When a pressure gradient is applied through a charged selective membrane, the transmembrane electrical potential difference, called the filtration potential, results from both the applied pressure and induced concentration difference across the membrane. In this work we investigate the electrokinetic properties relative to both active and support layers of a composite ceramic membrane close to the nanofiltration range. First, the volume charge density of the active layer is obtained by fitting a transport model to experimental rejection rates (which are controlled by the active layer only). Next, the value of the volume charge density is used to compute the theoretical filtration potential through the active layer. For sufficiently high permeate volume fluxes, the concentration difference across the active layer becomes constant, which allows assessing the membrane potential of the active layer. Experimental measurements of the overall filtration potential arising through the whole membrane are performed. The contribution of the support layer to this overall filtration potential is put in evidence. That implies that the membrane potential of the active layer cannot be deduced directly from the overall filtration potential measurements. Finally, the contribution of the support layer is singled out by subtracting the theoretical filtration potential of the active layer from the experimental filtration potential measured across the whole membrane (i.e., support + active layers). The amphoteric behavior of both layers is put in evidence, which is confirmed by electrophoretic measurements carried out with the powdered support layer and by recently reported tangential streaming potential measurements.
Tangential streaming potential technique is an attractive way to characterize the electrokinetic properties of various kinds of materials such as films or flat membranes with a dense or a porous structure. However, the interpretation of data in terms of zeta potential is usually carried out by doing the implicit assumption of nonconducting substrates. In the present paper, we investigate the electrokinetic properties of a commercial ultrafiltration membrane, the porous structure of which affects the streaming potential because streaming and conduction currents involved in the streaming potential process do not flow through identical paths (the streaming current flows only through the slit channel formed by the two membrane samples facing each other whereas a non-negligible part of the conduction current is likely to flow through the membrane pores filled with electrolyte solution). The correct zeta potential value is determined from an extrapolation method for which a set of measurements with various channel heights is required. A very good agreement is obtained with zeta potential values deduced from consecutive streaming potential and total conductance measurements (referred in the text as the direct method). The ratio of the correct zeta potential to the apparent one (given by Helmholtz−Smoluchowski equation) is dependent on the pH which suggests a non-negligible contribution of surface conductance within the membrane pores.
Iterative solvers preconditioned with algebraic multigrid have been devised as an optimal technology to speed up the response of large sparse linear systems. In this work, this technique was implemented in the framework of the dual delineation approach. This involves a single groundwater flow solve and a pure advective transport solve with different right-hand sides. The new solver was compared with traditional preconditioned iterative methods and direct sparse solvers on several two- and three-dimensional benchmark problems spanning homogeneous and heterogeneous formations. For the groundwater flow problems, using the algebraic multigrid preconditioning speeds up the numerical solution by one to two orders of magnitude. Contrarily, a sparse direct solver was the most efficient for the pure advective transport processes such as the forward travel time simulations. Hence, the best sparse solver for the more general advection-dispersion transport equation is likely to be P\'eclet number dependent. When equipped with the best solvers, processing multimillion grid blocks by the dual delineation approach is a matter of seconds. This paves the way for routine time-consuming tasks such as sensitivity analysis. The paper gives practical hints on the strategies and conditions under which algebraic multigrid preconditioning for the class of nonlinear and/or transient problems would remain competitive.
Abstract Advective particle tracking is a conventional groundwater modeling technique that is widely used as a screening tool but lacks robustness as a reliable method for general applications. In this work, we investigate the suitability of industry‐standard, finite‐difference, grid‐based methods as an alternative to the conventional particle‐tracking approach. The presented method is classified as a particular case of the more general forward‐ or backward‐in‐time advective‐dispersive probabilistic transport approaches. The proposed method is used as a powerful screening tool to accurately delineate and visualize capture zones around abstraction wells or outflow boundaries, the swept zones formed by injection wells or inflow boundaries, and the partitions associated with injection‐pumping well doublets or inflowing‐outflowing boundary pairs. Moreover, we show that the forward or backward travel times and residence time distributions are robustly simulated and visualized on the computational grid with little computational effort. Two examples are given to illustrate the key advantages of this method in groundwater applications. The first example considers a synthetic pump‐and‐treat remediation system in an irregularly layered aquifer. The second example involves four doublet wells operating for heat extraction in the Dogger geothermal reservoir in the Paris Basin, a leading European scale project. The presented approach is far more comprehensive as a screening tool than the conventional method, providing a natural intermediate step before processing the more general time‐dependent advective‐dispersive simulations.
