scholarly journals Study of a Newtonian Fluid through Circular Channels with Slip Boundary Taking into Account Electrokinetic Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qian Sun ◽  
Yonghong Wu ◽  
Lishan Liu ◽  
B. Wiwatanapataphee
Keyword(s):  
Slip Length ◽  
Slip Flow ◽  
Electrolyte Solutions ◽  
Fourier Series Expansion ◽  
Wave Form ◽  
Electrical Field ◽  
Electrokinetic Effect ◽  
Numerical Investigations ◽  
System Parameters ◽  
Slip Boundary

We study the slip flow of fluids driven by the combined effect of electrical force and pressure gradient. The underlying boundary value problem is solved through the use of Fourier series expansion in time and Bessel function in space. The exact solutions and numerical investigations show that the slip length and electrical field parameters have significant effects on the velocity profile. By varying these system parameters, one can achieve smooth velocity profiles or wave form profiles with different wave amplitude and frequency. This opens the way for optimizing the flow by choosing the slip length, the electrical field, and electrolyte solutions.

scholarly journals SPONTANEOUS IMBIBITION PROCESS IN MICRO–NANO FRACTAL CAPILLARIES CONSIDERING SLIP FLOW

Fractals ◽  
2018 ◽  
Vol 26 (02) ◽  
pp. 1840002 ◽  
Author(s):  
YINGHAO SHEN ◽  
CAOXIONG LI ◽  
HONGKUI GE ◽  
XUEJING GUO ◽  
SHAOJUN WANG
Keyword(s):  
Fluid Transport ◽  
Slip Length ◽  
Fractal Theory ◽  
Slip Flow ◽  
Gas Production ◽  
Spontaneous Imbibition ◽  
Equivalent Diameter ◽  
Slip Effect ◽  
Analytic Equation ◽  
Slip Boundary

An imbibition process of water into a matrix is required to investigate the influences of large-volume fracturing fluids on gas production of unconventional formations. Slip flow has been recognized by recent studies as a major mechanism of fluid transport in nanotubes. For nanopores in shale, a slip boundary is nonnegligible in the imbibition process. In this study, we established an analytic equation of spontaneous imbibition considering slip effects in capillaries. A spontaneous imbibition model that couples the analytic equation considering the slip effect was constructed based on fractal theory. We then used a model for various conditions, such as slip boundary, pore structure, and fractal dimension of pore tortuosity, to capture the imbibition characteristics considering the slip effect. A dynamic contact angle was integrated into the modeling. Results of our study verify that the slip boundary influences water imbibition significantly. The imbibition speed is significantly improved when slip length reaches the equivalent diameter of a tube. Therefore, disregarding the slip effect will underestimate the imbibition speed in shale samples.

scholarly journals AFM Slip Length Measurements for Water at Selected Phyllosilicate Surfaces

2021 ◽  
Vol 5 (4) ◽  
pp. 44
Author(s):  
Chen Zhang ◽  
Xuming Wang ◽  
Jiaqi Jin ◽  
Lixia Li ◽  
Jan D. Miller
Keyword(s):  
Boundary Condition ◽  
Silica Surface ◽  
Slip Length ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Exclusion Zone ◽  
Slip Boundary ◽  
Hydrophobic Silica ◽  
Synthetic Materials ◽  
Length Measurements

Most reported slip length measurements have been made at the surfaces of synthetic materials and modified synthetic materials. In contrast, few slip length measurements at the surface of unmodified natural mineral surfaces have been reported. In this regard, flow at the silica face surfaces of the phyllosilicate minerals, talc and mica, was considered. A slip boundary condition was expected at the nonpolar hydrophobic silica surface of talc leading to enhanced flow, and a no-slip boundary condition was expected at the hydrophilic silica surface of mica. Atomic force microscopy (AFM) slip length measurements were made at the talc and mica surfaces. The slip length results for the hydrophobic silica surface of talc were contrasted to the results for the hydrophilic silica surface of mica (no-slip flow). The results are discussed based on molecular dynamics simulations (MDS), as reported in the literature, and AFM images of surface nanobubbles. For nonpolar hydrophobic surfaces (such as talc), it is doubtful that the MDS interfacial water structure and the water exclusion zone (3.2 Å) account for the AFM slip flow with slip lengths as great as 95 nm. Rather, a better explanation for the AFM slip flow condition is based on reduced interfacial viscosity due to the presence of dissolved gas and the accommodation of pancake nanobubbles at the talc surface having a height dimension of magnitude similar to the slip length.

scholarly journals Simulation of the Slip Velocity Effect in an AC Electrothermal Micropump

