Spatiotemporal multistability in viscoelastic microcavity flows: Topological decoupling and rheological competition

Precise prediction of heat transport in porous media holds crucial significance in Earth Sciences for diverse applications, ranging from the design of geothermal systems to utilizing heat as a tracer in aquifers. Traditionally, the description of heat transport has been simplified by assuming local thermal equilibrium (LTE), where the temperature within the fluid and solid phases in the representative elementary volume is presumed to reach an instant equilibrium. In reality, assuming two distinct phases coupled by heat transfer across their surface area describes the complete physics and is referred to as the local thermal non-equilibrium (LTNE) model. While earlier research delved into the theoretical aspects of LTNE effects, a notable gap exists due to the absence of experimental data to elucidate the heat transport mechanism in porous aquifers containing natural grains. To address this gap and investigate LTNE on a granular scale, we conducted systematic flow-through experiments employing porous media containing glass spheres with distinct grain sizes of 5, 10, 15, 20, 25 and 30 mm. Each sphere contained a small temperature sensor for the solid temperature, accompanied by sensors in the adjacent pore space to measure the fluid temperature. Our findings revealed that the temperature difference between two phases grows with increasing grain size and flow velocity ranging from 9 to 61 m d-1, thereby highlighting qualitative LTNE effects in relation to grain size and flow velocity. To further enhance our understanding, we used a numerical model to investigate the heat transfer coefficient, fitting the LTNE model to the experimental data. These simulation results indicated evidence of non-uniform flow which we included into our model to estimate its effects on heat transport. This comprehensive approach contributes valuable insights into the intricate interplay of LTNE effects, grain sizes, and flow velocity, advancing our understanding of heat transport in natural porous media.

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTTransport in pores with sterically stabilized particlesSanjay Misra and H. Scott FoglerCite this: Langmuir 1993, 9, 5, 1306–1314Publication Date (Print):May 1, 1993Publication History Published online1 May 2002Published inissue 1 May 1993https://pubs.acs.org/doi/10.1021/la00029a025https://doi.org/10.1021/la00029a025research-articleACS PublicationsRequest reuse permissionsArticle Views64Altmetric-Citations1LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail Other access optionsGet e-Alertsclose Get e-Alerts

Historically, the dominant conceptual paradigm of porous media flow, solute mixing and transport was based on steady two-dimensional flows in heterogeneous porous media. Although it is now well recognised that novel transport phenomena can arise in unsteady and/or three-dimensional flows at both the pore- or Darcy-scales, appropriate methods for analysis and understanding of these more complex flows have not been widely employed. In this primer we advocate for methods borrowed from dynamical systems (chaos) theory, which aim to uncover the \emph{Lagrangian kinematics} of these flows: namely how fluid particle trajectories (which form a dynamical system) are organized and interact and the associated impacts on solute transport and mixing. This dynamical systems approach to transport is inherently Lagrangian, and the Lagrangian kinematics form Lagrangian coherent structures (LCSs), special sets of trajectories that divide the Lagrangian frame into chaotic mixing regions, poorly mixing hold-up regions (and in some cases non-mixing ``islands'') and the transport barriers that organise these regions. Hence the dynamical systems approach provides insights into flows that may exhibit chaotic, regular (non-chaotic) or mixed Lagrangian kinematics, and also into how LCSs organize solute transport and mixing. Novel experimental methods are only recently permitting visualization of LCSs are in porous media flows. In this primer we review the dynamical systems approach to porous media flow and transport and connect the associated tools and techniques with the latest research findings from pore to Darcy scales. This primer provides an introduction to the methods and tools of dynamical systems theory. Once familiar with these approaches, porous media researchers will be better positioned to know when to expect complex Lagrangian kinematics, how to uncover and understand LCSs and their impacts ...

