Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

Condensational growth of atmospheric aerosol particles in an expanding water saturated air flow

Aerosol particles and water vapour are two important constituents of the atmosphere. Their interaction, i.e. thecondensation of water vapour on particles, brings about the formation of cloud, fog, and raindrops, causing the water cycle on the earth, and being responsible for climate changes. Understanding the roles of water vapour and aerosol particles in this interaction has become an essential part of understanding the atmosphere. In this work, the heterogeneous nucleation on pre-existing aerosol particles by the condensation of water vapour in theflow of a capillary nozzle was investigated. Theoretical and numerical modelling as well as experiments on thiscondensation process were included. Based on reasonable results from the theoretical and numerical modelling, an idea of designing a new nozzle condensation nucleus counter (Nozzle-CNC), that is to utilise the capillary nozzle to create an expanding water saturated air flow, was then put forward and various experiments were carried out with this Nozzle-CNC under different experimental conditions. Firstly, the air stream in the long capillary nozzle with inner diameter of 1.0~mm was modelled as a steady, compressible and heat-conducting turbulence flow by CFX-FLOW3D computational program. An adiabatic and isentropic cooling in the nozzle was found. A supersaturation in the nozzle can be created if the inlet flow is water saturated, and its value depends principally on flow velocity or flow rate through the nozzle. Secondly, a particle condensational growth model in air stream was developed. An extended Mason's diffusion growthequation with size correction for particles beyond the continuum regime and with the correction for a certain particle Reynolds number in an accelerating state was given. The modelling results show the rapid condensational growth of aerosol particles, especially for fine size particles, in the nozzle stream, which, on the one hand, may induce evident `over-sizing' and `over-numbering' effects in aerosol measurements as nozzle designs are widely employed for producing accelerating and focused aerosol beams in aerosol instruments like optical particle counter (OPC) and aerodynamical particle sizer (APS). It can, on the other hand, be applied in constructing the Nozzle-CNC. Thirdly, based on the optimisation of theoretical and numerical results, the new Nozzle-CNC was built. Under various experimental conditions such as flow rate, ambient temperature, and the fraction of aerosol in the total flow, experiments with this instrument were carried out. An interesting exponential relation between the saturation in the nozzle and the number concentration of atmospheric nuclei, including hygroscopic nuclei (HN), cloud condensation nuclei (CCN), and traditionally measured atmospheric condensation nuclei (CN), was found. This relation differs from the relation for the number concentration of CCN obtained by other researchers. The minimum detectable size of this Nozzle-CNC is 0.04?m. Although further improvements are still needed, this Nozzle-CNC, in comparison with other CNCs, has severaladvantages such as no condensation delay as particles larger than the critical size grow simultaneously, low diffusion losses of particles, little water condensation at the inner wall of the instrument, and adjustable saturation --- therefore the wide counting region, as well as no calibration compared to non-water condensation substances.