Search

The advantage of using porous materials for biofuel cells and biosensors is their very large internal surface area (where electron exchange takes place) compared to the overall material volume, yielding much larger current densities than on a bare solid electrode of the same size. However, limitations occur because of mass transfer resistance through the pores. We describe here a bottom-up approach to optimize the design of such materials, through the analysis and modeling of their porous structure. Electrodes prepared by replicating stacked Langmuir-Blodgett films, with 1-μm diameter interconnected spherical pores, were studied. Since pore window dimensions are around 100 nm, Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) has been performed to obtain a 3D reconstruction of the porous medium. Then, a determination of the geometrical characteristics has been achieved through image analysis. The structure of the sphere packing, the shape and size of the connections between spheres, the distances between spheres, the sphere diameters and the specific surface area have been analyzed. The porous medium is close to a face-centered cubic arrangement of spherical pores, but several deviations from ideality are present: missing pores (point defects), stacking errors (dislocations), and incomplete connection between spheres (only 50% of the ideal sphere connections are present). The consequence of such defects on transport is studied through image-based simulations of mass diffusion in the actual porous medium and in similar ideal media.

Fungal pellets are hierarchical systems that can be found in an ample variety of applications. Modeling transport phenomena in this type of systems is a challenging but necessary task to provide knowledge-based processes that improve the outcome of their biotechnological applications. In this work, an upscaled model for total mass and momentum transport in fungal pellets is implemented and analyzed, using elements of the volume averaging and adjoint homogenization methods departing from the governing equations at the microscale in the intracellular and extracellular phases. The biomass is assumed to be composed of a non-Newtonian fluid and the organelles impervious to momentum transport are modeled as a rigid solid phase. The upscaled equations contain effective-medium coefficients, which are predicted from the solution of adjoint closure problems in a three-dimensional periodic domains representative of the microstructure. The construction of these domains was performed for Laccaria trichodermophora based on observations of actual biological structures. The upscaled model was validated with direct numerical simulations in homogeneous portions of the pellets core. It is shown that no significant differences are observed when the dolipores are open or closed to fluid flow. By comparing the predictions of the average velocity in the extracellular phase resulting from the upscaled model with those from the classical Darcy equation (i.e., assuming that the biomass is a solid phase) the contribution of the intracellular fluid phase was evidenced. This work sets the foundations for further studies dedicated to transport phenomena in this type of systems., Competing Interests: Declaration of competing interest The authors have no relevant financial or non-financial interests to disclose., (Copyright © 2024 The Authors. Published by Elsevier Ltd.. All rights reserved.)

Modeling of diffusion/enzymatic reaction in porous electrodes operating in direct electron transfer mode is developed. The solution at the pore-scale is extremely cumbersome due to the complex geometry of the porous material. The upscaled model is much easier to solve, while keeping the essential of the physico-chemical behavior. The method to carry out the solution can be described as follows•The effective diffusion coefficient involved in the macroscopic equations is accurately computed by solving a closure problem in a representative elementary volume.•Electrochemical parameters are identified by a direct resolution of the macroscopic model solved with a COMSOL Multiphysics code coupled to a curve fit procedure carried out on voltammetry experimental results using a Matlab code. Electrodes with different thicknesses may be considered in the fitting procedure to improve accuracy. An alternative use of the COMSOL Multiphysics code is to predict the electrode behavior and further optimize its design, if all the electrochemical parameters are identified.•To validate the upscaled model, the pore scale model may be solved with direct numerical simulations carried out in a 3D microstructure using another COMSOL Multiphysics code to compare with the solution of the upscaled model in the 1D-reduced geometry., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2022 The Authors. Published by Elsevier B.V.)

This work reports on new developments of an unsteady-state method to measure the permeability and porosity of permeable porous materials, extending the so-called Gas Research Institute method beyond its classical use. These extensions allow one to carry out measurements on samples having a cylindrical shape in the case of one- or three-dimensional (or axisymmetric) flows. They rely on the derivation of the quasi-analytical solutions that are required to interpret the experimental data by solving an inverse problem. The only simplifying assumption is that the compressibility of the probing gas can be treated as a constant over the range of pressure variations during measurement. The relevance of the method, together with the validity of this hypothesis, is checked over a wide range of porosity and permeability values through a sensitivity analysis and a comparison with direct numerical simulations of the complete initial boundary value problem. The efficiency of the method is further illustrated with experiments performed on four different porous materials in one-dimension and axisymmetric configurations for permeabilities ranging between 10 -14 and 10 -19 m 2 . The potential capability of diagnosing heterogeneous and/or anisotropic materials is highlighted. These new developments open the way for further extensions to samples of arbitrary shapes or partially saturated by a trapped fluid.