Micromachines ◽  
2020 ◽  
Vol 11 (9) ◽  
pp. 825
Author(s):  
Fraj Echouchene ◽  
Thamraa Al-shahrani ◽  
Hafedh Belmabrouk
Keyword(s):  
Flow Field ◽  
Slip Velocity ◽  
Slip Length ◽  
Substrate Material ◽  
The Finite Element Method ◽  
Electrical Field ◽  
Slip Boundary ◽  
Poisson Equations ◽  
Pumping Efficiency ◽  
Velocity Effect

The principal aim of this study was to analyze the effect of slip velocity at the microchannel wall on an alternating current electrothermal (ACET) flow micropump fitted with several pairs of electrodes. Using the finite element method (FEM), the coupled momentum, energy, and Poisson equations with and without slip boundary conditions have been solved to compute the velocity, temperature, and electrical field in the microchannel. The effects of the frequency and the voltage, and the electrical and thermal conductivities, respectively, of the electrolyte solution and the substrate material, have been minutely analyzed in the presence and absence of slip velocity. The slip velocity was simulated along the microchannel walls at different values of slip length. The results revealed that the slip velocity at the wall channel has a significant impact on the flow field. The existence of slip velocity at the wall increases the shear stress and therefore enhances the pumping efficiency. It was observed that higher average pumping velocity was achieved for larger slip length. When a glass substrate was used, the effect of the presence of the slip velocity was more manifest. This study shows also that the effect of slip velocity on the flow field is very important and must be taken into consideration in an ACET micropump.

A Rheological Study of Carbon Black Suspensions and Determination of Significant Factors Affecting the Slip Flow in In-Mold Coating (IMC) Using Design of Experiments

2011 ◽  
Vol 239-242 ◽  
pp. 232-237
Author(s):  
Chuckaphun Aramphongphun ◽  
Chompunoot Chareonwutilap
Keyword(s):  
Carbon Black ◽  
Design Of Experiments ◽  
Slip Length ◽  
Slip Flow ◽  
Research Work ◽  
Consumer Products ◽  
Viscosity Data ◽  
Factors Affecting ◽  
Slip Boundary ◽  
Significant Factors

In-mold coating (IMC) of plastic parts is a promising coating process in automotive and consumer products industry. An IMC material, such as carbon black suspension, can potentially be used as a top coat or paint. IMC is performed by injecting a reactive liquid polymer onto a part’s surface in the end of the forming process while the part is still in the mold. The coating material flows under high pressure by compressing the part’s surface, which causes a microchannel of 75-125 micron thickness. The IMC flow, particularly in a microchannel, tends to cause the slip boundary at the channel wall. This research work aims to (i) study rheological properties of carbon black suspended in acrylic resin in both macro- and micro-scale, (ii) study slipping at the wall in the microchannel, and (iii) determine significant factors affecting the slip flow of the carbon black suspension. A custom-built microslit rheometer was developed to conduct experiments to serve these purposes. By analyzing the viscosity data, a slip parameter called slip length could be determined. Statistical design of experiments was then applied to determine the effect of three factors including channel gap, operating temperature, and carbon black content on the slip boundary conditions of the microflow. The results showed that these three factors significantly affected the slip length of the flow of carbon black suspension.

scholarly journals Morphological evolution of microscopic dewetting droplets with slip

2017 ◽  
Vol 828 ◽  
pp. 271-288 ◽  
Author(s):  
Tak Shing Chan ◽  
Joshua D. McGraw ◽  
Thomas Salez ◽  
Ralf Seemann ◽  
Martin Brinkmann
Keyword(s):  
Slip Length ◽  
Morphological Evolution ◽  
Early Time ◽  
Slip Boundary Condition ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Navier Slip ◽  
Slip Boundary ◽  
Quasistatic Regime

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

Examination of the Slip Boundary Condition by µ-PIV and Lattice Boltzmann Simulations

2002 ◽  
Author(s):  
Derek C. Tretheway ◽  
Luoding Zhu ◽  
Linda Petzold ◽  
Carl D. Meinhart
Keyword(s):  
Boundary Condition ◽  
Shear Rate ◽  
Channel Flow ◽  
Lattice Boltzmann ◽  
Slip Velocity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
Lattice Boltzmann Simulations ◽  
Bounce Back

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier’s hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9–L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1−P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates.

scholarly journals ESTIMATION OF THE SLIP LENGTH IN THE FLOW OF LIQUID IN MICRO-CHANNELS

2018 ◽  
Vol 40 (2) ◽  
pp. 12-19
Author(s):  
Y.Y. Kovetska
Keyword(s):  
Slip Length ◽  
Slip Flow ◽  
Gas Bubbles ◽  
Hydrophobic Surface ◽  
Dissipative Heating ◽  
Research Review ◽  
Surface Shear Stress ◽  
Surface Shear ◽  
Lower Viscosity ◽  
Micro Channels

