Fully Developed Flow of Power-Law Fluid Through a Cylindrical Microfluidic Pipe: Pressure Drop and Electroviscous Effects

2008 ◽  
Author(s):  
Ram P. Bharti ◽  
Dalton J. E. Harvie ◽  
Malcolm R. Davidson
Keyword(s):  
Pressure Drop ◽  
Field Strength ◽  
Charge Density ◽  
Power Law ◽  
Maximum Velocity ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Electrical Field ◽  
Electrical Field Strength ◽  
Fluid Behaviour

Pressure drop and electroviscous effects in the axisymmetric, steady, fully developed, pressure-driven flow of incompressible power-law fluids through a cylindrical microchannel at low Reynolds number (Re = 0.01) have been investigated. The Poisson-Boltzmann equation (describing the electrical potential) and the momentum equations in conjunction with electrical force and power-law fluid rheology have been solved numerically using the finite difference method. The pipe wall is considered to have uniform surface charge density (S = 4) and the liquid is assumed to be a symmetric electrolyte solution. In particular, the influence of the dimensionless inverse Debye length (K = 2, 20) and power-law flow behaviour index (n = 0.2, 1, 1.8) on the EDL potential, ion concentrations and charge density profiles, induced electrical field strength, velocity and viscosity profiles and pressure drop have been studied. As expected, the local EDL potential, local charge density and electrical field strength increases with decreasing K and/or increasing S. The velocity profiles cross-over away from the charged pipe wall with increasing K and/or decreasing n. The maximum velocity at the center of the pipe increases with increasing n and/or increasing S and/or decreasing K. The shear-thinning fluid viscosity is strongly dependent on K and S, whereas the shear-thickening viscosity is very weakly dependent on K and S. For fixed K, as the fluid behaviour changes from Newtonian (n = 1) to shear-thinning (n < 1), the induced electrical field strength increases and maximum velocity reduces. On the other hand, the change in fluid behaviour from Newtonian (n = 1) to shear-thickening (n > 1) decreases the electrical field strength and increases the maximum velocity. The non-Newtonian effects on maximum velocity and pressure drop are stronger in shear-thinning fluids at small K and large S, the shear-thickening fluids show opposite influence. Electroviscous effects enhance with decreasing K and/or increasing S. The electroviscous effects show complex dependence on the non-Newtonian tendency of the fluids. The shear-thickening (n > 1) fluids and/or smaller K show stronger influence on the pressure drop and thus, enhance the electroviscous effects than that in shear-thinning (n < 1) fluids and/or large K where EDL is very thin.

scholarly journals Space/Interface Charge Analysis of the Multi-Layer Oil Gap and Oil Impregnated Pressboard Under the Electrical-Thermal Combined Stress

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1099 ◽  
Author(s):  
Runhao Zou ◽  
Jian Hao ◽  
Ruijin Liao
Keyword(s):  
Field Strength ◽  
Charge Density ◽  
Total Charge ◽  
Insulation System ◽  
Electrical Field ◽  
Electrical Field Strength ◽  
Interface Charge ◽  
Combined Action ◽  
Paper Insulation ◽  
Main Curve

In oil-paper insulation systems, it is easy to accumulate space/interface charge under a direct current (DC) electrical field. At present, direct measurement of space/interface charge for a thick multi-layer insulation system is not possible. It is necessary to study the multi-layer oil-paper insulation system via simulation method. In this paper, the space/interface charge simulation based on the bipolar charge transport model and a simulation parameter using FEM for the multi-layer oil–paper insulation system was proposed. The influence of electrical field strength, temperature, and the combined influence of the electrical field strength and temperature on the space/interface charge behaviors were analyzed, respectively. A new method for calculating the space/interface charge density and the total charge quantity of the multi-layer oil-paper insulation under the combined action of electrical field strength and temperature was presented. Results show that the interface charge density absolute value and the total charge quantity at steady state both increases with the electrical field strength and temperature in an exponential way, respectively. Besides, temperature has a more significant influence on the charge density and the total charge quantity than the electrical field strength. The electrical field strength–temperature shifting factor αT’ was introduced for the translation of the charge density curves or the total charge quantity curves to construct the charge density main curve or the total charge quantity main curve under the combined action of electrical field strength and temperature. The equations for calculating the charge density or the total charge quantity of the multi-layer oil-paper insulation was provided, which could be used to calculate the charge density or the total charge quantity under the combined action of electrical field strength and temperature.

