The effect of polar lipids on tear film dynamics

In this paper we present a mathematical model describing the effect of polar lipids on the evolution of a precorneal tear film, with the aim of explaining the interesting experimentally observed phenomenon that the tear film continues to move upwards even after the upper eyelid has become stationary. The polar lipid is an insoluble surface species that locally alters the surface tension of the tear film. In the lubrication limit, the model reduces to two coupled nonlinear partial differential equations for the film thickness and the concentration of lipid. We solve the system numerically and observe that the presence of the lipid causes an increase in flow of liquid up the eye. We further exploit the size of the parameters in the problem to explain the initial evolution of the system

A state-dependent parameterization of saturated-unsaturated zone interaction

The relevance of groundwater as an important source of root zone moisture by means of capillary rise is increasingly being recognized. This is partly reflected in many current land surface schemes, which increasingly replace a one-way (i.e., downward) drainage of water by a two-way interaction flux between the root zone and a groundwater system. A fully physically correct implementation of this two-way saturated-unsaturated interaction flux requires transient simulations using the highly nonlinear Richards' equation, which is a computationally demanding approach. We test a classic simple approximation that computes the root zone¿groundwater interaction flux as the net effect of a downward drainage flux and an upward capillary rise flux against the Darcy equation for quasi steady state conditions. We find that for a wet root zone and/or shallow groundwater, the errors within this approximation are significant and of the same magnitude as the interaction flux itself. We present a new closed-form parameterization of the Darcy equation¿based fluxes that accounts both for root zone soil moisture and depth to the water table. Parameter values for this parameterization are listed for 11 different, widely applied soil texture descriptions. The high numerical efficiency of the proposed method makes it suitable for inclusion into demanding applications, e.g., a Monte Carlo framework, or high spatial resolution

The drainage of a foam lamella

We present a mathematical model for the drainage of a surfactant-stabilised foam lamella, including capillary, Marangoni and viscous effects and allowing for diffusion, advection and adsorption of the surfactant molecules. We use the slender geometry of a lamella to formulate the model in the thin-film limit and perform an asymptotic decomposition of the liquid domain into a capillary-static Plateau border, a time-dependent thin film and a transition region between the two. By solving a quasi-steady boundary-value problem in the transition region, we obtain the flux of liquid from the lamella into the Plateau border and thus are able to determine the rate at which the lamella drains. Our method is illustrated initially in the surfactant-free case. Numerical results are presented for three particular parameter regimes of interest when surfactant is present. Both monotonic profiles and those exhibiting a dimple near the Plateau border are found, the latter having been previously observed in experiments. The velocity field may be uniform across the lamella or of parabolic Poiseuille type, with fluid either driven out along the centre-line and back along the free surfaces or vice versa. We find that diffusion may be negligible for a typical real surfactant, although this does not lead to a reduction in order because of the inherently diffusive nature of the fluid-surfactant interaction. Finally, we obtain the surprising result that the flux of liquid from the lamella into the Plateau border increases as the lamella thins, approaching infinity at a finite lamella thickness

Examination of the seepage face boundary condition in subsurface and coupled surface/subsurface hydrological models

A seepage face is a nonlinear dynamic boundary that strongly affects pressure head distributions, water table fluctuations, and flow patterns. Its handling in hydrological models, especially under complex conditions such as heterogeneity and coupled surface/subsurface flow, has not been extensively studied. In this paper, we compare the treatment of the seepage face as a static (Dirichlet) versus dynamic boundary condition, we assess its resolution under conditions of layered heterogeneity, we examine its interaction with a catchment outlet boundary, and we investigate the effects of surface/subsurface exchanges on seepage faces forming at the land surface. The analyses are carried out with an integrated catchment hydrological model. Numerical simulations are performed for a synthetic rectangular sloping aquifer and for an experimental hillslope from the Landscape Evolution Observatory. The results show that the static boundary condition is not always an adequate stand-in for a dynamic seepage face boundary condition, especially under conditions of high rainfall, steep slope, or heterogeneity; that hillslopes with layered heterogeneity give rise to multiple seepage faces that can be highly dynamic; that seepage face and outlet boundaries can coexist in an integrated hydrological model and both play an important role; and that seepage faces at the land surface are not always controlled by subsurface flow. The paper also presents a generalized algorithm for resolving seepage face outflow that handles heterogeneity in a simple way, is applicable to unstructured grids, and is shown experimentally to be equivalent to the treatment of atmospheric boundary conditions in subsurface flow models

A numerical study of two-phase flow with dynamic capillary pressure using an adaptive moving mesh method

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a travelling wave ansatz and efficient numerical methods. The travelling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is paid to the non-monotonic profiles. The travelling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach

Modeling water resources management at the basin level: review and future directions

Water quality / Water resources development / Agricultural production / River basin development / Mathematical models / Simulation models / Water allocation / Policy / Economic aspects / Hydrology / Reservoir operation / Groundwater management / Drainage / Conjunctive use / Surface water / GIS / Decision support systems / Optimization methods / Water supply

Predicting Stream Nitrogen Concentration From Watershed Features Using Neural Networks

The present work describes the development and validation of an artificial neural network (ANN) for the purpose of estimating inorganic and total nitrogen concentrations. The ANN approach has been developed and tested using 927 nonpoint source watersheds studied for relationships between macro-drainage area characteristics and nutrient levels in streams. The ANN had eight independent input variables of watershed parameters (five on land use features, mean annual precipitation, animal unit density and mean stream flow) and two dependent output variables (total and inorganic nitrogen concentrations in the stream). The predictive quality of ANN models was judged with “hold-out” validation procedures. After ANN learning with the training set of data, we obtained a correlation coefficient r of about 0.85 in the testing set. Thus, ANNs are capable of learning the relationships between drainage area characteristics and nitrogen levels in streams, and show a high ability to predict from the new data set. On the basis of the sensitivity analyses we established the relationship between nitrogen concentration and the eight environmental variables

Optimization Study For The Cross-Section Of A Concrete Gravity Dam: Genetic Algorithm Model And Application

Concrete gravity dams have trapezoidal shape in their cross section and shall guarantee the global stability against acting loads like hydrostatic and uplift pressures through his gravitational actions (self-weight and others). This study focuses on the shape optimization of concrete gravity dams using genetic algorithms. In this case, the dam cross section area is considered as the objective function and the design variables are the geometric parameters of the gravity dam. The optimum cross-section of a concrete gravity dam is achieved by the Genetic Algorithm (GA) through a Matlab routine developed by the author. Sliding, overturning and floating verifications are implemented in the program. In order to assess the efficiency of the proposed methodology for gravity dams optimization, one application is presented adopting the concrete gravity dam of Belo Monte Hydropower Plant (HPP), considering normal loading condition and others assumptions presented.Peer Reviewe