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Ström OE, Beech JP, Tegenfeldt JO. Geometry-Dependent Elastic Flow Dynamics in Micropillar Arrays. MICROMACHINES 2024; 15:268. [PMID: 38398996 PMCID: PMC10893274 DOI: 10.3390/mi15020268] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2023] [Revised: 01/31/2024] [Accepted: 02/06/2024] [Indexed: 02/25/2024]
Abstract
Regular device-scale DNA waves for high DNA concentrations and flow velocities have been shown to emerge in quadratic micropillar arrays with potentially strong relevance for a wide range of microfluidic applications. Hexagonal arrays constitute another geometry that is especially relevant for the microfluidic pulsed-field separation of DNA. Here, we report on the differences at the micro and macroscopic scales between the resulting wave patterns for these two regular array geometries and one disordered array geometry. In contrast to the large-scale regular waves visible in the quadratic array, in the hexagonal arrays, waves occur in a device-scale disordered zig-zag pattern with fluctuations on a much smaller scale. We connect the large-scale pattern to the microscopic flow and observe flow synchronization that switches between two directions for both the quadratic and hexagonal arrays. We show the importance of order using the disordered array, where steady-state stationary and highly fluctuating flow states persist in seemingly random locations across the array. We compare the flow dynamics of the arrays to that in a device with sparsely distributed pillars. Here, we observe similar vortex shedding, which is clearly observable in the quadratic and disordered arrays. However, the shedding of these vortices couples only in the flow direction and not laterally as in the dense, ordered arrays. We believe that our findings will contribute to the understanding of elastic flow dynamics in pillar arrays, helping us elucidate the fundamental principles of non-Newtonian fluid flow in complex environments as well as supporting applications in engineering involving e.g., transport, sorting, and mixing of complex fluids.
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Affiliation(s)
| | | | - Jonas O. Tegenfeldt
- Division of Solid State Physics, Department of Physics and NanoLund, Lund University, P.O. Box 118, 22100 Lund, Sweden; (O.E.S.); (J.P.B.)
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2
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Yokokoji A, Varchanis S, Shen AQ, Haward SJ. Rheological effects on purely-elastic flow asymmetries in the cross-slot geometry. SOFT MATTER 2023; 20:152-166. [PMID: 38055332 DOI: 10.1039/d3sm01209c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/08/2023]
Abstract
Viscoelastic flows in the cross-slot geometry can undergo a transition from a steady symmetric to a steady asymmetric flow state, ostensibly due to purely-elastic effects arising beyond a critical flow rate, or Weissenberg number Wi. However, some reports suggest that shear thinning of the fluid's viscosity may also play an important role in this transition. We employ a series of polymer solutions of varying rheological properties to investigate in detail how the interplay between fluid elasticity and shear thinning affects the onset and development of asymmetric flows in the cross-slot. Flow velocimetry is performed on each of the polymer solutions, and is used to assess the degree of flow asymmetry I in the cross-slot as a function of both Wi and a dimensionless parameter S quantifying the flow-rate-dependent extent of shear thinning. Typically, the flow field breaks symmetry as Wi is increased beyond a critical value, but the magnitude of I is found to also be dependent on S. For a few specific polymer solutions, the flow field recovers symmetry above a second, higher critical Wi as S becomes small. The experimental results are summarized in a flow state diagram in Wi-S space, showing the relationship between flow asymmetry and fluid rheology. Finally, to gain a deeper understanding of the effects of shear thinning, numerical simulations are performed using the linear simplified Phan-Thien-Tanner model. We demonstrate that the degree of both shear thinning and elasticity of the fluid, and their interplay, are important factors controlling elastic instabilities in the cross-slot geometry.
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Affiliation(s)
- Arisa Yokokoji
- Okinawa Institute of Science and Technology Graduate Univerisity, Onna-son, Okinawa 904-0495, Japan.
| | - Stylianos Varchanis
- Okinawa Institute of Science and Technology Graduate Univerisity, Onna-son, Okinawa 904-0495, Japan.
| | - Amy Q Shen
- Okinawa Institute of Science and Technology Graduate Univerisity, Onna-son, Okinawa 904-0495, Japan.
| | - Simon J Haward
- Okinawa Institute of Science and Technology Graduate Univerisity, Onna-son, Okinawa 904-0495, Japan.
