Mathematical Studies in Colloid Transport

主要研究人员和他们的同事对细菌和其他胶体物质通过可变孔隙度的非线性现象进行了系统的研究。他们假设孔隙度是胶体浓度的函数，这使得控制流动的反应-扩散-对流方程的时间导数项具有非线性。研究人员利用能量论证和半群分析等技术，解决了这些类型的生物膜问题的适位性和定性行为问题。他们还使用动力系统方法研究了这些系统中行波前的存在性。他们努力的一个重要部分是与地球科学领域的同事互动，以确定他们研究的模型在物理上是有充分根据的。胶体的存在，其中一些细菌物质是例子，在地下含水层系统可以对污染物的运输产生深远的影响。例如，碳氢化合物可以形成微生物生长的基质，然后在含水层的固体表面形成生物膜。生物膜的行为在采矿工业中对于金属从矿石中浸出，在石油工业中对于控制生物膜堆积防止石油开采堵塞，特别是在环境水资源地区对于原位生物修复具有重要意义。实验证明，细菌物质的存在可以促进有害化学物质（如滴滴涕）在土壤中的传播；在其他情况下，生物膜可以形成屏障，阻止这些污染物的运输。研究人员研究了模拟污染物和胶体颗粒相互作用的数学方程，以及这些相互作用对地下区域流动特性的影响。一个目标是通过检验各种模型的有效性来理解不同的机制如何影响流体动力流动。

Logan 9708421 The principal investigators and their colleagues undertake a systematic study of nonlinear phenomena in the transport of bacterial and other colloidal substances through domains of variable porosity. They assume that the porosity is a function of the colloid concentration, which places a nonlinearity in the time-derivative term of the resulting reaction-diffusion-convection equations that govern the flow. The investigators address issues of well-posedness and qualitative behavior for some of these types of biofilm problems, using techniques such as energy arguments and semigroup analysis. They also study the existence of traveling wavefronts in these systems using dynamical systems methods. A significant part of their effort is to interact with colleagues in the geosciences in order to be certain that the models they study are physically well-founded. The presence of colloids, of which some bacterial substances are examples, in subsurface aquifer systems can have a profound effect on the transport of contaminants. For example, hydrocarbons can form a substrate for microbial growth which can then result in the formation of a biofilm on the solid surfaces of the aquifer. The behavior of biofilms in important in the mining industry for the leaching of metals from ores, in the petroleum industry for the control of biofilm accumulation to prevent plugging in oil recovery, and especially in the environmental water resources area for in-situ bioremediation. It has been demonstrated experimentally that the presence of bacterial substances can enhance the transport of harmful chemicals, like DDT, through the soil; in other cases, biofilms can form barriers that block the transport of such contaminants. The investigators study mathematical equations that model the interaction of contaminants and colloidal particles and the effects of these interactions on the flow characteristics of subsurface domains. One goal is to understand, through exami ming the validity of various models, how different mechanisms affect the hydrodynamic flow.