Analytical Modelling of Laminar Developing Flow Between Hydrophobic Surfaces with Different Slip-Velocities

2021 ◽  
Author(s):  
Sankar Vijay ◽  
Jaimon Cletus ◽  
Arun MG ◽  
Ranjith S Kumar
Keyword(s):  
Velocity Profile ◽  
Slip Length ◽  
Central Line ◽  
Momentum Equation ◽  
Layer Growth ◽  
Parallel Plates ◽  
Entrance Length ◽  
Navier Slip ◽  
Free Region ◽  
Separation Of Variable

Abstract Theoretical analysis of the entrance hydrodynamics of microchannels is an important design aspect in connection with the development of microfluidic devices. In this paper, pressure-driven fluid flow in the entrance region of two infinite hydrophobic parallel plates with dissimilar slip-velocities is analytically modelled. The linearized momentum equation is solved by applying the Navier-slip model at the boundaries to achieve the most generalized two-dimensional form. The velocity profile is obtained by combining the developed and developing velocities, which is estimated by invoking the separation of variable method. It is observed that the velocity profile is asymmetric and the shear-free region can be shifted from the geometrical central line by altering the wall hydrophobicity. Moreover, the zero shear zone is transferred more towards the surface having high hydrophobicity. The expression for wall shear stress is obtained analytically using Newton's law of viscosity. Moreover, the boundary layer growth from the upper and lower walls are found to be entirely different and they merge at the entrance length and is noticed to be off-setted from the geometric centre-line. The effect of slip-length on the entrance length is analysed and an empirical correlation is deduced.

Effects of Absolute Pressure on Fluid Slip in a Hydrophobic Microchannel

2003 ◽  
Author(s):  
Derek C. Tretheway ◽  
Carl D. Meinhart
Keyword(s):  
Velocity Profile ◽  
Layer Thickness ◽  
Bubble Size ◽  
Slip Length ◽  
Hydrophobic Surface ◽  
Surface Modeling ◽  
Absolute Pressure ◽  
Parallel Plates ◽  
Gas Layer ◽  
Hydrophobic Microchannel

This work examines the effects of absolute pressure on fluid slip in a hydrophobic microchannel. Previous experiments with hydrophobic surfaces have indicated the presence of an apparent fluid slip. The mechanism responsible for the apparent fluid slip observed by Pit. et. al. (Phys. Rev. Lett., 85, 980–983), Zhu and Granick (Phys. Rev. Lett., 87, 096105), and Tretheway and Meinhart (Phys. of Fluids, 14, L9-L12) is unknown. Recently, Tyrell and Attard () have observed the presence of nanobubbles on a hydrophobic surface. Modeling these nanobubbles as a thin gas layer and solving for the velocity profile between two infinite parallel plates yields an apparent fluid slip consistent with the experimentally observed results. As the slip length is highly dependent on the nanobubble or gas layer thickness, increases in absolute pressure should decrease the bubble size and reduce the measured slip. This work explores the proposed mechanism by measuring velocity profiles and calculating slip lengths at varying absolute pressures.

Effects of Saturated and Degassed Solutions on Flow Through a Hydrophobic Microchannel

2004 ◽  
Author(s):  
Derek C. Tretheway ◽  
Shannon Stone ◽  
Carl D. Meinhart
Keyword(s):  
Velocity Profile ◽  
Layer Thickness ◽  
Slip Length ◽  
Hydrophobic Surface ◽  
Absolute Pressure ◽  
Parallel Plates ◽  
Gas Concentration ◽  
Flow Through ◽  
Gas Layer ◽  
Hydrophobic Microchannel

This work examines the effects of soluble gasses and absolute pressure on fluid slip in a hydrophobic microchannel. Previous experiments with hydrophobic surfaces have indicated the presence of an apparent fluid slip. Tretheway and Meinhart (Phys. of Fluids 16, 1509) proposed a mechanism responsible for the apparent fluid slip observed by Pit. et. al. (Phys. Rev. Lett., 85, 980–983), Zhu and Granick (Phys. Rev. Lett., 87, 096105), and Tretheway and Meinhart (Phys. of Fluids, 14, L9-L12). Tyrell and Attard (Phys. Rev. Lett. 87, 176104) observed the presence of nanobubbles on a hydrophobic surface. Tretheway and Meinhart (Phys. of Fluids 16, 1509) modeled these nanobubbles as a thin gas layer and solved for the velocity profile between two infinite parallel plates, which yields an apparent fluid slip consistent with the experimentally observed results. As the slip length is highly dependent on the nanobubble or gas layer thickness, varying the soluble gas concentration or absolute pressure should increase and decrease the apparent fluid slip. This work explores the proposed mechanism by measuring velocity profiles and calculating slip lengths for various saturated and degassed solutions and a range of absolute pressures.