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3
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Ström OE, Beech JP, Tegenfeldt JO. Short and long-range cyclic patterns in flows of DNA solutions in microfluidic obstacle arrays. LAB ON A CHIP 2023; 23:1779-1793. [PMID: 36807458 DOI: 10.1039/d2lc01051h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
We observe regular patterns emerging across multiple length scales with high-concentration DNA solutions in microfluidic pillar arrays at low Reynolds numbers and high Deborah numbers. Interacting vortices between pillars lead to long-range order in the form of large travelling waves consisting of DNA at high concentration and extension. Waves are formed in quadratic arrays of pillars, while randomizing the position of the pillar in each unit cell of a quadratic array leads to suppression of the long-range patterns. We find that concentrations exceeding the overlap concentration of the DNA enables the waves, and exploring the behavior of the waves as a function of flow rate, buffer composition, concentration and molecular length, we identify elastic effects as central to the origin of the waves. Our work may not only help increase the low throughput that often limits sample processing in microfluidics, it may also provide a platform for further studies of the underlying viscoelastic mechanisms.
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Affiliation(s)
- Oskar E Ström
- Division of Solid State Physics, Department of Physics, Lund University, Lund, Sweden.
| | - Jason P Beech
- Division of Solid State Physics, Department of Physics, Lund University, Lund, Sweden.
| | - Jonas O Tegenfeldt
- Division of Solid State Physics, Department of Physics, Lund University, Lund, Sweden.
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4
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Chen H, Poitzsch ME. Dynamics of Polymers Flowing through Porous Media: Interplay of Solvent Properties, Flow Rates, and Wetting. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01902] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Hsieh Chen
- Aramco Americas: Aramco Research Center-Boston, Cambridge, Massachusetts02139, United States
| | - Martin E. Poitzsch
- Aramco Americas: Aramco Research Center-Boston, Cambridge, Massachusetts02139, United States
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5
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Abstract
Abstract
Flow of complex fluids in porous structures is pertinent in many biological and industrial processes. For these applications, elastic turbulence, a viscoelastic instability occurring at low Re—arising from a non-trivial coupling of fluid rheology and flow geometry—is a common and relevant effect because of significant over-proportional increase in pressure drop and spatio-temporal distortion of the flow field. Therefore, significant efforts have been made to predict the onset of elastic turbulence in flow geometries with constrictions. The onset of flow perturbations to fluid streamlines is not adequately captured by Deborah and Weissenberg numbers. The introduction of more complex dimensionless numbers such as the M-criterion, which was meant as a simple and pragmatic method to predict the onset of elastic instabilities as an order-of-magnitude estimate, has been successful for simpler geometries. However, for more complex geometries which are encountered in many relevant applications, sometimes discrepancies between experimental observation and M-criteria prediction have been encountered. So far these discrepancies have been mainly attributed to the emergence from disorder. In this experimental study, we employ a single channel with multiple constrictions at varying distance and aspect ratios. We show that adjacent constrictions can interact via non-laminar flow field instabilities caused by a combination of individual geometry and viscoelastic rheology depending (besides other factors) explicitly on the distance between adjacent constrictions. This provides intuitive insight on a more conceptual level why the M-criteria predictions are not more precise. Our findings suggest that coupling of rheological effects and fluid geometry is more complex and implicit and controlled by more length scales than are currently employed. For translating bulk fluid, rheology determined by classical rheometry into the effective behaviour in complex porous geometries requires consideration of more than only one repeat element. Our findings open the path towards more accurate prediction of the onset of elastic turbulence, which many applications will benefit.
Article Highlights
We demonstrate that adjacent constrictions “interact” via the non-laminar flow fields caused by individual constrictions, implying that the coupling of rheological effects and fluid geometry is more complex and implicit.
The concept of characterizing fluid rheology independent of flow geometry and later coupling back to the geometry of interest via dimensionless numbers may fall short of relevant length scales, such as the separation of constrictions which control the overlap of flow fields.
By providing direct experimental evidence illustrating the cause of the shortcoming of the status-quo, the expected impact of this work is to challenge and augment existing concepts that will ultimately lead to the correct prediction of the onset of elastic turbulence.