Polymeric flow through porous media is relevant in industrial applications, such as enhanced oil recovery, microbial mining, and groundwater remediation. Biological processes, such as drug delivery and the transport of cells and particles in the body, also depend on the viscoelastic flow through the porous matrix. Large elastic stresses induced due to confined geometries can lead to elastic instability for the viscoelastic fluid flow through porous media. We have numerically studied viscoelastic flow through a channel having two closely placed cylinders to investigate pore scale elastic instabilities. We have discovered three distinct flow states in the region between the cylinders. These flow states are closely coupled with the topology of the polymeric stress field. The transition between the flow states can be identified with two critical Weissenberg numbers (Wicr1 and Wicr2), where the Weissenberg number (Wi) is the ratio of elastic to viscous forces. At Wi<Wicr1, the flow is stable, symmetric, and eddy free. For Wicr1<Wi<Wicr2, eddies form in the region between the cylinders. We have measured the area occupied by the eddies for different flow conditions and fluid rheological parameters. At Wi>Wicr2, the eddy disappears and the flow around the cylinders becomes asymmetric. We have quantified the flow asymmetry around the cylinders for different flow rates and fluid rheology. We have also studied the effect of the cylinders' diameter and separation on the eddies' size (Wicr1<Wi<Wicr2) and flow asymmetry (Wi>Wicr2). We have also investigated the effect of fluid rheology and cylinders' diameter and separation on the value of critical Weissenberg numbers.

Improvements in imaging techniques have enabled the reconstruction of complex porous media which can be analyzed by computer simulations. The two most popular methods for numerical analysis of transport in porous media are direct numerical simulation (DNS) and pore network modeling (PNM). This work aims at assessing the suitability of these techniques to study dry and wet transport properties of porous transport layers for fuel cells and electrolyzers by comparing numerical predictions to experimental data for mercury intrusion, and transport properties. The microstructures of different materials are obtained using micro X-ray computed tomography and characterized by measuring mercury intrusion porosimetry (MIP) curves, dry permeability and diffusivity. Their results are compared to numerically predicted MIP, and dry and wet permeability and diffusivity. Results show that DNS is capable of accurately predicting intrusion, and transport properties without using any fitting parameters. Accurate predictions could be achieved with a PNM when the inscribed diameter method was used for pore size distribution, and the equivalent diameter was used to estimate pore transport properties. While DNS provides more accurate results without necessitating any calibration, a properly constructed PNM is shown to provide relatively good estimations of transport properties at a reduced computational expense.

Proton exchange membrane (PEM) water electrolysis is a technology designed to produce H2 using only water and electricity as inputs; it has gained increased attention in industry and academia due to its advantages over incumbent H2 generation processes (of which the most widely used are steam reforming and coal gasification) namely, low temperature, carbon-neutral and intermittent operation. PEM electrolysis can be instrumental for creating a hydrogen economy, although still much research needs to be carried out before widespread industrial adoption is achieved. PEM water electrolyzers suffer energy losses associated with the chemical reactions and the transport of charge and mass; of these phenomena, mass transport in PEM electrolyzers is the least understood subject, given the complex nature of the interaction of multiphase flows (mainly consisting of liquid water and evolved gases) through micrometric pores. The subject of multiphase flow in water electrolysis and its relationship with the mass transport phenomena in PEM water electrolysis has been a prevalent subject in the literature. Despite numerous attempts at pinpointing the relationship between mass transport overpotential and the operating parameters, there is no clear consensus about which transport mechanisms dominate, nor about how the component design of PEM electrolyzers affects the mass transport. While the effect of temperature and current density on mass transport losses has been extensively studied and is well understood, there are significantly fewer studies that focus on the effect of water flow and pressure. Both water flow and pressure have a direct effect on mechanisms such as bubble nucleation and two-phase flows that occur in the porous structures within a PEM electrolyzer (electrodes and porous transport layers, PTLs). In this work, I studied the effect of water flow and pressure on the mass transport phenomena in PEM electrolyzers. Chapters 1 and 2 provide an introduction to the topic as well as a description of the materials and experimental setups used. Chapter 3 of this thesis depicts the visualization and modeling of bubble nucleation in an operating PEM electrolyzer. I discovered that bubble detachment radii are largely independent of water flow and I identified two types of bubbles: bubbles that detach after reaching a critical size, and bubbles that fill up the pores of a PTL before detaching. Chapter 3 consists of the measurements I carried out regarding the transport of evolved gas through the water-filled pores of a PTL, where I observed that water flow severely impedes the gas transport through the pores and that such impediment is related to a shear stress exerted by the water flow on the pores. Chapter 5 shows the measuring of mass transport losses using electrochemical impedance spectroscopy (EIS) on an operating PEM electrolyzer; the results indicate that pressure and water flow affect the diffusion of gas in the electrode and that the mass transport overpotential depends on design parameters of the PEM electrolyzer, such as electrode thickness and hydrophobicity. Overall, I derived a theoretical framework based on the assumption that the evolved gas in a PEM electrolyzer permeates through the PTL after diffusing from the active sites to the bubble nucleation sites. Such framework, constructed on the basis of the models regarding gas transport in porous media, can be used to explain the mass transport loses in a PEM electrolyzer that arise from operating with increased water flows and pressures. The model I derived can be used in future work as a guideline to optimize the components of a PEM electrolyzer, in particular regarding the hydrophobicity and pore size distribution of PTLs as well as the composition of the catalyst ink to produce the electrodes. Moreover, this work can also be used to further understand the mass transport losses and optimize the operation of PEM electrolyzers to decrease the energy consumption of H2 generation.

