| The ion transport model is a widely used mathematical model,which has great research prospects in biological ion transport,physical semiconductor devices and chemical electrosolution ion flows.There have been some studies on the transport model of a single type of ion distribution and the derivation of the model by using the energy variation method.However,few studies have been done on multiple ions transport models.In this paper,we derive a more general multi-ion hydrodynamic model by using energy variational method,which may also be called the generalized Poisson-Nernst-Planck-NavierStokes equations(PNP-NS equations).In this process,we analyze the forces exerted on the ions,apply the energy variational method to the ions and combine with Newton's third law to obtain the motion transport equations describing the interaction between macroscopic ion transport and microscopic ion transport.In addition,for this system of equations,the Lennard-Jones repulsive force between charged particles of finite sizes is given,and then the charged particle transport model is analyzed under this condition.This thesis is organised as follows.First,in the first chapter and the second chapter,we introduce some research background and present the current research status of the charged particle transport model,and describe the prerequisite knowledge to deduce the model.Second,in Chapter 3,we introduce the research methods,analyze the motion of multiple types of charged particles subject to microscopic and macroscopic forces,and use the research methods to derive the generalized PNP-NS equations.Then,in Chapter 4,we include the micro-interaction of charged particles under the influence of finite volume effect,add the energy of repulsion between the ions to the total energy,and then derive the PNP-NS equations under the influence of this condition.Finally,we propose several unsolved related problems and suggest some useful methods to attack these problems. |
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