文献详情
Poisson-Boltzmann equation with a random field for charged fluids
文献类型：期刊
期刊名称：Journal of physics. Condensed matter : an Institute of Physics journal
年：2019
ISSN：1361-648X
关键词：Poisson-Boltzmann Equation,charged fluids,field theory,monte carlo,path integral,stochastic process
所属部门：物理学系
摘要：The classical Poisson-Boltzmann equation (CPBE), which is a mean field theory by averaging the ion fluctuation, has been widely used to study ion distributions in charged fluids. In this study, we derive a modified Poisson-Boltzmann equation with a random field from the field theory and recover the ion fluctuation through a multiplicative noise added in the CPBE. The Poisson-Boltzmann equation with a random field (RFPBE) captures the effect of the ion fluctuation and gives different ion distribu ...More
The classical Poisson-Boltzmann equation (CPBE), which is a mean field theory by averaging the ion fluctuation, has been widely used to study ion distributions in charged fluids. In this study, we derive a modified Poisson-Boltzmann equation with a random field from the field theory and recover the ion fluctuation through a multiplicative noise added in the CPBE. The Poisson-Boltzmann equation with a random field (RFPBE) captures the effect of the ion fluctuation and gives different ion distributions in the charged fluids compared to the CPBE. To solve the RFPBE, we propose a Monte Carlo method based on the path integral representation. Numerical results show that the effect of the ion fluctuation strengthens the ion diffusion into the domain and intends to distribute the ions in the fluid uniformly. The final ion distribution in the fluid is determined by the competition between the ion fluctuation and the electrostatic forces exerted by the boundaries. The RFPBE is general and feasible for high dimensional systems by taking the advantage of the Monte Carlo method. We use the RFPBE to study a two dimensional system as an example, in which the effect of ion fluctuation is clearly captured.? 2019 IOP Publishing Ltd. ...Hide

DOI：10.1088/1361-648X/ab27da
百度学术：Poisson-Boltzmann equation with a random field for charged fluids
语言：外文
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