A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Development of a method for quantitative determination of the cytotoxic agent piplartine (piperlongumine) in multiple skin layers

This study reports the development of a simple and reproducible method, with high rates of recovery, to extract the cytotoxic agent piplartine from skin layers, and a sensitive and rapid UV‐HPLC method for its quantification. Considering the potential of piplartine for topical treatment of skin cancer, this method may find application for formulation development and pharmacokinetics studies to assess cutaneous bioavailability. Porcine skin was employed as a model for human tissue. Piplartine was extracted from the stratum corneum (SC) and remaining viable skin layers (VS) using methanol, vortex homogenization and bath sonication, and subsequently assayed by HPLC using a C₁₈ column, and 1:1 (v/v) acetonitrile–water (adjusted to pH 4.0 with acetic acid 0.1%) as mobile phase. The quantification limit of piplartine was 0.2 μg/mL (0.6 μm ), and the assay was linear up to 5 μg/mL (15.8 μm ), with within‐day and between‐days assay coefficients of variation and relative errors <15%. Piplartine recovery from SC and VS varied from 86 to 96%. The method was suitable to assay samples from skin penetration studies, enabling detection of differences in cutaneous delivery in different skin compartments resulting from treatment with various formulations and time periods.     

A survey of dual-feasible and superadditive functions

Dual-feasible functions are valuable tools that can be used to compute both lower bounds for different combinatorial problems and valid inequalities for integer programs. Several families of functions have been used in the literature. Some of them were defined explicitly, and others not. One of the main objectives of this paper is to survey these functions, and to state results concerning their quality. We clearly identify dominant subsets of functions, i.e. those which may lead to better bounds or stronger cuts. We also describe different frameworks that can be used to create dual-feasible functions. With these frameworks, one can get a dominant function based on other ones. Two new families of dual-feasible functions obtained by applying these methods are proposed in this paper.