Untersuchung der Plasmagrenzschidht in einer Niederdruckentladung

1962 ◽  
Vol 17 (11) ◽  
pp. 962-967 ◽  
Author(s):  
Werner Ott
Keyword(s):  
Field Strength ◽  
Charge Density ◽  
Space Charge ◽  
Debye Length ◽  
Linear Increase ◽  
Space Charge Density ◽  
Zero Field ◽  
Linear Extrapolation ◽  
Electrical Field ◽  
Electrical Field Strength

The electrical field in the space charge sheath between a Hg low-pressure plasma and an insulated plane wall was measured with an electron beam probe. Near the wall, the field strength was observed to increase linearly. Linear extrapolation to zero field strength is used here to define the thickness of the sheath which turned out to be 3 to 5 times the DEBYE length. On the other hand, the potential, the electrical field strength, and the space charge density in the sheath were, now, calculated (using BOHM'S criterion). Also theoretically, a (approximately) linear increase of field strength is found. A linear extrapolation of the theoretical values gives a boundary layer thickness about 6.7 to 6.9 times the DEBYE length, if the wall is at floating potential. Some differences are found between the experimental and the theoretical values of the wall potential and the space charge density in the sheath.

Electrohydrodynamic Printing via Spinneret with Conductive Probe

2013 ◽  
Vol 562-565 ◽  
pp. 1155-1160
Author(s):  
Yi Hong Lin ◽  
Guang Qi He ◽  
Hai Yan Liu ◽  
Jin Wei ◽  
Jian Yi Zheng ◽  
...  
Keyword(s):  
Field Strength ◽  
Applied Voltage ◽  
Industrial Application ◽  
Control Level ◽  
Direct Write ◽  
Electrical Field ◽  
Nano Structure ◽  
Electrical Field Strength ◽  
Electrohydrodynamic Printing ◽  
The Stability

Stability jet ejection and precision deposition are the two keys for industrial application of electrohydrodynamic printing. In this paper, inserted conductive probe is utilized to gain stability jet, which would increase the electrical field strength, reduce the back flow, onset and sustaining voltage. Lower applied voltage would enhance the stability of electrospun jet, in which fine jet can be used to direct-write orderly Micro/Nano-structure. With the guidance and constrain of inserted probe, the oscillating angle range of electrohydrodynamic jet is decreased to 3°from 15°, and the width of printed structures is 21μm in average that is much narrower than that printed from spinneret without probe (74μm in average). Spinneret with tip provides a good way to improve the control level of electrohydrodynamic printing, which would accelerate the industrial application of electrohydrodynamic printed Micro/Nano structure.

Drops of power-law fluids falling on a coated vertical fibre

2014 ◽  
Vol 751 ◽  
pp. 184-215
Author(s):  
Liyan Yu ◽  
John Hinch
Keyword(s):  
Solitary Waves ◽  
Power Law ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Bond Number ◽  
Power Law Fluid ◽  
Shear Thinning Fluids ◽  
Power Law Fluids ◽  
Shear Thickening Fluids ◽  
The Stability

AbstractWe study the solitary wave solutions in a thin film of a power-law fluid coating a vertical fibre. Different behaviours are observed for shear-thickening and shear-thinning fluids. For shear-thickening fluids, the solitary waves are larger and faster when the reduced Bond number is smaller. For shear-thinning fluids, two branches of solutions exist for a certain range of the Bond number, where the solitary waves are larger and faster on one and smaller and slower on the other as the Bond number decreases. We carry out an asymptotic analysis for the large and fast-travelling solitary waves to explain how their speeds and amplitudes change with the Bond number. The analysis is then extended to examine the stability of the two branches of solutions for the shear-thinning fluids.

