Transient Flows of Newtonian Fluid through a Rectangular Microchannel with Slip Boundary

Wiwatanapataphee, Benchawan; Wu, Yong; Suharsono, Suharsono

doi:10.1155/2014/530605

Cited by 6 publications

(12 citation statements)

References 48 publications

(65 reference statements)

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“…They presented hybrid analytical-numerical solutions for time-dependent slip flow in parallel-plate or circular channel, where the transient motion is caused by flow start-up with a step change, or a periodic time variation of the pressure gradient. Unsteady slip flows forced by a time-periodic pressure gradient through circular, annular and rectangular microchannels were investigated by Wu et al [4], and Wiwatanapataphee et al [5,6]. More recently, Crane and McVeigh [7] studied unsteady axisymmetric slip flow along an impulsively started cylinder.…”

Section: Introductionmentioning

confidence: 99%

“…On assuming steady and uniform slip lengths, our problems for starting Couette flow between two parallel flat plates and between two coaxial cylinders, and starting pressure-driven flow through a parallel-plate, rectangular, circular, and annular channel are then presented in Sections 3-8. Figures 1,3,6,8,10,13,16 show the definition sketches for these problems.…”

Section: Introductionmentioning

confidence: 99%

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Starting flow in channels with boundary slip

2016

Meccanica

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This paper contains a collection of problems and their analytical solutions for starting flows under the effect of boundary slip in channels of various geometries. The startup flows examined in this work include: (i) plane Couette flow between two plates, (ii) rotary Couette flow between two coaxial cylinders, (iii) Poiseuille flow through a parallel-plate channel, (iv) Poiseuille flow through a rectangular channel, (v) Poiseuille flow through a circular channel, and (iv) Poiseuille flow through an annulus. It is first shown that, using a depletion layer to model the effective slip, the slip length may attain its steady state much faster than the starting flow will do. This supports the use of a constant Navier slip length in the present problems. Transient solutions are derived in the form of eigenfunction expansions, where the eigenvalues are determined, by solving the characteristic equations numerically, as a function of the channel geometry and the slip lengths. From the leading eigenvalue, it is found that the boundary slip will in general lengthen the transient period of a starting flow.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Starting flow in channels with boundary slip

2016

Meccanica

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“…It is worth mentioning some other investigations of the unsteady slip flows, Refs. [45][46][47][48][49], where the Navier's slip condition, Eq. (1), was used, including the case of the oscillatory flow studied in Ref.…”

Section: Introductionmentioning

confidence: 99%

Start-up slip flow in a microchannel with a rectangular cross section

Авраменко

Tyrinov

Shevchuk³

2015

Theor. Comput. Fluid Dyn.

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The paper outlines results of the theoretical study of an incompressible fluid flow in a rectangular microchannel subject to a sudden time-dependent pressure drop. The momentum equation together with the independent and dependent variables was reduced to a self-similar form by means of the symmetry analysis. The problem was solved using two analytical approaches, the Fourier method and the method of eigenfunction decomposition, as well as numerically by means of the lattice Boltzmann method. The unsteady two-dimensional velocity profiles in the microchannel were predicted using the infinite series and validated against the numerical solution. As expected, the flow pattern asymptotically attains the fully developed state, which is reached more rapidly for smaller Knudsen numbers. The analytical solution yielded expressions for the calculation of the hydraulic resistance coefficient.

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“…General remarks on microchannels and applications are given in many papers, in particular [49,74,75,85]. The papers just cited develop explicit exact solutions of pde problems, similar to those of §1.2, for various simple geometries for the cross-sectional shape Ω of the microchannel; rectangles in [85], circular cross-section in [74]. This paper has a different focus, namely that of describing qualitative properties and bounds on solutions to functionals of solutions of the pde problem.…”

Section: Introduction 1overviewmentioning

confidence: 99%

Some isoperimetric results concerning undirectional flows in microchannels

Keady,

Wiwatanapataphee

2016

Preprint

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Three isoperimetric results are treated. (i) At a given pressure gradient, for all channels with given (cross-sectional) area that which maximises the steady flow Q steady has a circular cross-section. (ii) Consider flows starting from prescribed initial conditions developing from a prescribed imposed pressure gradient, either periodic or steady. For such flows, amongst all channels with given area, that which generically has the slowest approach to the long-term, periodic or steady, flow is the circular disk cross-section. (iii) Similar results for polygonal, n-gon, channels, with the optimising shape being the regular n-gon are discussed. This arXiv preprint will supplement the journal paper (submitted just before this supplement): the journal paper reports, concisely, the isoperimetric results of Theorems 1, 2 and 3. Items here additional to the journal paper include further isoperimetric results, estimates involving geometric functionals besides area such as perimeter and moment of inertia, perturbation analysis of nearly circular domains, and reporting on some previously published conjectures.

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Transient Flows of Newtonian Fluid through a Rectangular Microchannel with Slip Boundary

Cited by 6 publications

References 48 publications

Starting flow in channels with boundary slip

Starting flow in channels with boundary slip

Start-up slip flow in a microchannel with a rectangular cross section

Some isoperimetric results concerning undirectional flows in microchannels

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