Transport of aggregating nanoparticles in porous media
<p>&#160;</p><p>A&#160;&#160; novel&#160;&#160; mathematical&#160;&#160; model&#160;&#160; was&#160;&#160; developed&#160;&#160; to&#160;&#160; describe&#160;&#160; the&#160;&#160; transport&#160;&#160; 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&#160; be found suspended&#160; in the&#160; aqueous phase&#160; or attached&#160; reversibly and/or&#160;&#160; irreversibly&#160;&#160; onto&#160;&#160; the&#160;&#160; solid&#160;&#160; matrix.&#160;&#160; The&#160; Derjaguin-Landau-Verwey-Overbeek (DLVO)&#160; theory&#160;&#160; was&#160;&#160; used&#160;&#160; to&#160;&#160; account&#160;&#160; for&#160;&#160; possible&#160;&#160; repulsive&#160;&#160; interactions&#160;&#160; between aggregates allowing for both reaction-limited aggregation (RLA), and diffusion-limited aggregation (DLA) cases to be considered.&#160;&#160; The governing coupled partial differential equations were solved initially by employing adaptive operator splitting methods, which decoupled&#160;&#160; the&#160;&#160; reactive&#160;&#160; transport&#160;&#160; and&#160;&#160; aggregation&#160;&#160; into&#160;&#160; distinct&#160;&#160; physical&#160;&#160; 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,&#160;&#160; aggregation&#160;&#160; was&#160;&#160; shown&#160;&#160; to &#160;&#160;either&#160;&#160; decrease&#160;&#160; or&#160;&#160; increase&#160;&#160; nano particle attachment&#160;&#160; onto&#160;&#160; the&#160;&#160; solid&#160;&#160; matrix&#160;&#160; and&#160;&#160; to&#160;&#160; yield&#160; either&#160; early&#160;&#160; or&#160; retarded&#160; breakthrough. Finally,&#160;&#160; useful&#160;&#160; conclusions&#160;&#160; were&#160;&#160; drawn&#160;&#160; regarding&#160;&#160; the&#160;&#160; particle&#160;&#160; distribution&#160;&#160; density&#160; &#160;at various points in time and space.</p>