Slip Length and Problem of Anomalous Velocity Profile

2005 ◽  
Author(s):  
Kokou Dadzie ◽  
Gilbert Méolans
Keyword(s):  
Velocity Profile ◽  
Slip Length ◽  
Anomalous Velocity

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.

Investigation of the influence of the flow structure on the accuracy of flow measurement before a hydrometric structure in an open channel

2020 ◽  
pp. 41-44
Author(s):  
Anatoly Kusher
Keyword(s):  
Velocity Profile ◽  
Flow Velocity ◽  
Water Flow ◽  
Flow Measurement ◽  
Water Discharge ◽  
Critical Depth ◽  
Flow Measurements ◽  
Study Results ◽  
Flow Velocity Profile ◽  
Upstream Flow

The reliability of water flow measurement in irrigational canals depends on the measurement method and design features of the flow-measuring structure and the upstream flow velocity profile. The flow velocity profile is a function of the channel geometry and wall roughness. The article presents the study results of the influence of the upstream flow velocity profile on the discharge measurement accuracy. For this, the physical and numerical modeling of two structures was carried out: a critical depth flume and a hydrometric overfall in a rectangular channel. According to the data of numerical simulation of the critical depth flume with a uniform and parabolic (1/7) velocity profile in the upstream channel, the values of water discharge differ very little from the experimental values in the laboratory model with a similar geometry (δ < 2 %). In contrast to the critical depth flume, a change in the velocity profile only due to an increase in the height of the bottom roughness by 3 mm causes a decrease of the overfall discharge coefficient by 4…5 %. According to the results of the numerical and physical modeling, it was found that an increase of backwater by hydrometric structure reduces the influence of the upstream flow velocity profile and increases the reliability of water flow measurements.

Theoretical Principles of Streaming Current Detection

1989 ◽  
Vol 21 (6-7) ◽  
pp. 443-453 ◽  
Author(s):  
S. K. Dentel ◽  
K. M. Kingery
Keyword(s):  
Velocity Profile ◽  
Electrophoretic Mobility ◽  
Double Layer ◽  
Initial Attempt ◽  
Streaming Current ◽  
Coagulant Dosage ◽  
Model Predictions ◽  
Double Layer Model ◽  
Simplifying Assumptions ◽  
Current Detection

In spite of the increased use of streaming current detectors (SCDs) as a means of monitoring and/or controlling coagulant dosage, knowledge regarding fundamental workings is incomplete. This paper provides an initial attempt at predicting and verifying functioning compared to electrophoretic mobility. The instrument's components -- the sensor and the signal processor -- are first described. Equations modelling electro-double layer behavior in its sensor are then developed. Simplifying assumptions include the use of a capacitance model of the double layer and a triangular velocity profile for fluid within the sensor's annulus. More complex modelling approaches are also suggested which incorporate the Gouy-Chapman electro-double layer model and an exact solution for the velocity profile. Experimental results confirm predictions of the simplified model under conditions of low potential. A monotonic relationship exists between streaming current electrophoretic mobility, which is required for its use as a control parameter. Deviations from model predictions are suggested to be due to charge characteristics of the sensor surfaces themselves.

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