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Zhu S, Zhang S, Xue X, Zhang J, Xu J, Liu Z. Influencing factors for effective establishment of residual resistance factor of polymer solution in porous media. JOURNAL OF POLYMER RESEARCH 2022. [DOI: 10.1007/s10965-022-03066-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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7
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Ahuja VR, van der Gucht J, Briels W. Large Scale Hydrodynamically Coupled Brownian Dynamics Simulations of Polymer Solutions Flowing through Porous Media. Polymers (Basel) 2022; 14:polym14071422. [PMID: 35406296 PMCID: PMC9003297 DOI: 10.3390/polym14071422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2022] [Revised: 03/19/2022] [Accepted: 03/25/2022] [Indexed: 11/20/2022] Open
Abstract
Large scale simulations of polymer flow through porous media provide an important tool for solving problems in enhanced oil recovery, polymer processing and biological applications. In order to include the effects of a wide range of velocity and density fluctuations, we base our work on a coarse-grain particle-based model consisting of polymers following Brownian dynamics coupled to a background fluid flow through momentum conserving interactions. The polymers are represented as Finitely Extensible Non-Linear Elastic (FENE) dumbbells with interactions including slowly decaying transient forces to properly describe dynamic effects of the eliminated degrees of freedom. Model porous media are constructed from arrays of parallel solid beams with circular or square cross-sections, arranged periodically in the plane perpendicular to their axis. No-slip boundary conditions at the solid–fluid interfaces are imposed through interactions with artificial particles embedded within the solid part of the system. We compare the results of our simulations with those of standard Smoothed Particle Hydrodynamics simulations for Newtonian flow through the same porous media. We observe that in all cases the concentration of polymers at steady state is not uniform even though we start the simulations with a uniform polymer concentration, which is indicative of shear-induced cross-flow migration. Furthermore, we see the characteristic flattening of the velocity profile experimentally observed for shear-thinning polymer solutions flowing through channels as opposed to the parabolic Poiseuille flow profile for Newtonian fluids.
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Affiliation(s)
- Vishal Raju Ahuja
- Shell India Markets Private Limited, Shell Technology Centre Bangalore, Plot No 7, Bangalore Hardware Park, Devanahalli Industrial Park, Mahadeva Kodigehalli, Bengaluru 562149, Karnataka, India
- Correspondence: (V.R.A.); (W.B.)
| | - Jasper van der Gucht
- Physical Chemistry and Soft Matter, Wageningen University, Building 124, Stippeneng 4, 6708 WE Wageningen, The Netherlands;
| | - Wim Briels
- Computational Chemical Physics, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
- Forschungszentrum Jülich, IBI 4, D-52425 Jülich, Germany
- Correspondence: (V.R.A.); (W.B.)
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8
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Pore-Scale Flow Fields of the Viscosity-Lost Partially Hydrolyzed Polyacrylamide Solution Caused by Sulfide Ion. ENERGIES 2022. [DOI: 10.3390/en15062048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The rheology of a partially hydrolyzed polyacrylamide (HPAM) solution plays an important role in its oil recovery during polymer flooding. However, multiple factors in brine, such as sulfide ions, cause a dramatic loss in the viscosity and oil recovery. To better understand the sulfide-induced viscosity loss and the consequent flow mechanisms in pore networks, the morphology of polymer solutions with and without sulfide ion was observed by scanning electron microscopy; and the variations of the pore scale flow fields were demonstrated by a microscopic visualization seepage experiment combined with Micro-PIV (Microscale Particle Image Velocimetry). The results showed that, with the presence of sulfide ion, the microstructure of the polymer changed from a uniform three-dimensional network structure to loose and uneven floccules, which resulted in viscosity loss (over 70% with 5-mg/L sulfide ion). Moreover, higher concentrations of sulfide ions (5 mg/L and 10 mg/L) resulted in earlier shear thinning characteristics than those with lower sulfide concentrations. Due to viscosity loss, the average flow velocity in the main stream of the microscopic seepage experiment increased more significantly than that without sulfide. However, the viscosity loss alone cannot independently explain the severe viscous fingering during the subsequent post-water flooding, which was about five times greater than that of the primary water flooding in terms of the velocity ratio between the mainstream and margin. A further pore-scale flow field analysis exhibited an eccentric and a bimodal velocity distribution in the throat along the radial and axial directions, respectively. The former distribution indicated that the adsorbed polymer on the pore wall was broken through by hydraulic shear due to the collapsed structure caused by sulfide ion. The latter suggested that another sulfide-induced impact was an earlier-occurring non-Newtonian characteristic with a low shear rate. Therefore, instead of viscosity loss, elastic loss is the dominant mechanism affecting the characteristics of the aggregate flow field under the action of sulfide. Microscopic flooding combined with Micro-PIV is a feasible and essential method to reveal pore scale flow mechanisms.
