Fluid dynamics of basal entrainment by geophysical gravity-driven flows

Geophysical gravity-driven flows -- including avalanches, debris flows, pyroclastic flows and submarine turbidity currents -- are multiphase natural hazards that flow under the influence of gravity. Despite their differences, they share much of the same physics, having the potential to pick up material from beneath, a process called basal entrainment during which the flow may increase in volume and velocity manyfold. Due to their complexity and unpredictability there are still many unanswered questions about their mechanics, so that many of the theoretical models in use are based on insufficient data sets and may not apply to a general case. Here, basal entrainment by geophysical gravity-driven flows is studied by isolating the process in idealised laboratory experiments. The avalanche is simplified and controlled in such a way that any changes can be confidently attributed to the entrainment process alone. Further, the methods available in the laboratory allow the continuous, passive study of entrainment, so that for the first time full data sets of internal measurements are obtained, from experiments ranging from simple to complex. The data obtained is easily exploited for confirmation of the mathematical models developed in this thesis. Experiments which simulated entraining avalanches as Newtonian dam-breaks along a horizontal flume and as viscoplastic dam-breaks along an inclined flume both showed an increase in front position, dependent on the amount of material available, amongst other changes. The experimental results allow the development of a theoretical thin-film model in both cases which is solved numerically and compares favourably with the data obtained. The Newtonian model reproduced the flow characteristics excellently and the viscoplastic model successfully simulated the effects of entrainable material. The possibility of performing similar experiments using a granular suspension is also investigated, with promising results. This work shows that the effect of entrainment on gravity-driven flows can be quantified and modelled mathematically as a non-local transport process. This has implications for hazard modelling: if the quantity of available loose material is known, and its characteristics are similar to those of the flowing avalanche, the avalanche and the entrainable bed can be modelled as a continuous flow over a rigid base. Thus it is suggested that the models developed be tested in more realistic cases, e.g. in the case of an avalanche entraining material with different characteristics, or in a more complex geometry, in order to better mimic what happens in nature.

Dam Break of Newtonian Fluids and Granular Suspensions

Nicolas Andreini

The objective of this thesis was to increase our understanding of two-phase geophysical flows (e.g. debris flows) by providing velocity profiles in idealized laboratory avalanches. To that end, we developed a new experimental platform made up of an inclined flume coupled to an imaging system to measure velocity in granular suspension. The inclined flume was 3.5 m long and 10 cm wide and could be inclined from 0 to 35°. A reservoir with the capacity for 10 l of fluid was located in the upper part of the flume and closed with a pneumatic controlled gate. Velocity profiles were obtained using Particle Image Velocimetry (PIV) and index-of-refraction matching of the solid and liquid phases. We used transparent PMMA beads with mean diameters of 200 µm and the interstitial fluid was composed of a mixture of three fluids. The interstitial fluid was adapted in order to match the refraction index and the density of the solid phase. Using pulsed laser and a high speed camera we were able to measure velocity profiles at frequencies up to 1000 Hz with very good precision. Two additional cameras tracked the front position along the flume with a frequency of 30 Hz and a spatial resolution of 1 mm. Prior to acquiring data on the granular suspension, we tested our system on Newtonian fluids. Eight flow configurations were selected with different fluids (glycerol and triton X100), different slopes and different released masses. Velocity profiles were found to be parabolic far from the front as well as very close to the contact line. However, near the front, quantitative theoretical predictions given by lubrication theory diverged from experimental results. Velocities were significantly overestimated (∼ 400%) by the theory at low Reynolds numbers (Re < 2) and slightly underestimated (∼ 10%) at high Reynolds numbers (Re > 8). Very good agreement with theory far from the front indicated that the accuracy of the setup was good (reliable calibration procedure and image processing methods). Experiments on granular suspensions revealed a variety of behaviors depending on the particle concentration, the slope and the mass released. At solid fractions up to 45%, suspensions behaved as homogeneous viscous fluids. For the duration of the experiment, it was not possible to detect any inhomogeneity due to migration or sedimentation. In the range of shear rate tested and with the precision allowed by the setup no shear thickening or shear thinning was observed since velocity profiles remained perfectly Newtonian. For slightly more concentrated suspensions (up to 55%), we found that the flow dynamics at the bulk scale could still be described using a viscous theory. However, at the local scale, migration gave rise to concentration inhomogeneities producing a blunted velocity profile. The shape of the blunted profile was well described by the Mills and Snabre migration model coupled to a Krieger-Dougherty effective viscosity. However, magnitudes of the velocities were largely overestimated, most probably because we fitted the effective viscosity at higher shear rates. Above 55%, small released masses with high solid fractions stopped after a finite time and separation between fluid and solid phases occurred. The solid frame stayed at rest while the fluid seeped through the granular media eroding the front. For larger released masses, we observed successions of different regimes: After an inertial regime and a pseudo-viscous regime, the flow slowed down, corresponding to a new regime in which the shearing was localized in a thin layer at bottom and there was no shearing of the front. At the same time, we observed that the free surface deformed and became wavy. Fractures developed on the top of the flow and, if they grew sufficiently, modified the local velocity field substantially. Finally, at longer time (≥ 4 min) an intermittent motion (stick-slip) was observed with phases during which the suspension was flowing in a quasi-steady regime and phases during which the suspension was at a halt.

