An official website of the United States government
Microfluidic devices offer well-defined physical environments that are suitable for effective cell seeding and in vitro three-dimensional (3D) cell culture experiments. These platforms have been employed to model in vivo conditions for studying mechanical forces, cell–extracellular matrix (ECM) interactions, and to elucidate transport mechanisms in 3D tissue-like structures, such as tumor and lymph node organoids. Studies have shown that fluid flow behavior in microfluidic slides (µ-slides) directly influences shear stress, which has emerged as a key factor affecting cell proliferation and differentiation. This study investigates fluid flow in the porous channel of a µ-slide using computational fluid dynamics (CFD) techniques to analyze the impact of perfusion flow rate and porous properties on resulting shear stresses. The model of the µ-slide filled with a permeable biomaterial is considered. Porous media fluid flow in the channel is characterized by adding a momentum loss term to the standard Navier–Stokes equations, with a physiological range of permeability values. Numerical simulations are conducted to obtain data and contour plots of the filtration velocity and flow-induced shear stress distributions within the device channel. The filtration flow is subsequently measured by performing protein perfusions into the slide embedded with native human-derived ECM, while the flow rate is controlled using a syringe pump. The relationships between inlet flow rate and shear stress, as well as filtration flow and ECM permeability, are analyzed. The findings provide insights into the impact of shear stress, informing the optimization of perfusion conditions for studying tissues and cells under fluid flow.
more »
« less
Dispersion controlled by permeable surfaces: surface properties and scaling
Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.
more »
« less
- Award ID(s):
- 1742175
- PAR ID:
- 10036076
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 801
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 13 to 42
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A large eddy simulation (LES) is performed for a turbulent open channel flow over a porous sediment bed at permeability Reynolds number of ReK∼2.56 (Reτ = 270) representative of aquatic systems. A continuum approach based on the upscaled, volume-averaged Navier−Stokes (VaNS) equations is used by defining smoothly varying porosity across the sediment water interface (SWI) and modeling the drag force in the porous bed using a modified Ergun equation with Forchheimer corrections for inertial terms. The results from the continuum approach are compared with a pore-resolved direct numerical simulation (PR-DNS) in which turbulent flow over a randomly packed sediment bed of monodispersed particles is investigated [Karra et al.,J. Fluid Mech. 971, A23 (2023)] A spatially varying porosity profile generated from the pore-resolved DNS is used in the continuum approach. Mean flow, Reynolds stress statistics, and net momentum exchange between the freestream and the porous bed are compared between the two studies, showing reasonably good agreement. Small deviations within the transitional region between the sediment bed and the freestream as compared to the PR-DNS results are attributed to the local protrusions of particles in a randomly packed bed that are absent in the continuum approach but are present in the PR-DNS. A better representation of the effective permeability in the top transition layer that accounts for roughness effect of exposed particles is necessary. The continuum approach significantly reduces the computational cost, thereby making it suitable to study hyporheic exchange of mass and momentum in large scale aquatic domains with combined influence of bedform and bed roughness.more » « less
-
null (Ed.)In this paper, we consider an important problem for modeling complex coupled phenomena in porous media at multiple scales. In particular, we consider flow and transport in the void space between the pores when the pore space is altered by new solid obstructions formed by microbial growth or reactive transport, and we are mostly interested in pore-coating and pore-filling type obstructions, observed in applications to biofilm in porous media and hydrate crystal formation, respectively. We consider the impact of these obstructions on the macroscopic properties of the porous medium, such as porosity, permeability and tortuosity, for which we build an experimental probability distribution with reduced models, which involves three steps: (1) generation of independent realizations of obstructions, followed by, (2) flow and transport simulations at pore-scale, and (3) upscaling. For the first step, we consider three approaches: (1A) direct numerical simulations (DNS) of the PDE model of the actual physical process called BN which forms the obstructions, and two non-DNS methods, which we call (1B) CLPS and (1C) LP. LP is a lattice Ising-type model, and CLPS is a constrained version of an Allen–Cahn model for phase separation with a localization term. Both LP and CLPS are model approximations of BN, and they seek local minima of some nonconvex energy functional, which provide plausible realizations of the obstructed geometry and are tuned heuristically to deliver either pore-coating or pore-filling obstructions. Our methods work with rock-void geometries obtained by imaging, but bypass the need for imaging in real-time, are fairly inexpensive, and can be tailored to other applications. The reduced models LP and CLPS are less computationally expensive than DNS, and can be tuned to the desired fidelity of the probability distributions of upscaled quantities.more » « less
-
Estimating flow and transport properties of porous media that undergo deformation as a result of applying an external pressure or force is important to a wide variety of processes, ranging from injecting a fracking liquid into shale formations, to CO sequestration in spent oil reservoirs. We propose a novel model for estimating the effective flow and transport properties of such porous media. Assuming that the solid matrix of a porous medium undergoes elastic deformation, and given its initial porosity before deformation, as well as the Young’s modulus of its grains, the model uses an extension of the Hertz–Mindlin theory of contact between grains to compute the new PSD that results from applying an external pressure P to the medium, and utilizes the updated PSD in the effective-medium approximation (EMA) to estimate the effective flow and transport properties at pressure P. In the present part of this series, we use the theory to predict the effective permeability as a function of the applied pressure. Comparison between the predictions and experimental data for twenty-four types of sandstones indicates excellent agreement between the two.more » « less
-
Sea ice regulates heat exchange between the ocean and atmosphere in Earth’s polar regions. The thermal conductivity of sea ice governs this exchange, and is a key parameter in climate modelling. However, it is challenging to measure and predict due to its sensitive dependence on temperature, salinity and brine microstructure. Moreover, as temperature increases, sea ice becomes permeable, and fluid can flow through the porous microstructure. While models for thermal diffusion through sea ice have been obtained, advective contributions to transport have not been considered theoretically. Here, we homogenize a multiscale advection–diffusion equation that models thermal transport through porous sea ice when fluid flow is present. We consider two-dimensional models of convective flow and use an integral representation to derive bounds on the thermal conductivity as a function of the Péclet number. These bounds guarantee enhancement in the thermal conductivity due to the added flow. Further, we relate the Péclet number to temperature, making these bounds useful for global climate models. Our analytic approach offers a mathematical theory which can not only improve predictions of atmosphere–ice–ocean heat exchanges in climate models, but can provide a theoretical framework for a range of problems involving advection–diffusion processes in various fields of application.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2016.431