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Haward SJ, Hopkins CC, Shen AQ. Stagnation points control chaotic fluctuations in viscoelastic porous media flow. Proc Natl Acad Sci U S A 2021; 118:e2111651118. [PMID: 34521756 PMCID: PMC8463809 DOI: 10.1073/pnas.2111651118] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/14/2021] [Indexed: 11/18/2022] Open
Abstract
Viscoelastic flows through porous media become unstable and chaotic beyond critical flow conditions, impacting widespread industrial and biological processes such as enhanced oil recovery and drug delivery. Understanding the influence of the pore structure or geometry on the onset of flow instability can lead to fundamental insights into these processes and, potentially, to their optimization. Recently, for viscoelastic flows through porous media modeled by arrays of microscopic posts, Walkama et al. [D. M. Walkama, N. Waisbord, J. S. Guasto, Phys. Rev. Lett 124, 164501 (2020)] demonstrated that geometric disorder greatly suppressed the strength of the chaotic fluctuations that arose as the flow rate was increased. However, in that work, disorder was only applied to one originally ordered configuration of posts. Here, we demonstrate experimentally that, given a slightly modified ordered array of posts, introducing disorder can also promote chaotic fluctuations. We provide a unifying explanation for these contrasting results by considering the effect of disorder on the occurrence of stagnation points exposed to the flow field, which depends on the nature of the originally ordered post array. This work provides a general understanding of how pore geometry affects the stability of viscoelastic porous media flows.
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Affiliation(s)
- Simon J Haward
- Micro/Bio/Nanofluidics Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Cameron C Hopkins
- Micro/Bio/Nanofluidics Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Amy Q Shen
- Micro/Bio/Nanofluidics Unit, Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
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10
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11
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Raihan MK, Jagdale PP, Wu S, Shao X, Bostwick JB, Pan X, Xuan X. Flow of Non-Newtonian Fluids in a Single-Cavity Microchannel. MICROMACHINES 2021; 12:836. [PMID: 34357246 PMCID: PMC8306080 DOI: 10.3390/mi12070836] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/06/2021] [Revised: 07/15/2021] [Accepted: 07/16/2021] [Indexed: 11/23/2022]
Abstract
Having a basic understanding of non-Newtonian fluid flow through porous media, which usually consist of series of expansions and contractions, is of importance for enhanced oil recovery, groundwater remediation, microfluidic particle manipulation, etc. The flow in contraction and/or expansion microchannel is unbounded in the primary direction and has been widely studied before. In contrast, there has been very little work on the understanding of such flow in an expansion-contraction microchannel with a confined cavity. We investigate the flow of five types of non-Newtonian fluids with distinct rheological properties and water through a planar single-cavity microchannel. All fluids are tested in a similarly wide range of flow rates, from which the observed flow regimes and vortex development are summarized in the same dimensionless parameter spaces for a unified understanding of the effects of fluid inertia, shear thinning, and elasticity as well as confinement. Our results indicate that fluid inertia is responsible for developing vortices in the expansion flow, which is trivially affected by the confinement. Fluid shear thinning causes flow separations on the contraction walls, and the interplay between the effects of shear thinning and inertia is dictated by the confinement. Fluid elasticity introduces instability and asymmetry to the contraction flow of polymers with long chains while suppressing the fluid inertia-induced expansion flow vortices. However, the formation and fluctuation of such elasto-inertial fluid vortices exhibit strong digressions from the unconfined flow pattern in a contraction-expansion microchannel of similar dimensions.
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Affiliation(s)
- Mahmud Kamal Raihan
- Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA; (M.K.R.); (P.P.J.); (S.W.); (J.B.B.)
| | - Purva P. Jagdale
- Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA; (M.K.R.); (P.P.J.); (S.W.); (J.B.B.)
| | - Sen Wu
- Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA; (M.K.R.); (P.P.J.); (S.W.); (J.B.B.)
- College of Marine Engineering, Dalian Maritime University, Dalian 116026, China;
| | - Xingchen Shao
- Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, MD 21218, USA;
| | - Joshua B. Bostwick
- Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA; (M.K.R.); (P.P.J.); (S.W.); (J.B.B.)
| | - Xinxiang Pan
- College of Marine Engineering, Dalian Maritime University, Dalian 116026, China;
- Maritime College, Guangdong Ocean University, Zhanjiang 524088, China
| | - Xiangchun Xuan
- Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, USA; (M.K.R.); (P.P.J.); (S.W.); (J.B.B.)