One of the factors leading to a decrease in the efficiency of polymer electrolyte membrane (PEM) electrolyzers is the blockage of water transport pathways through the porous transport layer (PTL). The oxygen bubbles generated from the electrochemical reaction at the catalyst layer accumulate in the PTL, impeding the transport pathways and reaction sites for the reactant water (1). An improved understanding of oxygen bubble accumulation and water transport behaviour in porous transport layers is essential to reduce mass transport losses in PEM electrolyzers. This study presents a method to stochastically generate a PTL composed of sintered titanium (Ti) powders and investigate the transport properties using pore network modeling. A microscale X-ray computed tomography (µ-CT) was performed for a sintered Ti powder PTL sample to obtain a 2D density map. The density map contains material content information, providing higher intensity at the positions with higher material content. With the density map as an input, a stochastic model of the PTL was generated by placing Ti powder particles at positions decided by the density map and a probability function until the model reached the target volume (2). Two critical parameters are considered in this model: the seeding parameter, α, and a filling radius, β. The seeding parameter controls the number of Ti powder “seeds” that act as nucleation sites. The second parameter, the filling radius, allows the model to mimic the morphology of the sintered regions. The structural properties of the stochastic model are investigated by comparing the pore size distribution, throat size distribution, and the porosity profile to the µ-CT reconstruction. Pore network modeling is an alternative to continuum modeling for simulating transport in porous media. Pore network modeling simplifies the solution of differential equations for mass transport by treating the pore space as a network of pores and narrow throats (3). Using pore network modeling as the analysis tool, the in-plane permeabilities of the µ-CT reconstruction and the stochastic model were compared. The stochastic modeling of PTLs will facilitate the detailed parametric studies of PTL structural property impacts on transport and provide novel insights into mass transport behavior in PEM electrolyzers.References H. Ito, T. Maeda, A. Nakano, Y. Hasegawa, N. Yokoi, C. M. Hwang, M. Ishida, A. Kato, and T. Yoshida, International journal of hydrogen energy 35(18), 9550-9560 (2010). A. Ebrahimi Khabbazi, J. Hinebaugh, A. Bazylak, Science Bulletin, 61(8), 601-611(2016).A. Putz, J. Hinebaugh, M. Aghighi, H. Day, A. Bazylak, and J. T. Gostick, ECS Transactions, 58(1), 79-86 (2013).

