtain a deeper insight of transport phenomena in nanoscale. Two-dimensional Nernst and ionic conservation equations are used to obtain electroosmotic potential distribution in flow field. In the proposed study, transport equations for flow, ionic concentration and electroosmotic potential are solved numerically via finite volume method. Moreover, Debye-Hu¨ckle (DH) approximation and symmetry condition, which limit the application, are avoided. Thus, the present model is suitable for prediction of electroosmotic flows through nanochannels as well as complicated asymmetric geometries with large nonuniform zeta potential distribution. For homogeneous zeta potential distribution, it has been shown that by reduction of channel height to values comparable with EDL thickness, Poisson-Boltzmann model produces inaccurate results and must be avoided. Furthermore, for overlapped electric double layer in nanochannels with heterogeneous zeta potential distribution it has been found that the present model returns modified ionic concentration and electroosmotic potential distribution compare to previous EDL overlapped models due to 2D solution of ionic concentration distribution. Finally, velocity profiles in EDL overlapped nanochannels are investigated and it has been showed that for pure electroosmotic flow the velocity profile deviates from the expected plug-like profile towards a parabolic profile.

scholarly journals The pulsatile propagation of a finger of air within a fluid-occluded cylindrical tube

2008 ◽  
Vol 601 ◽  
pp. 1-23 ◽  
Author(s):  
BRADFORD J. SMITH ◽  
DONALD P. GAVER
Keyword(s):  
Pressure Drop ◽  
Tube Wall ◽  
Reverse Flow ◽  
Stress Gradient ◽  
Mechanical Damage ◽  
Cylindrical Tube ◽  
Dimensionless Frequency ◽  
Stagnation Points ◽  
Unsteady Regime ◽  
Film Thinning

We computationally investigate the unsteady pulsatile propagation of a finger of air through a liquid-filled cylindrical rigid tube. The flow field is governed by the unsteady capillary number CaQ(t)=μQ*(t*)/πR2γ, where R is the tube radius, Q* is the dimensional flow rate, t* is the dimensional time, μ is the viscosity, and γ is the surface tension. Pulsatility is imposed by CaQ(t) consisting of both mean (CaM) and oscillatory (CaΩ components such that CaQ(t)=CaM+CaΩ sin(Ωt). Dimensionless frequency and amplitude parameters are defined, respectively, as Ω=μωR/γ and A=2CaΩ/Ω, with Ω epresenting the frequency of oscillation. The system is accurately described by steady-state behaviour if CaΩ<CaM; however, when CaΩ>CaM, reverse flow exists during a portion of the cycle, leading to an unsteady regime. In this unsteady regime, converging and diverging surface stagnation points translate dynamically along the interface throughout the cycle and may temporarily separate to create internal stagnation points at high Ω. For CaΩ<10CaM, the bubble tip pressure drop ΔPtip may be estimated accurately from the pressure measured downstream of the bubble tip when corrections for the downstream viscous component of the pressure drop are applied. The normal stress gradient at the tube wall ∂τn/∂z is examined in detail, because this has been shown to be the primary factor responsible for mechanical damage to epithelial cells during pulmonary airway reopening (Bilek, Dee & Gaver III 2003; Kay et al. 2004). In the unsteady regime, local film-thinning produces high ∂τn/∂z at low CaΩ; however, film thickening at moderate Ca protects the tube wall from large ∂τn/∂z. This stress field is highly dynamic and exhibits intriguing spatial and temporal characteristics that may be used to reduce ventilator-induced lung injury.

An experimental study of the effect of uniform strain on thermal fluctuations in grid-generated turbulence

1980 ◽  
Vol 99 (3) ◽  
pp. 545-573 ◽  
Author(s):  
Z. Warhaft
Keyword(s):  
Heat Flux ◽  
Decay Rate ◽  
Time Scale ◽  
Cross Correlation ◽  
Thermal Fluctuation ◽  
Thermal Fluctuations ◽  
Length Scale ◽  
Scale Size ◽  
Velocity Scale ◽  
Scale Ratio

The effect of homogeneous strain on passive scalar fluctuations, and the resultant evolution of the scalar field when the strain is removed, is experimentally studied by passing thermal fluctuations in decaying grid turbulence through a four-to-one axisymmetric contraction. Using amandoline(Warhaft & Lumley 1978a) to vary the scale size of the initial thermal fluctuations and hence the pre-contraction mechanical/thermal time-scale ratio,r, it is shown, for values ofrgreater than unity, that asris increased so is the post-contraction thermal decay rate, i.e. the contraction does not cause the thermal-fluctuation decay rate to equilibrate to a constant value. In these experiments the post-contraction thermal decay rate is always greater than the pre-contraction decay rate, i.e. the contraction accelerates the thermal-fluctuation decay. Moreover, the mechanical/thermal time-scale ratio in the post-contraction region is driven further from unity. In terms of scale size the uniform strain has the effect of increasing the thermal length scale by an amount equal in value to the contraction ratio if the pre-contraction thermal length scale is comparable to that of the pre-contraction velocity scale. However, if the pre-contraction thermal length scale is smaller than the pre-contraction velocity scale then the effect of the contraction on the thermal scale is less marked. The contraction induces significant negative cross-correlation ρuθbetween the longitudinal velocityuand thermal fluctuations θ even if the pre-contraction cross-correlation is close to zero. The magnitude of ρuθand hence the post-contraction heat flux is varied and the coherence structure is studied. It is shown that the thermal-fluctuation decay rate is insensitive to the magnitude of the heat flux, the latter of which decays rapidly compared to the relatively slow decay of turbulence energy in the post-contraction region. It is also shown that ρuθtends towards zero in this axisymmetric homogeneous flow at a faster rate than in isotropic turbulence. In accord with previous investigations, the return toward isotropy of the velocity field is very slow.

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