A 3D Numerical Study of Interface Effects Influencing Viscous Gravity Currents in a Parabolic Fissure, with Implications for Modeling with 1D Nonlinear Diffusion Equations

Abstract

Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in a parabolic fissure from first principals. The parabolic fissure is formed by extruding an upward opening parabola in a horizontal direction. In this setting, permeability is a power law function of height, resulting in a generalized Boussinesq equation. To gauge the effects neglected by this model, 3D Navier-Stokes multiphase flow simulations are conducted for the same geometry. Parameter variations are performed to assess the nature of errors induced by applying the 1D model to a realistic scenario, where the initial and boundary conditions can not be matched exactly. Numerical simulations reveal an undercutting effect observed in laboratory experiments, but not modeled when the Dupuit-Forchheimer assumption is applied. By selectively controlling the effects placed on the free surface in 3D simulations, we are able to demonstrate that free surface slope is the primary driver of the undercutting effect. A consistent lag and overshoot flow regime is observed in the 3D simulations as compared to the 1D model, based on the choice of initial condition. This implies that the undercutting effect is partially induced by the initial condition. Additionally, the presented numerical evidence shows that some of the flow behavior unaccounted for in the 1D model scales with the 1D model parameters.

Editorial for Special Issue “Advances in Experimental and Computational Rheology”

“…The special issue "Advances in Experimental and Computational Rheology" joins fifteen works covering some of the latest advances in the fields of experimental and computational rheology applied to a diverse class of materials and processes, which can be grouped into four main topics: rheology [1][2][3][4][5], effect of process variables [6][7][8][9], rheometry and processing [10,11], and theoretical modeling [12][13][14][15] The characterization of rheological behavior is the main topic of five contributions, covering the following material systems: lubricating greases (Delgado et al [1]), Carbopol ® dispersion in water and in water/glycerol solutions (Varges et al [2]), natural hydraulic lime grouts (Baltazar et al [3]), fresh cement pastes (Rubio-Hernández [4]), and legume-protein-stabilized emulsions (Félix et al [5]).…”

“…García-Sandoval et al [13] studied the capability of the Bautista-Manero-Puig model to predict shear banding in polymer-like micellar solutions. Furtak-Cole and Telyakovskiy [14] resorted to 3D modelling techniques to assess the applicability of a simple 1D model for the flow in aquifers and fissures. Green et al [15] proposed modifications of a previously developed constitutive model for shear thickening colloidal solutions, which explicitly accounts for the evolution of its microstructure during flow, and assessed its accuracy.…”