Research review of phenomenon for slip flow in micro and nanocannels is presented in the paper. The analysis of theoretical and experimental data characterizing the slip length is carried out. In slip flow in microchannels the slip length is affected by the contact angle of the liquid with the surface, shear stress, pressure, dissipative heating, the amount and nature of the dissolved gas in the liquid, electrical characteristics, surface roughness. Studies of flow in microchannels with hydrophobic walls, which are based on molecular dynamics, showed that the slip length has order of 20 nm. This is much less than the values observed in the experiment. The introduction of an effective (apparent) slip length suggests the existence of a thin layer of gas bubbles near the hydrophobic surface or liquid layer with low value of viscosity and density. Since the idealized model for the total coverage of a hydrophobic surface by gas bubbles gives, as a rule, overestimated values of the slip length in comparison with experimental ones, some researchers consider the inhomogeneous coating of the wall by gas bubbles. In this case, the effect of a layer with a lower viscosity on the slip length turns out to be weaker.

MEMS-Scale Turbomachinery Based Vacuum Roughing Pump

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Anthony J. Gannon ◽  
Garth V. Hobson ◽  
Michael J. Shea ◽  
Christopher S. Clay ◽  
Knox T. Millsaps
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
3D Simulations ◽  
Slip Boundary ◽  
Wall Shear

This study forms part of a program to develop a micro-electro-mechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the no-slip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slip-flow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient two-dimensional (2D) simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear, and slip-flow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specified-shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional (3D) simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present, this relationship was far weaker.

scholarly journals Pressure-Driven Thermal Slip Flow in the Elliptical Channel with Radial Oscillatory Wall

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Nattawan Chuchalerm ◽  
Benchawan Wiwatanapataphee ◽  
Wannika Sawangtong
Keyword(s):  
Slip Length ◽  
Ritz Method ◽  
Slip Flow ◽  
Temperature Fields ◽  
Thermal Slip ◽  
Fully Developed Flow ◽  
Navier Slip ◽  
Heat Transfer Phenomenon ◽  
Flow Heat ◽  
Velocity And Temperature Fields

This paper is aimed at presenting thermal slip flow driven by oscillatory pressure gradient in a deformable microchannel of elliptic cross-section. The fully developed flow of Newtonian fluid is considered, and Navier slip is applied on the boundary. The boundary value problem is formulated and applied to the coronary blood flow-heat transfer phenomenon during thermotherapy treatment. Its semianalytical solutions of velocity and temperature fields are carried out by the Ritz method. The effects of oscillatory wall and slip length on velocity and temperature fields of blood are investigated.

Multistability Control of Hysteresis and Parallel Bifurcation Branches through a Linear Augmentation Scheme

2019 ◽  
Vol 75 (1) ◽  
pp. 11-21 ◽  
Author(s):  
T. Fonzin Fozin ◽  
G. D. Leutcho ◽  
A. Tchagna Kouanou ◽  
G. B. Tanekou ◽  
R. Kengne ◽  
...  
Keyword(s):  
Coupling Parameter ◽  
Phase Portraits ◽  
Coexisting Attractors ◽  
Nonlinear Dynamical ◽  
Numerical Investigations ◽  
System Parameters ◽  
Chua’S Oscillator ◽  
Control Scheme ◽  
Periodic Attractors ◽  
Basin Of Attractions

AbstractMultistability analysis has received intensive attention in recently, however, its control in systems with more than two coexisting attractors are still to be discovered. This paper reports numerically the multistability control of five disconnected attractors in a self-excited simplified hyperchaotic canonical Chua’s oscillator (hereafter referred to as SHCCO) using a linear augmentation scheme. Such a method is appropriate in the case where system parameters are inaccessible. The five distinct attractors are uncovered through the combination of hysteresis and parallel bifurcation techniques. The effectiveness of the applied control scheme is revealed through the nonlinear dynamical tools including bifurcation diagrams, Lyapunov’s exponent spectrum, phase portraits and a cross section basin of attractions. The results of such numerical investigations revealed that the asymmetric pair of chaotic and periodic attractors which were coexisting with the symmetric periodic one in the SHCCO are progressively annihilated as the coupling parameter is increasing. Monostability is achieved in the system through three main crises. First, the two asymmetric periodic attractors are annihilated through an interior crisis after which only three attractors survive in the system. Then, comes a boundary crisis which leads to the disappearance of the symmetric attractor in the system. Finally, through a symmetry restoring crisis, a unique symmetric attractor is obtained for higher values of the control parameter and the system is now monostable.

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