Stability of power-law fluids in creeping plane Poiseuille: The effect of wall compliance

Pourjafar, M.; Hamedi, Hossein; Sadeghy, Kayvan

doi:10.1016/j.jnnfm.2014.11.006

Cited by 10 publications

(16 citation statements)

References 17 publications

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“…For the work to be applicable to biomechanical systems, we intend to allow the fluid flowing through the core of the channel to be non-Newtonian. Instability of non-Newtonian fluids in permeable and compliant channels has been investigated in separate works in the past [28][29][30], but there is no such data available in the literature for poroelastic channels. Such data are important because physiological fluids such as blood, mucus, and synovia are known to exhibit a variety of non-Newtonian behavior, chief among them are their time-and shear-dependent viscosity.…”

Section: Introductionmentioning

confidence: 99%

Pressure-driven flows of Quemada fluids in a channel lined with a poroelastic layer: A linear stability analysis

Pourjafar

Sadeghy

2017

Journal of Non-Newtonian Fluid Mechanics

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Laminar flow of a thixotropic fluid obeying the Quemada model is numerically investigated in a channel lined with a poroelastic layer saturated with a Newtonian fluid. Having assumed that the solid matrix in the poroelastic layer obeys the linear elastic model, basic flow/deformation were obtained in the main channel and also in the poroelastic layer using the biphasic mixture theory. The basic state was then subjected to infinitesimally-small, normal-mode perturbations and their vulnerability to poroelastic instability was studied based on the linear, temporal stability analysis. The eigenvalue problem so obtained was then solved numerically using the spectral collocation method. The main objective of the work was to investigate the role played by the pororelastic layer's parameters (i.e., porosity, flexibility, permeability, density, and thickness) on the stability picture. The roles played by the rheological behavior of the core fluid and the fluid flowing through the poroelastic layer were also investigated. Numerical results were obtained at low-permeability limit, typical of physiological systems, demonstrating that the effect of the layer's properties can be stabilizing or destabilizing depending on the rheological properties of the two fluids involved in the problem. In general, thixotropy was found to have a stabilizing effect on the core flow. The same was found to be true as to the effect of a fluid's shear-thinning. The analysis also served to show that the effect of a fluid's yield stress might also be stabilizing.

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Section: Introductionmentioning

confidence: 99%

Pressure-driven flows of Quemada fluids in a channel lined with a poroelastic layer: A linear stability analysis

Pourjafar

Sadeghy

2017

Journal of Non-Newtonian Fluid Mechanics

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“…The effect of wall stiffness on fluid-dynamic in microchannels has itself received great attention in the last decade. 20,[22][23][24][25] Gervais et al 22 and Hardy et al 20 theoretically and experimentally showed that PDMS channel walls are deformed under the effect of an imposed pressure-driven flow. These results were also confirmed in more recent experimental studies.…”

Section: Introductionmentioning

confidence: 99%

“…These results were also confirmed in more recent experimental studies. 23,25 In particular, by increasing the flow rate, i.e., by increasing the stress acting on the channel walls, the channel is more and more deformed. This phenomenon acquires then a great importance in several microfluidics applications such as those related with inertial particle migration and focusing.…”

Section: Introductionmentioning

confidence: 99%

“…Very recently, it has been shown that non-Newtonian fluids in pressure-driven flows can give fluid instability even in straight channels with walls made of soft materials. 25 Thus, rheology in a micro channel depends on the properties of the channel walls. As discussed above, microfluidic techniques based on particle migration in microchannel have been proved to be reliable for deriving the fluid relaxation time; those experiments, however, have been only carried out in PMMA devices.…”

Section: Introductionmentioning

confidence: 99%

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Is microrheometry affected by channel deformation?