Gas transport in porous media under dynamic conditions

The orientation of an ellipsoid falling in a viscoelastic fluid is studied by methods of perturbation theory. For small fall velocity, the fluid's rheology is described by a second-order fluid model. The solution of the problem can be expressed by a dual expansion in two small parameters: the Reynolds number representing the inertial effect and the Weissenberg number representing the effect of the non-Newtonian stress. Then the original problem is split into three canonical problems: the zeroth-order Stokes problem for a translating ellipsoid and two first-order problems, one for inertia and one for second-order rheology. A Stokes operator is inverted in each of the three cases. The problems are solved numerically on a three-dimensional domain by a finite element method with fictitious domains, and the force and torque on the body are evaluated. The results show that the signs of the perturbation pressure and velocity around the particle for inertia are reversed by viscoelasticity. The torques are also of opposite sign: inertia turns the major axis of the ellipsoid perpendicular to the fall direction; normal stresses turn the major axis parallel to the fall. The competition of these two effects gives rise to an equilibrium tilt angle between 0° and 90° which the settling ellipsoid would eventually assume. The equilibrium tilt angle is a function of the elasticity number, which is the ratio of the Weissenberg number and the Reynolds number. Since this ratio is independent of the fall velocity, the perturbation results do not explain the sudden turning of a long body which occurs when a critical fall velocity is exceeded. This is not surprising because the theory is valid only for slow sedimentation. However, the results do seem to agree qualitatively with ‘shape tilting’ observed at low fall velocities.

A generalization of averaging theorems for porous medium analysis

The objective of this work is to characterize the onset of laterally asymmetric flow of viscoelastic solutions around a confined microfluidic cylinder, which was encountered in a recent study [Rodrigues et al., J. Non-Newtonian Fluid Mech. 289, 104406 (2020)]. To this end, two non-Newtonian fluids were employed in the same micro-geometry. Two microchannels were studied, both with a cylinder of diameter 75 μm, aspect ratio (channel height over width) of 0.37, and blockage ratio (cylinder diameter over channel width) of 0.28, differing only on the width of the pressure taps, located 500 μm up- and downstream from the respective cylinder face, on opposing walls. The working fluids consist of two poly(ethylene oxide) solutions: an elastic weakly shear-thinning fluid and an elastic shear-thinning fluid. Micro-Particle Image Velocimetry and streak imaging techniques were used to evaluate the flow over a Weissenberg number range 100≤Wi≤500, while maintaining a low Reynolds number, Re < 1. The elastic shear-thinning solution showed laterally asymmetric flow past the cylinder with both pressure tap designs, while with the weakly shear-thinning solution asymmetric flow was only observed with the wider pressure tap intake. In both cases, the fluids preferentially chose the cylinder/wall gap opposing the upstream pressure tap, which was found to influence the flow greatly, seemingly associated with time-dependent flow and possibly the lateral flow asymmetry itself. This work brings to light the necessary compromise between optimal pressure tap design for quality pressure measurements and minimal flow interference, due to the increased susceptibility of elastic microfluidic flows to flow perturbations.

Improvements in imaging techniques, such as micro- and nano-computer tomography (CT) and focus ion beam scanning electron microscopy (FIB-SEM), have enabled the reconstruction of complex porous media that can then be analyzed by computer simulation to estimate effective transport properties, e.g., ref. [1, 2]. Experimental setups have also been developed to measure dry and partially-saturated gas diffusivity and permeability of gas diffusion layers (GDLs) and catalyst layer (CLs), e.g., ref. [3, 4]. Based on the available literature, a comparison between micro-scale simulation results and experimental data must be performed to assess the accuracy of direct numerical simulation CT image analysis for dry and partially-saturated transport property estimation. In the later case, the validity of computational methods to predict water intrusion, such as full morphology/morphological image opening [1] and watershed segmentation [5], should also be assessed by comparing mercury intrusion experiments to numerical predictions, and by direct comparison of numerical results to CT images. Finally, these transport properties should be integrated into complete fuel cell models where volume-averaging techniques are used to properly estimate channel-porous media interactions. Such interactions however are seldom studied in literature.The proposed contribution aims at first studying the validity of two popular methods for numerical estimation of effective transport properties from three-dimensional reconstructed porous media, i.e., direct numerical simulation (DNS) and pore network modeling (PNM). Two fuel cell gas diffusion media and an electrolyzer porous transport layer are analyzed by CT and characterized by measuring mercury intrusion porosimetry (MIP), and dry permeability and diffusivity. A comparison of numerical and experimental results shows that DNS tools in OpenFCST [6] are capable of accurately predicting intrusion, and transport properties without using any fitting parameters. Accurate predictions are also achieved with the PNM implementation in OpenPNM [7] when the inscribed diameter method is used to estimate the pore size distribution, and the equivalent diameter is used to estimate pore transport properties. These tools open an avenue for computational design of porous materials.Effective transport properties must be integrated into volume-averaged fuel cell models where porous media-channel interactions are of paramount importance. These interactions however, as well as the method used for volume averaging fuel cell equations, are seldom studied in detail. Therefore, the second contribution of the talk aims at analyzing channel-porous media interactions by developing a compressible volume-averaged channel-porous media model in OpenFCST, and validating it with respect to permeability and diffusion bridge experiments in the literature. Comparison of numerical and experimental results show that, depending on the volume-averaging methodology used, experimentally obtained transport properties do not correspond to the input parameters needed in volume-averaged models. Finally, the numerical model is used to estimate flow by-pass in serpentine and inter-digitated channels, as well as compressibility effects [8].