EPFL2012

Bio Simulation of Brain Ventricle Dilation in Normal Pressure Hydrocephalus

Kamal Shahim

Hydrocephalus is a brain disease wherein the ventricles dilate and compress the parenchyma towards the skull. It is primarily characterized by the disruption of the cerebrospinal fluid (CSF) flow within the ventricular system. Normal pressure hydrocephalus (NPH) is a form of hydrocephalus for which the enlargement of ventricles occurs although the intracranial pressure (ICP) remains close to normal. The pressure gradient between the source of CSF production in the ventricles and the absorption sites is reported to be very low (∼1 mm Hg), i.e. within the experimental errors. The mechanism of NPH evolution is still obscure and its distinction from the other causes of dementia such as Alzheimer and neurodegenerative diseases is difficult. The present work contributes to a better understanding of the NPH mechanism in terms of CSF disturbances and/or parenchyma defects. To this end, imaging techniques such as Magnetic resonance imaging (MRI), Diffusion tensor imaging (DTI) and Magnetic resonance elastography (MRE) are used together with a finite element (FE) model. As a final step, NPH onset and evolution are clarified via a theoretical model for healthy and NPH brains assuming a spherical geometry. The proposed mechanism is further analyzed in a realistic 3D model of the brain parenchyma. Geometries of ventricular system and skull are obtained from MRI images of a human brain. DTI data are used to establish the fiber tracts direction as well as the local frame of anisotropic elasticity and permeability. The brain parenchyma is considered as a poro-elastic material where the tissue displacement and CSF flow are modeled using the Biot's theory. A link between the CSF diffusion and CSF permeability in brain parenchyma is established and the importance of space dependent CSF content and transverse isotropic (TI) permeability is highlighted in case of low pressure gradient hydrocephalus. Calculations are carried out to simulate the ventricular dilation using FE softwares such as MATLAB® and COMSOL®. The numerical results show that consideration of space dependent CSF content and TI permeability leads to a much more realistic model for NPH in terms of CSF velocity and CSF content. Anisotropic MRE experiment is conducted over selected slices of a healthy human brain. The experimental results are statistically refined and further used to assess the healthy brain stiffness as well as the degree of anisotropy in elasticity. Moreover, the constitutive behavior of the white matter is modeled as a composite material containing fiber tracts surrounded by a matrix; with the assumption of a low fiber-matrix bonding and fiber tract undulation. A non-linear elastic model is proposed in order to take into account the load transfer from white matter matrix to fiber tracts when these are fully stretched. The unknown value of the elastic coefficients in a sick brain is determined by using inverse modeling, i.e. by adjusting these coefficients so that the right ventricle dilation is obtained. It is demonstrated that NPH development can be associated with a degradation of the brain parenchyma elastic stiffness in NPH patients. It is shown that during NPH development, a load transfer from the white matter matrix (cell bodies and interstitial fluid) to fiber tracts takes place, initiating elastic anisotropy in white matter tissues at rather large strains. An analytical approach is developed to seek the underlying NPH mechanism in a simplified model of brain. Without further refinement in the constitutive equation or adding complexity to the material behavior, the Biot's formulation is regarded as the basis. However, an absorption term is added to the Biot's model to consider the possible transparenchymal CSF resorption. The ventricle stability concept is introduced and is further utilized to investigate the equilibrium positions. The influence of different biomechanical parameters on the stable ventricle geometry is assessed and the healthy and NPH equilibrium positions are found to be dependent in particular on the CSF seepage through the ventricle wall and the absorption and permeability coefficients of the brain parenchyma. Although very simple, the proposed analytical model is able to predict the onset and development of NPH conditions as a deviation from healthy conditions. Incorporating the stability concept in a more realistic geometry of brain (3D), the respective equilibrium positions are recaptured using the parameter values provided by the analytical spherical model. The disruption of ventricle surface during the NPH development increases CSF seepage and consequently the medium permeability. A dilation dependent permeability is moreover incorporated in a 3D model of the brain. The results emphasize the importance of strain dependent permeability which favors the ventricle equilibrations in more realistic geometries of brain. Future works might consider the time dependent deformation (creep effects and stress induced remodeling) of ventricles and the incorporation of anisotropic permeability and elasticity in the 3D model. The geometry should be extended to the full ventricular system including the subarachnoid spaces (SAS).

EPFL2011

Dam Break of Newtonian Fluids and Granular Suspensions

Nicolas Andreini

EPFL2012

Bio Simulation of Brain Ventricle Dilation in Normal Pressure Hydrocephalus

Kamal Shahim

EPFL2011