The Saffman-Taylor problem on a sphere

The Saffman-Taylor problem addresses the morphological instability of an interface separating two immiscible, viscous fluids when they move in a narrow gap between two flat parallel plates (Hele-Shaw cell). In this work, we extend the classic Saffman-Taylor situation, by considering the flow between two curved, closely spaced, concentric spheres (spherical Hele-Shaw cell). We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. The effect of the spherical cell (positive) spatial curvature on the shape of the interfacial patterns is investigated. We show that stability properties of the fluid-fluid interface are sensitive to the curvature of the surface. In particular, it is found that positive spatial curvature inhibits finger tip-splitting. Hele-Shaw flow on weakly negative, curved surfaces is briefly discussed.Comment: 26 pages, 4 figures, RevTex, accepted for publication in Phys. Rev.

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

Long-term oncological outcomes of endoscopic full-thickness resection after previous incomplete resection of low-risk T1 CRC (LOCAL-study): study protocol of a national prospective cohort study

Background: T1 colorectal cancer (CRC) without histological high-risk factors for lymph node metastasis (LNM) can potentially be cured by endoscopic resection, which is associated with significantly lower morbidity, mortality and costs compared to radical surgery. An important prerequisite for endoscopic resection as definite treatment is the histological confirmation of tumour-free resection margins. Incomplete resection with involved (R1) or indeterminate (Rx) margins is considered a strong risk factor for residual disease and local recurrence. Therefore, international guidelines recommend additional surgery in case of R1/Rx resection, even in absence of high-risk factors for LNM. Endoscopic full-thickness resection (eFTR) is a relatively new technique that allows transmural resection of colorectal lesions. Local scar excision after prior R1/Rx resection of low-risk T1 CRC could offer an attractive minimal invasive strategy to achieve confirmation about radicality of the previous resection or a second attempt for radical resection of residual luminal cancer. However, oncologic safety has not been established and long-term data are lacking. Besides, surveillance varies widely and requires standardization. Methods/design: In this nationwide, multicenter, prospective cohort study we aim to assess feasibility and oncological safety of completion eFTR following incomplete resection of low-risk T1 CRC. The primary endpoint is to assess the 2 and 5 year luminal local tumor recurrence rate. Secondary study endpoints are to assess feasibility, percentage of curative eFTR-resections, presence of scar tissue and/or complete scar excision at histopathology, safety of eFTR compared to surgery, 2 and 5 year nodal and/or distant tumor recurrence rate and 5-year disease-specific and overall-survival rate. Discussion: Since the implementation of CRC screening programs, the diagnostic rate of T1 CRC is steadily increasing. A significant proportion is not recognized as cancer before endoscopic resection and is therefore resected through conventional techniques primarily reserved for benign polyps. As such, precise histological assessment is often hampered due to cauterization and fragmentation and frequently leads to treatment dilemmas. This first prospective trial will potentially demonstrate the effectiveness and oncological safety of completion eFTR for patients who have undergone a previous incomplete T1 CRC resection. Hereby, substantial surgical overtreatment may be avoided, leading to treatment optimization and organ preservation.Cellular mechanisms in basic and clinical gastroenterology and hepatolog

The western painted turtle genome, a model for the evolution of extreme physiological adaptations in a slowly evolving lineage

Background: We describe the genome of the western painted turtle, Chrysemys picta bellii, one of the most widespread, abundant, and well-studied turtles. We place the genome into a comparative evolutionary context, and focus on genomic features associated with tooth loss, immune function, longevity, sex differentiation and determination, and the species' physiological capacities to withstand extreme anoxia and tissue freezing.Results: Our phylogenetic analyses confirm that turtles are the sister group to living archosaurs, and demonstrate an extraordinarily slow rate of sequence evolution in the painted turtle. The ability of the painted turtle to withstand complete anoxia and partial freezing appears to be associated with common vertebrate gene networks, and we identify candidate genes for future functional analyses. Tooth loss shares a common pattern of pseudogenization and degradation of tooth-specific genes with birds, although the rate of accumulation of mutations is much slower in the painted turtle. Genes associated with sex differentiation generally reflect phylogeny rather than convergence in sex determination functionality. Among gene families that demonstrate exceptional expansions or show signatures of strong natural selection, immune function and musculoskeletal patterning genes are consistently over-represented.Conclusions: Our comparative genomic analyses indicate that common vertebrate regulatory networks, some of which have analogs in human diseases, are often involved in the western painted turtle's extraordinary physiological capacities. As these regulatory pathways are analyzed at the functional level, the painted turtle may offer important insights into the management of a number of human health disorders

Fingering phenomena for driven coating films

A theoretical and numerical model is formulated to describe the instability and the long-time evolution of both gravity-driven and surface-shear-stress-driven thin coating films. A single evolution equation, of higher-order diffusive type, models the flow for either problem. It is derived using the lubrication approximation. For partially wetting systems, the effect of finite contact angle is incorporated in the equation using a particular disjoining pressure model. The base state, in each case, is a two-dimensional steadily propagating capillary front. Slight perturbations of the base state, applied along the front, initiate the fingering instability. Early-time results accurately reproduce the wavelengths of fastest growth and the corresponding eigenmodes as reported in published linear stability analyses. As time proceeds, depending on parameter values, various fingering patterns arise. For conditions of perfect wetting with the substrate downstream of the moving front covered with a thin precursor layer, predicted nonlinear finger evolution agrees well with published experiments. The ultimate pattern, in this case, is a steadily translating pattern of wedge-shaped fingers. Alternatively, for partially wetting systems that exhibit sufficiently large static contact angles, long straight-sided fingers or rivulets are formed. Finally, for larger contact angles, or at relatively low speeds, we predict that the flowing rivulets will become unstable and break up into strings of isolated droplets

Three-dimensional direct numerical simulation of surface-tension-gradient effects on the leveling of an evaporating multicomponent fluid

Mathematical and numerical modeling of drying coating layers is of interest to both industrial and academic communities. Compositional changes that occur during the drying process make the implementation of practical and efficient numerical models rather difficult. In this paper we present a three-dimensional mathematical and numerical model based on the lubrication approximation for the flow of drying paint films on horizontal substrates. The paint is modeled as a multicomponent liquid with one nonvolatile and one volatile component, termed the "resin" and the "solvent" respectively. Our model includes the effects of surface tension and gravitational forces as well as surface tension gradient effects which arise due to solvent evaporation. The dependence of viscosity, diffusivity, and evaporation rate on resin concentration is also incorporated in the model. A closed-form Linearized solution has been found for coating layers that are of almost uniform thickness. The numerical solution agrees closely with the linear solution in the appropriate Limit. A model simulation demonstrates the effect of surface tension gradients due to compositional changes in a three-dimensional flow field, and we suggest methods by which these gradients may be used to obtain a more uniform final coating layer