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.

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.

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.

Numerical Investigation of Slip Flow and Heat Transfer in Rotating Rectangular Microchannels

2012 ◽  
Author(s):  
Pratanu Roy ◽  
N. K. Anand ◽  
Debjyoti Banerjee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Convective Heat Transfer ◽  
Secondary Flow ◽  
Convective Heat ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Fluid Temperature ◽  
Slip Boundary ◽  
Flow And Heat Transfer

Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The pseudo forces namely the centrifugal force and the Coriolis force arising as a consequence of the rotating reference frame change the flow pattern significantly from the parabolic profile in a non-rotating channel. The convective heat transfer process is also influenced by the secondary flow introduced by the rotational effect. Moreover, if the microchannel wall is hydrophobic, slip flow can occur inside the channel when the conventional no slip boundary condition is no longer valid. In this work, we have numerically investigated the flow and heat transfer inside a straight rotating rectangular microchannel in the slip flow regime. A pressure based finite volume technique in a staggered grid was applied to solve the steady incompressible Navier-Stokes and energy equations. It has been observed that, depending on the rotational velocity, different slip velocities are induced at the channel walls. The average fluid temperature increases with the increase of rotation as convective heat transfer mechanism is increased due to the secondary flow. However, the slip boundary condition has a negligible effect on the temperature profiles.

Dispersion due to Electroosmotic Flow Through a Circular Tube With Axial Step Changes of Zeta Potential and Hydrodynamic Slippage

2013 ◽  
Author(s):  
Qi Zhou ◽  
Chiu-On Ng
Keyword(s):  
Boundary Condition ◽  
Zeta Potential ◽  
Dispersion Coefficient ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Axial Position ◽  
Hydrodynamic Dispersion ◽  
Lubrication Approximation ◽  
Slip Boundary ◽  
Zeta Potentials

The hydrodynamic dispersion of a neutral non-reacting solute due to steady electro-osmotic flow in a circular channel with longitudinal step changes of zeta potential and hydrodynamic slippage is analyzed in this study. The channel wall is periodically micro-patterned along the axial position with alternating slip-stick stripes of distinct zeta potentials. Existing studies on electrically driven hydrodynamic dispersion are based on flow subject to either the no-slip boundary condition on the capillary surface or the simplification of lubrication approximation. Taking wall slippage into account, a homogenization analysis is performed in this study to derive the hydrodynamic dispersion coefficient without subject to the long-wave constraint of the lubrication approximation, but for a general case where the length of one periodic unit of wall pattern is comparable with the channel radius. The flow and the hydrodynamic dispersion coefficient are calculated numerically, using the packages MATLAB and COMSOL, as functions of controlling parameters including the period length of the wall pattern, the area fraction of the slipping region (EOF-suppressing) in a periodic unit, the ratio of the two zeta potentials, the intrinsic hydrodynamic slip length, the Debye parameter, and the Péclet number. The dispersion coefficient is found to show notable, non-monotonic in certain situations, dependence on these controlling parameters. It is noteworthy that the introduction of hydrodynamic slippage will generate much richer behaviors of the hydrodynamic dispersion than the situation with no-slip boundary condition, as slippage interacts with zeta potentials in the EOF-suppressing and EOF-supporting regions (either likewise or oppositely charged).

Slip-Flow Pressure Drop in Microchannels of General Cross Section

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
M. Bahrami ◽  
A. Tamayol ◽  
P. Taheri
Keyword(s):  
Boundary Condition ◽  
Pressure Drop ◽  
Cross Section ◽  
Slip Flow ◽  
Homogeneous Boundary Condition ◽  
Slip Boundary Condition ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Cross Sectional ◽  
Slip Boundary

In the present study, a compact analytical model is developed to determine the pressure drop of fully-developed, incompressible, and constant properties slip-flow through arbitrary cross section microchannels. An averaged first-order Maxwell slip boundary condition is considered. Introducing a relative velocity, the difference between the bulk flow and the boundary velocities, the axial momentum reduces to Poisson’s equation with homogeneous boundary condition. Square root of area is selected as the characteristic length scale. The model of Bahrami et al. (2006, “Pressure Drop of Laminar, Fully Developed Flow in Microchannels of Arbitrary Cross Section,” ASME J. Fluids Eng., 128, pp. 1036–1044), which was developed for no-slip boundary condition, is extended to cover the slip-flow regime in this study. The proposed model for pressure drop is a function of geometrical parameters of the channel: cross sectional area, perimeter, polar moment of inertia, and the Knudsen number. The model is successfully validated against existing numerical and experimental data collected from different sources in literature for several shapes, including circular, rectangular, trapezoidal, and double-trapezoidal cross sections and a variety of gases such as nitrogen, argon, and helium.