Comparative study on electro-microfiltration (EMF) of water containing different carbon nanotubes (CNTs)

2013 ◽  
Vol 67 (6) ◽  
pp. 1247-1253 ◽  
Author(s):  
Yu-Hsiang Weng ◽  
Hsin-Chieh Wu ◽  
Kung-Cheh Li
Keyword(s):  
Carbon Nanotubes ◽  
Field Strength ◽  
Removal Efficiency ◽  
Pure Water ◽  
Applied Pressure ◽  
Convective Transport ◽  
Single Wall Carbon Nanotubes ◽  
Electrical Field ◽  
Electrical Field Strength ◽  
Electrical Voltage

Disposal and penetration of carbon nanotubes (CNTs) into the environment have raised increasing concerns over the years. In this study, a laboratory scale electro-microfiltration (EMF) was used to treat water containing single wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs). The goal was to examine and compare the performance during EMF of SWCNT and MWCNT. The results showed that the initial flux was increased as the applied electrical voltage increased. At an applied pressure of 49 kPa, the final flux was comparable to pure water flux when the applied electrical field strength was greater than the critical electrical field strength (Ecritical). In addition, dissolved organic carbon (DOC) removal efficiency increased as the electrical voltage increased. Due to high convective transport of organic matter toward the membrane at 98 kPa, a decrease in DOC removal efficiency with increasing electrical field strength was observed. Overall, the fluxes and DOC removal efficiencies for EMF of SWCNT and MWCNT were not significantly different with a 95% confidence.

scholarly journals Collapse of a neutrally buoyant suspension column: from Newtonian to apparent non-Newtonian flow regimes

2017 ◽  
Vol 826 ◽  
pp. 918-941 ◽  
Author(s):  
A. Bougouin ◽  
L. Lacaze ◽  
T. Bonometti
Keyword(s):  
Power Law ◽  
Temporal Evolution ◽  
Volume Fraction ◽  
Fluid Model ◽  
Particle Diameter ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Rheological Parameters ◽  
Power Law Fluids ◽  
Neutrally Buoyant

Experiments on the collapse of non-colloidal and neutrally buoyant particles suspended in a Newtonian fluid column are presented, in which the initial volume fraction of the suspension $\unicode[STIX]{x1D719}$, the viscosity of the interstitial fluid $\unicode[STIX]{x1D707}_{f}$, the diameter of the particles $d$ and the mixing protocol, i.e. the initial preparation of the suspension, are varied. The temporal evolution of the slumping current highlights two main regimes: (i) an inertial-dominated regime followed by (ii) a viscous-dominated regime. The inertial regime is characterized by a constant-speed slumping which is shown to scale as in the case of a classical inertial dam-break. The viscous-dominated regime is observed as a decreasing-speed phase of the front evolution. Lubrication models for Newtonian and power-law fluids describe most of situations encountered in this regime, which strongly depends on the suspension parameters. The temporal evolution of the propagating front is used to extract the rheological parameters of the fluid models. At the early stages of the viscous-dominated regime, a constant effective shear viscosity, referred to as an apparent Newtonian viscous regime, is found to depend only on $\unicode[STIX]{x1D719}$ and $\unicode[STIX]{x1D707}_{f}$ for each mixing protocol. The obtained values are shown to be well fitted by the Krieger–Dougherty model whose parameters involved, say a critical volume fraction $\unicode[STIX]{x1D719}_{m}$ and the exponent of divergence, depend on the mixing protocol, i.e. the microscale interaction between particles. On a longer time scale which depends on $\unicode[STIX]{x1D719}$, the front evolution is shown to slightly deviate from the apparent Newtonian model. In this apparent non-Newtonian viscous regime, the power-law model, indicating both shear-thinning and shear-thickening behaviours, is shown to be more appropriate to describe the front evolution. The present experiments indicate that the mixing protocol plays a crucial role in the selection of a shear-thinning or shear-thickening type of collapse, while the particle diameter $d$ and volume fraction $\unicode[STIX]{x1D719}$ play a significant role in the shear-thickening case. In all cases, the normalized effective consistency of the power-law fluid model is found to be a unique function of $\unicode[STIX]{x1D719}$. Finally, an apparent viscoplastic regime, characterized by a finite length spreading reached at finite time, is observed at high $\unicode[STIX]{x1D719}$. This regime is mostly observed for volume fractions larger than $\unicode[STIX]{x1D719}_{m}$ and up to a volume fraction $\unicode[STIX]{x1D719}_{M}$ close to the random close packing fraction at which the initial column remains undeformed on opening the gate.

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