Water transport in the Porous Transport Layer (PTL) plays an important role in the efficient operation of polymer electrolyte membrane fuel cells (PEMFC). Excessive water content as well as dry operating conditions are unfavorable for efficient and reliable operation of the fuel cell. The effect of thermal conductivity and porosity on water management are investigated by simulating two-phase ow in the PTL of the fuel cell using a network model. In the model, the PTL consists of a pore-phase and a solid-phase. Different models of the PTLs are generated using independent Weibull distributions for the pore-phase and the solid-phase. The specific arrangement of the pores and solid elements is varied to obtain different PTL realizations for the same Weibull parameters. The properties of PTL are varied by changing the porosity and thermal conductivity. The parameters affecting operating conditions include the temperature, relative humidity in the ow channel and voltage and current density. In addition, a novel high-speed capable Surface Plasmon Resonance (SPR) microscope was built based on Kretschmann's configuration utilizing a collimated Kohler illumination. The SPR allows thin film characterization in a thickness of approximately 0-200nm by measuring the changes in the refractive index. Various independent experiments were run to measure film thickness during droplet coalescence during condensation.

The ray dynamics of optical cavities exhibits bifurcation points: special geometries at which ray trajectories switch abruptly between stable and unstable. A prominent example is the Fabry–Perot cavity with two planar mirrors, which is widely employed for broad-area semiconductor lasers. Such cavities support lasing in a relatively small number of transverse modes, and the laser is highly susceptible to filamentation and irregular pulsations. Here, we demonstrate experimentally that a slight deviation from this bifurcation point (planar cavity) dramatically changes the laser performance. In a near-planar cavity with two concave mirrors, the number of transverse lasing modes increases drastically. While the spatial coherence of the laser emission is reduced, the divergence angle of the output beam remains relatively narrow. Moreover, the spatiotemporal lasing dynamics becomes significantly more stable compared to that in a Fabry–Perot cavity. Our near-planar broad-area semiconductor laser has higher brightness, better directionality, and hence allows shorter integration times than an incandescent lamp while featuring sufficiently low speckle contrast at the same time, making it a vastly superior light source for speckle-free imaging. Furthermore, our method of controlling spatiotemporal dynamics with extreme sensitivity near a bifurcation point may be applied to other types of high-power lasers and nonlinear dynamic systems.

Detailed measurements of the flow instability of dilute shear-thinning viscoelastic aqueous solutions, with relatively low zero-shear viscosities, in an obstructed microchannel flow are reported. We examine the flow behaviour resulting from a 100 μm post placed in the channel centreline over a range of Reynolds numbers ( $$5<Re<300$$ ) and Weissenberg numbers ( $$20<Wi<10^3$$ ). Micro-particle image velocimetry measurements show the onset of an upstream instability within a Reynolds number range and at a critical elasticity number corresponding to polymer concentrations above 25 ppm of long-chain polyacrylamide. The instability results in significant local fluctuations in the flow field approaching 30 % of the mean velocity. The magnitude of the local viscosity ratio in the region upstream of the post is proposed as a driving mechanism for the instability which resembles a buckling flow. Additionally, the classical instability owing to separation and vortex formation downstream of the post in Newtonian flow is suppressed and a very long stable wake is observed extending over 10 post-diameters downstream.