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12
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Solution properties and seepage characteristics of a dendritic hydrophobically associating polymer. JOURNAL OF POLYMER RESEARCH 2021. [DOI: 10.1007/s10965-021-02589-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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13
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Chen H, Poitzsch ME. Emergent slow dynamics of collapsed polymers flowing through porous media. Phys Rev E 2021; 103:L040501. [PMID: 34005983 DOI: 10.1103/physreve.103.l040501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 04/08/2021] [Indexed: 11/07/2022]
Abstract
Using hydrodynamic simulations, we study the single polymers flowing through model porous media (close-packed colloidal crystal). In good solvent or high flow rates, the polymer transport is similar to gel electrophoresis, with size-dependent sieving for L_{c}/L≲1 and size-independent biased reptation for L_{c}/L≳1 (L_{c} is the polymer contour length and L is the diameter of colloids forming the porous media). Importantly, in bad solvent and low flow rates, the polymers show an extra window of size-dependent velocity for 1≲L_{c}/L≲2, where the polymer transport is controlled by a globule-stretch transition at pore throats, and the transport velocity is much slower than reptation.
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Affiliation(s)
- Hsieh Chen
- Aramco Services Company: Aramco Research Center-Boston, Cambridge, Massachusetts 02139, USA
| | - Martin E Poitzsch
- Aramco Services Company: Aramco Research Center-Boston, Cambridge, Massachusetts 02139, USA
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14
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Rodríguez de Castro A, Goyeau B. A pore network modelling approach to investigate the interplay between local and Darcy viscosities during the flow of shear-thinning fluids in porous media. J Colloid Interface Sci 2021; 590:446-457. [PMID: 33561594 DOI: 10.1016/j.jcis.2021.01.081] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2020] [Revised: 01/14/2021] [Accepted: 01/25/2021] [Indexed: 11/25/2022]
Abstract
During the flow of non-Newtonian fluids in porous media, the relationships between macroscopic quantities are governed by extremely complex microscopic fluid dynamics resulting from solid-fluid interactions. Consequently, the Darcy-scale viscosity exhibited by a shear-thinning fluid depends on the injection velocity, contrarily to the case of Newtonian fluids. In the present work, pore network modelling is used to investigate the relationships between local and macroscopic viscosities during the flow of shear-thinning fluids in 3D porous media. Special efforts are devoted to 1) identifying the influence of the viscosity exhibited by the fluid within the constrictions of the preferential flow paths on the value of Darcy-scale viscosity and 2) proposing an analytical expression to upscale viscosity from the local viscosity values. To go further, the reduction in average hydraulic tortuosity stemming from the directional nature of shear-thinning behavior in 3D porous media will also be quantified. The results of the present study show that Darcy-scale viscosity can be accurately calculated as the flow-rate weighted average of local viscosities in the investigated media. Moreover, the velocity maps provided by the proposed pore network flow simulations are suitable to assess hydraulic tortuosity reduction as compared to the flow of a Newtonian fluid.
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Affiliation(s)
| | - Benoit Goyeau
- Laboratoire EM2C, UPR CNRS 288, Centrale-Supélec, Université Paris-Saclay, 3 rue Joliot-Curie, 91190 Gif-sur-Yvette, France
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15
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Hopkins CC, Haward SJ, Shen AQ. Tristability in Viscoelastic Flow Past Side-by-Side Microcylinders. PHYSICAL REVIEW LETTERS 2021; 126:054501. [PMID: 33605746 DOI: 10.1103/physrevlett.126.054501] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 01/04/2021] [Indexed: 05/13/2023]
Abstract
Viscoelastic flows through microscale porous arrays exhibit complex path selection and switching phenomena. However, understanding this process is limited by a lack of studies linking between a single object and large arrays. Here, we report experiments on viscoelastic flow past side-by-side microcylinders with variable intercylinder gap. With increasing flow rate, a sequence of two imperfect symmetry-breaking bifurcations forces selection of either one or two of the three possible flow paths around the cylinders. Tuning the gap length through the value where the first bifurcation becomes perfect reveals regions of bistability and tristability in a dimensionless flow rate-gap length phase diagram.
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Affiliation(s)
- Cameron C Hopkins
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Simon J Haward
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
| | - Amy Q Shen
- Okinawa Institute of Science and Technology Graduate University, Onna-son, Okinawa 904-0495, Japan
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