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 $\tilde{b}_{m}$.

scholarly journals Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 932
Author(s):  
Rodrigo González ◽  
Aldo Tamburrino ◽  
Andrea Vacca ◽  
Michele Iervolino
Keyword(s):  
Shear Stress ◽  
Analytical Solution ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Momentum Equation ◽  
Parallel Plates ◽  
Analytical Computation ◽  
Pulsatile Pressure ◽  
Pulsatile Pressure Gradient

The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.

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.

Maximum Velocity Decay in a Submerged Laminar Jet Issuing from a ‘Long Tube

1983 ◽  
Vol 7 (1) ◽  
pp. 41-43 ◽  
Author(s):  
M. Arulraja ◽  
G.W. Rankin ◽  
K. Sridhar
Keyword(s):  
Velocity Profile ◽  
Maximum Velocity ◽  
Momentum Equation ◽  
Experimental Fact ◽  
Laminar Jet ◽  
Developing Region ◽  
Other Information ◽  
Velocity Decay ◽  
Matching Schemes ◽  
Jet Axis

Decay of the maximum velocity of an incompressible, axisymmetric, submerged, laminar free jel is related to the second derivative of the velocity profile at the centre line by using the momentum equation along the jet axis with boundary layer approximations. Using this decay relation and the experimental fact that the velocity profile near the jet axis remains parabolic it is shown that maximum velocity decay is linear in the developing region. The length of the developing region and the location of the virtual origin are obtained by matching the maximum velocity variations at the boundary between the developing and fully developed regions. These values are compared with the results of conventional jet matching schemes and with other information available in the literature.

Some Measurements of Boundary-Layer Growth in a Two-Dimensional Diffuser

1959 ◽  
Vol 81 (3) ◽  
pp. 285-294 ◽  
Author(s):  
J. F. Norbury
Keyword(s):  
Boundary Layer ◽  
Static Pressure ◽  
Momentum Equation ◽  
Layer Growth ◽  
Area Ratio ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Static Pressure Distribution ◽  
Boundary Layer Growth ◽  
Flow Experiments

Low-speed experiments were carried out in a two-dimensional diffuser having a square throat and an area ratio of two to one. Measurements were made of static pressure distribution, velocity contours at throat and outlet, and boundary-layer growth along the four wall center lines. Visual flow experiments were performed using tufts and smoke filaments. Similar experiments were carried out with the throat boundary layers artificially thickened by means of round rods placed on the walls upstream. Disparities between the measured growth of momentum thickness and that predicted by the simple momentum equation are discussed, as well as the effect of the artificial thickening on diffuser efficiency.

Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

1968 ◽  
Vol 90 (2) ◽  
pp. 191-198 ◽  
Author(s):  
R. D. Haberstroh ◽  
L. V. Baldwin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Pipe Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.

Experimental Analysis of Microchannel Entrance Length Characteristics Using Microparticle Image Velocimetry

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Tariq Ahmad ◽  
Ibrahim Hassan
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Entrance Region ◽  
Working Fluid ◽  
Parallel Plates ◽  
Entrance Length ◽  
Number Range ◽  
Micro Piv ◽  
Image Velocimetry ◽  
Microparticle Image Velocimetry

The study of the entrance region of microchannels and microdevices is limited, yet important, since the effect on the flow field and heat transfer mechanisms is significant. An experimental study has been carried out to explore the laminar hydrodynamic development length in the entrance region of adiabatic square microchannels. Flow field measurements are acquired through the use of microparticle image velocimetry (micro-PIV), a nonintrusive particle tracking and flow observation technique. With the application of micro-PIV, entrance length flow field data are obtained for three different microchannel hydraulic diameters of 500 μm, 200 μm, and 100 μm, all of which have cross-sectional aspect ratios of 1. The working fluid is distilled water, and velocity profile data are acquired over a laminar Reynolds number range from 0.5 to 200. The test-sections were designed as to provide a sharp-edged microchannel inlet from a very large reservoir at least 100 times wider and higher than the microchannel hydraulic diameter. Also, all microchannels have a length-to-diameter ratio of at least 100 to assure fully developed flow at the channel exit. The micro-PIV procedure is validated in the fully developed region with comparison to Navier–Stokes momentum equations. Good agreement was found with comparison to conventional entrance length correlations for ducts or parallel plates, depending on the Reynolds range, and minimal influence of dimensional scaling between the investigated microchannels was observed. New entrance length correlations are proposed, which account for both creeping and high laminar Reynolds number flows. These correlations are unique in predicting the entrance length in microchannels and will aid in the design of future microfluidic devices.

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