The pore size distribution of a porous medium is often estimated from the retention curve or the invading fluid flow rate curve using simple relationships more or less explicitly based on the consideration that the porous medium is made of a bundle of cylindrical parallel tubes. This type of determination is tested using pore network simulations. Starting from two- or three-dimensional networks, the characteristics of which are known a priori, the estimation of the throat size distribution (TSD) is performed using the standard methods in the case of drainage. Results show a significant discrepancy with the input data. The disagreement is more pronounced when the fluid flow rate curve is employed together with the parallel tubes assumption. The physical origins of these shortcomings are identified. A method, based on pore network simulations combined with a genetic algorithm and the hill climbing algorithm, is then designed, which makes simultaneous use of the nonwetting fluid flow rate curve and the retention curve of the medium. Very significant improvement is achieved in the estimation of the TSD using this procedure.

Rough fractures often exhibit a broad spectrum of defect length scales ranging from the microscopic (roughness) scale to a macroscopic one (waviness) and further to the megascopic scale corresponding to the entire fracture. The influence of these multiple scales and their reciprocal interactions are expected to play a significant role on the transport properties at the megascale. Focusing on the pressure-driven slightly compressible gas slip flow, a two-scale method is presented allowing the determination of the global transmissivity of a fracture on the basis of an upscaled Reynolds model. This model is applied on a tessellation of the fracture, each tile being affected by a macroscopic transmissivity tensor which encompasses the microscale transport information as a result of the first upscaling process. Then, the megascale flow problem in this structure, made of a set of tiles characterized by a heterogeneous and anisotropic transmissivity tensor field, is solved using a boundary element method. Numerical results obtained with this two-scale method are compared to the transmissivity computed with direct simulations carried out at the microscale on the whole fracture. This is performed on two model rough fractures, namely, a spiral groove and a fractal fracture, while varying their mean apertures to investigate a wide range of the average Knudsen number characteristic of the flow at the megascale. A good agreement is obtained between the two approaches showing the robustness of the two-scale method to determine the global transmissivity of the fracture while significantly reducing the overall computational time.

Inertial flow in porous media occurs in many situations of practical relevance among which one can cite flows in column reactors, in filters, in aquifers, or near wells for hydrocarbon recovery. It is characterized by a deviation from Darcy's law that leads to a nonlinear relationship between the pressure drop and the filtration velocity. In this work, this deviation, also known as the nonlinear, inertial, correction to Darcy's law, which is subject to controversy upon its origin and dependence on the filtration velocity, is studied through numerical simulations. First, the microscopic flow problem was solved computationally for a wide range of Reynolds numbers up to the limit of steady flow within ordered and disordered porous structures. In a second step, the macroscopic characteristics of the porous medium and flow (permeability and inertial correction tensors) that appear in the macroscale model were computed. From these results, different flow regimes were identified: (1) the weak inertia regime where the inertial correction has a cubic dependence on the filtration velocity and (2) the strong inertia (Forchheimer) regime where the inertial correction depends on the square of the filtration velocity. However, the existence and origin of those regimes, which depend also on the microstructure and flow orientation, are still not well understood in terms of their physical interpretations, as many causes have been conjectured in the literature. In the present study, we provide an in-depth analysis of the flow structure to identify the origin of the deviation from Darcy's law. For accuracy and clarity purposes, this is carried out on two-dimensional structures. Unlike the previous studies reported in the literature, where the origin of inertial effects is often identified on a heuristic basis, a theoretical justification is presented in this work. Indeed, a decomposition of the convective inertial term into two components is carried out formally allowing the identification of a correlation between the flow structure and the different inertial regimes. These components correspond to the curvature of the flow streamlines weighted by the local fluid kinetic energy on the one hand and the distribution of the kinetic energy along these lines on the other hand. In addition, the role of the recirculation zones in the occurrence and in the form of the deviation from Darcy's law was thoroughly analyzed. For the porous structures under consideration, it is shown that (1) the kinetic energy lost in the vortices is insignificant even at high filtration velocities and (2) the shape of the flow streamlines induced by the recirculation zones plays an important role in the variation of the flow structure, which is correlated itself to the different flow regimes.

Modeling flow in porous media is usually focused on the governing equations for mass and momentum transport, which yield the velocity and pressure at the pore or Darcy scales. However, in many applications, it is important to determine the work (or power) needed to induce flow in porous media, and this can be achieved when the mechanical energy equation is taken into account. At the macroscopic scale, this equation may be postulated to be the result of the inner product of Darcy's law and the seepage velocity. However, near the porous medium boundaries, this postulate seems questionable due to the spatial variations of the effective properties (velocity, permeability, porosity, etc.). In this work we derive the macroscopic mechanical energy equation using the method of volume averaging for the simple case of incompressible single-phase flow in porous media. Our analysis shows that the result of averaging the pore-scale version of the mechanical energy equation at the Darcy scale is not, in general, the expected product of Darcy's law and the seepage velocity. As a matter of fact, this result is only applicable in the bulk region of the porous medium and, in the derivation of this result, the properties of the permeability tensor are determinant. Furthermore, near the porous medium boundaries, a more novel version of the mechanical energy equation is obtained, which incorporates additional terms that take into account the rapid variations of structural properties taking place in this particular portion of the system. This analysis can be applied to multiphase and compressible flows in porous media and in many other multiscale systems.

