This paper describes a comparison of some numerical methods for solving the advection-diffusion (AD) equation which may be used to describe transport of a pollutant. The one-dimensional advection-diffusion equation is solved by using cubic splines (the natural cubic spline and a ”special” AD cubic spline) to estimate first and second derivatives, and also by solving the same problem using two s...

We model the evolution of the concentration field of macromolecules in a symmetric field-flow fractionation (FFF) channel by a onedimensional advection-diffusion equation. The coefficients are precisely determined from the fluid dynamics. This model gives quantitative predictions of the time of elution of the molecules and the width in time of the concentration pulse. The model is rigorously su...

We present an algorithm for measuring the speed and thickness of reaction fronts, and from those quantities, the diffusivity and the reaction rate of the active chemical species. This front-tracking algorithm provides local measurements suitable for statistics and requires only a sequence of concentration fields. Though our eventual goal is front tracking in advection-reaction-diffusion, here w...

Turing first theorized that many biological patterns arise through the processes of reaction and diffusion [1]. Subsequently, reaction-diffusion systems have been studied in many fields, including computer graphics. We first show that for visual simulation purposes, reaction-diffusion equations can be made unconditionally stable using a variety of straightforward methods. Second, we propose an ...

This paper presents a complete dynamic modeling of a membrane distillation process. The model contains two consistent dynamic models. A 2D advection-diffusion equation for modeling the whole process and a modified heat equation for modeling the membrane itself. The complete model describes the temperature diffusion phenomenon across the feed, membrane, permeate containers and boundary layers of...