ELECTROKINETIC SLIP FLOW OF MICROFLUIDICS IN TERMS OF STREAMING POTENTIAL BY A LATTICE BOLTZMANN METHOD: A BOTTOM-UP APPROACH

2007 ◽  
Vol 18 (04) ◽  
pp. 693-700 ◽  
Author(s):  
XIN FU ◽  
BAOMING LI ◽  
JUNFENG ZHANG ◽  
FUZHI TIAN ◽  
DANIEL Y. KWOK
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary ◽  
Surface Energetics ◽  
Boltzmann Method

In traditional computational fluid dynamics, the effect of surface energetics on fluid flow is often ignored or translated into an arbitrary selected slip boundary condition in solving the Navier-Stokes equation. Using a bottom-up approach, we show in this paper that variation of surface energetics through intermolecular theory can be employed in a lattice Boltzmann method to investigate both slip and non-slip phenomena in microfluidics in conjunction with the description of electrokinetic phenomena for electrokinetic slip flow. Rather than using the conventional Navier-Stokes equation with a slip boundary condition, the description of electrokinetic slip flow in microfluidics is manifested by the more physical solid-liquid energy parameters, electrical double layer and contact angle in the mean-field description of the lattice Boltzmann method.

The Simulation of Liquid Flow in the Pore Network Model of Nanoporous Media

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Yaohao Guo ◽  
Lei Zhang ◽  
Hai Sun ◽  
Yongfei Yang ◽  
Zhi Xu ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Liquid Flow ◽  
Effective Viscosity ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Slip Effect ◽  
Pore Throat ◽  
Slip Boundary ◽  
Nanoporous Media ◽  
Nanoscale Effect

Abstract The fluid–solid interaction force shows significant influence on liquid flow at nanoscale. Vast experimental observations in recent literatures have shown that Darcy's law cannot be applied to nanoporous media. In this study, the slip length and effective viscosity are adapted to characterize the nanoscale effect. First, the nanoscale effect is investigated in nanotubes through computational fluid dynamic (CFD) modeling analysis. Slip boundary condition has been studied as an important discrepancy between macroscopic flow and nanoscale liquid flow. The effect of viscosity change becomes more notable with the slip length increasing. Then, the flow equation for pore network modeling is developed to capture nanoscale effect. The results show that the apparent permeability of nanoscale systems is significantly underestimated when slip effect is neglected. The size of the pore throat determines whether the slip effect needs to be considered, and critical diameter of neglecting the slip effect for circular throat is 79.17 Ls. It is necessary to take the variation of effective viscosity into account under slip boundary condition. With the pore throat size decreasing, the nanoscale effect increases. The nanoscale effect is more sensitive to pore throat size under hydrophobic conditions than hydrophilic conditions.

The moving contact line: the slip boundary condition

1976 ◽  
Vol 77 (4) ◽  
pp. 665-684 ◽  
Author(s):  
E. B. Dussan V.
Keyword(s):  
Boundary Condition ◽  
Flow Field ◽  
Contact Line ◽  
Slip Length ◽  
Slip Boundary Condition ◽  
Flow Fields ◽  
Length Scale ◽  
Slip Boundary ◽  
Moving Contact Line ◽  
Moving Contact

The singularity at the contact line which is present when the usual fluidmechanical modelling assumptions are made is removed by permitting the fluid to slip along the wall. The aim of this study is to assess the sensitivity of the overall flow field to the form of the slip boundary condition. Explicit solutions are obtained for three different slip boundary conditions. Two length scales emerge: the slip length scale and the meniscus length scale. It is found that on the slip length scale the flow fields are quite different; however, when viewed on the meniscus length scale, i.e. the length scale on which almost all fluidmechanical measurements are made, all of the flow fields appear the same. It is found that the characteristic of the slip boundary condition which affects the overall flow field is the magnitude of the slip length.

Incompressible slip flow past a semi-infinite flat plate

1965 ◽  
Vol 22 (3) ◽  
pp. 463-469 ◽  
Author(s):  
J. D. Murray
Keyword(s):  
Boundary Condition ◽  
Shear Stress ◽  
Viscous Fluid ◽  
Flat Plate ◽  
Slip Velocity ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Slip Boundary

An asymptotic solution to the Navier-Stokes equation is obtained for the incompressible flow of a viscous fluid past a semi-infinite flat plate when a slip boundary condition is applied at the plate. The results for the shear stress (and hence the slip velocity) on the plate differ basically from those obtained by previous authors who considered the same problem using some form of the Oseen equations.

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