Electro-osmotic flows (EOF) have seen remarkable applications in lab-on-a-chip based microdevices owing to their lack of moving components, durability, and nondispersive nature of the flow profiles under specifically designed conditions. However, such flows may typically suffer from classical Faradaic artifacts like electrolysis of the solvent, which affects the flow rate control. Such a problem has been seen to be overcome by employing time periodic EOFs. Electric field induced transport of a conductive liquid is another nontrivial problem that requires careful study of interfacial dynamics in response to such an oscillatory flow actuation. The present study highlights the role of electric field generated Maxwell stress and free surface potential along with the electric double layer thickness and forcing frequency, toward influencing the interfacial transport and fluid flow in free-surface electro-osmosis under a periodically varying external electric field, in a semi-analytical formalism. Our results reveal interesting regimes over which the pertinent interfacial phenomena as well as bulk transport characteristics may be favorably tuned by employing time varying electrical fields., (© 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The stability of a free surface under electro-osmotic flow in thin liquid films is investigated where the film thickness can be varied over the scale of a thick to thin electrical double layer while considering the relative contribution from the van der Waals forces. The role of interfacial Maxwell stress on thin film stability is highlighted. This configuration gives some interesting insights into the physics of free surface stability at a scale where various competing forces such as the Coulombic force, van der Waals force, and surface tension come into play. The effects of the mentioned forces are incorporated in the Navier-Stokes equations and a linear stability analysis of the resulting governing equations is performed to obtain the Orr-Sommerfeld equations. The characteristic stability curve of the system is obtained through an asymptotic analysis of the Orr-Sommerfeld equations in the long wave limit. In this study, special focus is given to the effect of the interfacial zeta potential on the free surface stability. It is found that when the free surface and the substrate zeta potential have the same polarity the system is unstable. Since the strength of the free surface potential depends upon the nature of the fluid substrate interaction, this study can help in choosing a proper combination of fluid and substrate to design microfluidic and nanofluidic channels with a desired flow rate without triggering the interfacial instability.

A new quasi-steady method for the determination of the apparent gas permeability of porous materials is presented in this paper along with the corresponding interpretative physical model derived from the unsteady flow equations. This method is mainly dedicated to the measurement of very low permeability of thin porous media, although thicker but more permeable samples may also be analyzed. The method relies on quasi-steady flow resulting from a (quasi) constant pressure maintained at the inlet face of the sample. Gas flow-rate, as low as 3 × 10(-10) m(3)/s, is determined from the record of pressure increase in a reservoir connected to the outlet face of the sample. An estimate of the characteristic time, t(c), to reach quasi-steady flow after imposing a constant pressure at the inlet is derived. It is validated by direct numerical simulations of the complete unsteady flow, clearly defining the required experimental duration for the method to apply. Experimental results obtained on rather permeable and thick rock samples are reported showing an excellent agreement of the measured permeability with that determined independently on the same sample whereas the experimental value of t(c) is also in very good agreement with the predicted one. The method is further employed on a composite material sheet allowing the identification of an apparent gas permeability of about 10(-23) m(2).

Recent experimental developments showed that the use of the radiation pressure, induced by a continuous laser wave, to control fluid-fluid interface deformations at the microscale, represents a very promising alternative to electric or magnetic actuation. In this article, we solve numerically the dynamics and steady state of the fluid interface under the effects of buoyancy, capillarity, optical radiation pressure and viscous stress. A precise quantitative validation is shown by comparison with experimental data. New results due to the nonlinear dependence of the optical pressure on the angle of incidence are presented, showing different morphologies of the deformed interface going from needle-like to finger-like shapes, depending on the refractive index contrast. In the transient regime, we show that the viscosity ratio influences the time taken for the deformation to reach steady state.

We study numerically the deformation of sessile dielectric drops immersed in a second fluid when submitted to the optical radiation pressure of a continuous Gaussian laser wave. Both drop stretching and drop squeezing are investigated at steady state where capillary effects balance the optical radiation pressure. A boundary integral method is implemented to solve the axisymmetric Stokes flow in the two fluids. In the stretching case, we find that the drop shape goes from prolate to near-conical for increasing optical radiation pressure whatever the drop to beam radius ratio and the refractive index contrast between the two fluids. The semiangle of the cone at equilibrium decreases with the drop to beam radius ratio and is weakly influenced by the index contrast. Above a threshold value of the radiation pressure, these "optical cones" become unstable and a disruption is observed. Conversely, when optically squeezed, the drop shifts from an oblate to a concave shape leading to the formation of a stable "optical torus." These findings extend the electrohydrodynamics approach of drop deformation to the much less investigated "optical domain" and reveal the openings offered by laser waves to actively manipulate droplets at the micrometer scale.