In the mixed-dimensional representation of fractured media, the fractures are considered as lower-dimensional manifolds. This concept is successively applied to the lines and points at the intersections between fractures leading to a hierarchical geometry of manifolds of codimension one. By imposing these modelling assumptions a priori in the continuous setting, a basis is formed for the...
The clearance of the metabolic waste in the body is handled by the lymphatic system. Except in the brain, which appears to be the only organ devoid of lymphatic channels. Indeed, the mechanisms underlying the clearance processes of the brain are still unknown, and the topic sparks debate and controversy. What is clear however, is that dysfunction of cerebral metabolic waste clearance is...
The interior of living cells can be considered as a porous medium consisting of three compartments: cytosol, chloroplasts and mitochondria. Diffusion and reactions take place inside the cytosol, inside the chloroplasts and on the surfaces of the mitochondria. Furthermore, biochemical species can be exchanged between the compartments. Consequently we need to solve a system of fully dimensional...
We present a general model concept and a flexible software framework for the description of plant-scale soil-root interaction processes including the essential fluid mechanical processes in the vadose zone. The model is developed in the framework of non-isothermal, multi-phase, multi-component flow and transport in porous media. The software is an extension of the open-source porous media flow...
Hierarchical network structures occur in many biological systems, since they are responsible for the transport of fluids, nutrients or oxygen. Such a network structure is, for example, the blood vessel network supplying organs with oxygenated blood or removing metabolic waste from the tissue. A further example is the root network of a plant, ensuring the plant‘s water supply.
One way to...
Plant tissues have developed several strategies to cope with multiple cycles of freezing and thawing events without being damaged. Some of these strategies are of physiological nature, others arise from structural properties. Understanding the involved strategies and mechanisms of plants exposed to frost conditions is of high interest, as they could potentially be used for the development of...
Once lung-cancer cells have invaded the brain tissue via the blood-vessel system, the cells proliferate and migrate in the tissue. The nutrients in the interstitial fluid ensure the proliferation and the basal reactions of the cancer cells. Over time, the cancer cells proliferate and form metastases. In experiments, multicellular lung-cancer spheroids are grown under fully-nutrient-supplied...
We characterize the deformations of a dry granular medium confined inside a horizontal Hele-Shaw cell where air is injected at a constant overpressure. The overpressure is systematically varied, and we show a range of flow regimes where for example the injected fluid form channel structures similar to viscous fingers in a porous medium. By combining experimental deformation data and numerical...
Experiments on confined two-phase flow systems, involving air and a dense suspension, have revealed highly non -trivial flow morphologies. As the air displaces the suspension, the grains that make up the suspension tend to accumulate along the interface, and can build up force chains that jam the accumulated region. This dynamics will generate...
The physical processes governing flow and transport in porous media span a wide array of spatial scales. Furthermore, in many applications it would be computationally intractable to resolve each scale of interest. To still capture the effects of the smaller-scale processes, one option is to couple together models of different dimensionality. In e.g. vascularized tissue and root networks, the...
Physicians often face multiple possible strategies treating a specific disease and it is crucial to have a predictive numerical methodology that can help with selection of the best option. Brain aneurysms are a result of a weakened blood vessel wall that, if not treated well, can have a lethal rupture. To prevent the rupture, multiple devices are available, including coils and flow diverters....
In this paper, a conjugate model is presented to evaluate the effect of vegetation on the surrounding environment. Vegetation intercepts solar radiation, providing shading to the ground, and offers natural cooling through evapotranspiration, cooling the air flowing through the vegetation. However, vegetation also slows down the air flow and its transpirative cooling potential is strongly...
This work has been motivated by the study of solid tumor growth, and more specifically, by the examination of the most frequently encountered type of pediatric primary bone tumors (osteosarcoma), characterised in their early stage by the formation of non-mineralised bone tissue, called osteoid [1]. As the tumor evolves in time, mineralisation of this growing tissue can take place.The objective...