et al. 2016

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Microrheometry is very important for exploring rheological behaviours of several systems when conventional techniques fail. Microrheometrical measurements are usually carried out in microfluidic devices made of Poly(dimethylsiloxane) (PDMS). Although PDMS is a very cheap material, it is also very easy to deform. In particular, a liquid flowing in a PDMS device, in some circumstances, can effectively deform the microchannel, thus altering the flow conditions. The measure of the fluid relaxation time might be performed through viscoelasticity induced particle migration in microfluidics devices. If the channel walls are deformed by the flow, the resulting measured value of the relaxation time could be not reliable. In this work, we study the effect of channel deformation on particle migration in square-shaped microchannel. Experiments are carried out in several PolyEthylene Oxyde solutions flowing in two devices made of PDMS and Poly(methylmethacrylate) (PMMA). The relevance of wall rigidity on particle migration is investigated, and the corresponding importance of wall rigidity on the determination of the relaxation time of the suspending liquid is examined. V C 2016 AIP Publishing LLC. [http://dx

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“…In a recent work, the effect of a fluid's viscous behavior has been investigated on the hydroelastic instability in creeping planar Poiseuille flow using the power-law model. 10) But, the effect of a fluid's yield stress on this type of instability still remains unexplored. In the present work, we intend to investigate the role played by a fluid's yield stress on the hydroelastic instability in plane channel flow.…”

Section: Introductionmentioning

confidence: 99%

Hydroelastic Instability of Viscoplastic Fluids in Plane Channel Flow

Jafargholinejad

Najafi

Sadeghy

2016

J. Soc. Rheol., Jpn

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In the present work, the effect of a fluid's yield stress is investigated on the hydroelastic instability in pressuredriven flow through a two-dimensional channel lined with a highly-compliant polymeric gel. Having assumed that the fluid obeys the Herschel-Bulkley model with the gel obeying the two-parameter Mooney-Rivlin model, analytical basic solutions were obtained for the fluid and solid sides at vanishingly-small Reynolds numbers. The stability of the basic solutions so-obtained was then investigated when subjected to infinitesimally-small, normal-mode perturbations. Having dropped all nonlinear perturbation terms, an eigenvalue problem was obtained which was numerically solved using the shooting method. The effect of the fluid's yield stress was then examined on the growth rate of the most unstable modes. Based on the numerical results obtained in this work, it is concluded that the yield stress has a destabilizing effect on pressure-driven flows of Bingham fluids in two-dimensional channels lined with compliant gels. For Herschel-Bulkley fluids, the effect of yield stress can be stabilizing or destabilizing depending on the power-law exponent (i.e., the degree of the fluid's shear-thinning). gel to obey the hyperelastic Mooney-Rivlin model, to the best of our knowledge, for the first time. This robust solid model better fits rheological data for soft polymeric gels, and so it is expected that more meaningful results could be obtained using this model. 12) Like Gkanis and Kumar 5) , we intend to focus on the creeping flow case only both because of its industrial implications in microfluidic field and also because it excludes complications which might arise through the rise of Tollmien-Schlichting (TS) waves. At this extreme, Gkanis and Kumar 5) have shown that for pressure-driven flow of Newtonian fluids in compliant channels, there are two types of instability for Re = 0: i) a finite-wavelength mode which becomes unstable for sufficiently thick solids, and (ii) a short-wavelength mode which arises due to the discontinuity of the first normal stress difference at the interface. It would be interesting to see how these modes are affected by a fluid's yield stress. To achieve its objectives, the work is organized as follows. In the next section we present the governing equations for the solid and the fluid side. We then proceed with obtaining the basic solution for each phase. The linearized equations governing the stability of the basic state are then introduced. The numerical method of solution is briefly described followed by presenting the numerical results. The work is summarized by highlighting its major findings. GOVERNING EQUATIONSWe consider the pressure-driven flow of a viscoplastic fluid in planar Poiseuille flow, as shown in Fig. 1. As can be seen in this figure, the upper and lower plates are lined with a complaint layer made of a soft polymeric gel having a thickness of HR with 2R representing the height of the channel. Assuming that the width of the channel is much larger than its height, we w...

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Stability of power-law fluids in creeping plane Poiseuille: The effect of wall compliance

Cited by 10 publications

References 17 publications

Pressure-driven flows of Quemada fluids in a channel lined with a poroelastic layer: A linear stability analysis

Pressure-driven flows of Quemada fluids in a channel lined with a poroelastic layer: A linear stability analysis

Is microrheometry affected by channel deformation?

Hydroelastic Instability of Viscoplastic Fluids in Plane Channel Flow

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