No Arabic abstract
Rapid and accurate simulation of cerebral aneurysm flow modifications by flow diverters (FDs) can help improving patient-specific intervention and predicting treatment outcome. However, with explicit FD devices being placed in patient-specific aneurysm model, the computational domain must be resolved around the thin stent wires, leading to high computational cost in computational fluid dynamics (CFD). Classic homogeneous porous medium (PM) methods cannot accurately predict the post-stenting aneurysmal flow field due to the inhomogeneous FD wire distributions on anatomic arteries. We propose a novel approach that models the FD flow modification as a thin inhomogeneous porous medium (iPM). It improves over classic PM approaches in that, first, FD is treated as a screen, which is more accurate than the classic Darcy-Forchheimer relation based on 3D PM. second, the pressure drop is calculated using local FD geometric parameters across an inhomogeneous PM, which is more realistic. To test its accuracy and speed, we applied the iPM technique to simulate the post stenting flow field in three patient-specific aneurysms and compared the results against CFD simulations with explicit FD devices. The iPM CFD ran 500% faster than the explicit CFD while achieving 94%-99% accuracy. Thus iPM is a promising clinical bedside modeling tool to assist endovascular interventions with FD and stents.
Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We provide a simple theoretical framework that embodies this feedback mechanism in a multi-phase model for flow through a fragile porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. This allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.
Flows through porous media can carry suspended and dissolved materials. These sediments may deposit inside the pore-space and alter its geometry. In turn, the changing pore structure modifies the preferential flow paths, resulting in a strong coupling between structural modifications and transport characteristics. Here, we compare two different models that lead to channel obstruction as a result of subsequent deposition. The first model randomly obstructs pore-throats across the porous medium, while in the second model the pore-throat with the highest flow rate is always obstructed first. By subsequently closing pores, we find that the breakdown of the permeability follows a power-law scaling, whose exponent depends on the obstruction model. The pressure jumps that occur during the obstruction process also follow a power-law distribution with the same universal scaling exponent as the avalanche size distribution of invasion percolation, independent of the model. This result suggests that the clogging processes and invasion percolation may belong to the same universality class.
We develop a 3D porous medium model for sap flow within a tree stem, which consists of a nonlinear parabolic partial differential equation with a suitable transpiration source term. Using an asymptotic analysis, we derive approximate series solutions for the liquid saturation and sap velocity for a general class of coefficient functions. Several important non-dimensional parameters are identified that can be used to characterize various flow regimes. We investigate the relative importance of stem aspect ratio versus anisotropy in the sapwood hydraulic conductivity, and how these two effects impact the radial and vertical components of sap velocity. The analytical results are validated by means of a second-order finite volume discretization of the governing equations, and comparisons are drawn to experimental results on Norway spruce trees.
We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier-Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.
We report forced radial imbibition of water in a porous medium in a Hele-Shaw cell. Washburns law is confirmed in our experiment. Radial imbibition follows scaling dynamics and shows anomalous roughening dynamics when the front invades the porous medium. The roughening dynamics depend on the flow rate of the injected fluid. The growth exponents increase linearly with an increase in the flow rate while the roughness exponents decrease with an increase in the flow rate. Roughening dynamics of radial imbibition is markedly different from one dimensional imbibition with a planar interface window. Such difference caused by geometric change suggests that universality class for the interface growth is not universal.