Abstract The substantial deformation exhibited by hyperelastic cylindrical shells under pressurization makes them an ideal platform for programmable inflatable structures. If negative pressure is applied, the cylindrical shell will buckle, leading to a sequence of rich deformation modes, all of which are fully recoverable due to the hyperelastic material choice. While the initial buckling event under vacuum is well understood, here, the post‐buckling regime is explored and a region in the design space is identified in which a coupled twisting‐contraction deformation mode occurs; by carefully controlling the geometry of our homogeneous shells, the proportion of contraction versus twist can be controlled. Additionally, bending as a post‐buckling deformation mode can be unlocked by varying the thickness of our shells across the circumference. Since these soft shells can fully recover from substantial deformations caused by buckling, then these instability‐driven deformations are harnessed to build soft machines capable of a programmable sequence of movements with a single actuation input.
ABSTRACTA new electrokinetic setup was developed for assessing the active layer ζ-potential of tubular membranes based on tangential streaming potential and electrical resistance measurements. Although the flow was not wholly laminar (because of the large hydraulic diameter of channels), the electrokinetics theory could be used to convert the streaming potential data into ζ-potentials because the electrical double layer lay within a laminar sublayer near the channel walls. Electrical resistance data allowed for the account of the conduction phenomenon through the membrane porous body. The new device was tested over a range of pH with a tubular ceramic membrane composed of three channels with a titania active layer. The isoelectric point was found to be in good agreement with that determined from salt retention data. The ζ-potential value determined at pH = 3.5 using the present device was compared with that obtained on a flat membrane made of the same material using the traditional microslit electrokinetic setup. A good agreement between the two measurements was observed. It was shown that neglecting the electric conduction phenomenon through the membrane porous body leads to a low underestimation of the ζ-potential (less than ~20%). This is related to the large size of channels. The contribution of the membrane porous body was found to be independent of the pH of solution. This suggests that the support layer of the membrane would make a decisive contribution to the electric conductivity of membrane porous body.Key Words:: Tangential streaming potentialZeta potentialTurbulent flowElectric conductanceSurface conductionTubular membrane
Coastal aquifers involve varying conditions in time and space, owing to the occurrence of free and moving boundaries, such as the water table, seepage face and saltwater intrusion interface. A fast Updating Procedure (FUP) is developed for solving these interfaces in steady and transient conditions with the finite element method. Several test examples, which involve confined and phreatic groundwater flow in coastal aquifers, are studied to demonstrate the FUP capability of predicting accurate results. Comparisons of the FUP numerical results are made against available analytical solutions, laboratory experiments measurements and other computer codes.To show also the capability of this technique to solve real field situations, it was applied to the coastal aquifer of Martil in Morocco to study and understand the aquifer response to changes in recharge and total rate of pumping water, and their effects on seawater intrusion.
Transport of pollutants in groundwater is simulated by means of a 3D finite element model. The obtained system of numerical equations is very large, sparse, non-symmetric and usually difficult to solve with standard iterative techniques. It is proposed to improve the convergence behavior of the solvers by preconditioning, where the existence of the preconditioning is guaranteed by using an M-matrix type of transformation. The usefulness of the method is demonstrated by solving several test examples, using different solvers as the minimal residual method and the stabilized biconjugate gradient method and different preconditioning schemes as diagonal scaling and incomplete factorization. It is shown that M-matrix preconditioning is very simple to implement, and proves to be very efficient and robust.
