Transport of aggregating nanoparticles in porous media

<p> </p><p>A   novel   mathematical   model   was   developed   to   describe   the   transport   of nanoparticles in water saturated, homogeneous porous media with uniform flow. The model accounts for the simultaneous migration and aggregation of nanoparticles. The nanoparticles can  be found suspended  in the  aqueous phase  or attached  reversibly and/or   irreversibly   onto   the   solid   matrix.   The  Derjaguin-Landau-Verwey-Overbeek (DLVO)  theory   was   used   to   account   for   possible   repulsive   interactions   between aggregates allowing for both reaction-limited aggregation (RLA), and diffusion-limited aggregation (DLA) cases to be considered.   The governing coupled partial differential equations were solved initially by employing adaptive operator splitting methods, which decoupled   the   reactive   transport   and   aggregation   into   distinct   physical   processes. Subsequently, the resulting equations were treated individually with proper use of either a finite difference scheme or a specialized ordinary differential equations solver. The results from various model simulations showed that the transport of nanoparticles inporous media is substantially different than the transport of conventional biocolloids. In particular,   aggregation   was   shown   to   either   decrease   or   increase   nano particle attachment   onto   the   solid   matrix   and   to   yield  either  early   or  retarded  breakthrough. Finally,   useful   conclusions   were   drawn   regarding   the   particle   distribution   density   at various points in time and space.</p>

Embedded operator splitting methods for perturbed systems

ABSTRACT It is common in classical mechanics to encounter systems whose Hamiltonian H is the sum of an often exactly integrable Hamiltonian H0 and a small perturbation ϵH1 with ϵ ≪ 1. Such near-integrability can be exploited to construct particularly accurate operator splitting methods to solve the equations of motion of H. However, in many cases, for example in problems related to planetary motion, it is computationally expensive to obtain the exact solution to H0. In this paper, we present a new family of embedded operator splitting (EOS) methods which do not use the exact solution to H0, but rather approximate it with yet another, EOS method. Our new methods have all the desirable properties of classical methods which solve H0 directly. But in addition they are very easy to implement and in some cases faster. When applied to the problem of planetary motion, our EOS methods have error scalings identical to that of the often used Wisdom–Holman method but do not require a Kepler solver, nor any coordinate transformations, or the allocation of memory. The only two problem specific functions that need to be implemented are the straightforward kick and drift steps typically used in the standard second-order leap-frog method.