The mechanism of fragmentation processes in aqueous nanodroplets charged with ions is studied by molecular dynamics (MD) simulations. By using constant-temperature MD, the evaporation of the water is naturally taken into account and sequences of ion fragmentation events are observed. The size of the critical radius of the charged droplet just before the fragmentation and the distribution of the sizes of the fragments are estimated. Comparison of the Rayleigh critical radius for fragmentation and simulation data is within 0.23 nm. This seemingly small difference arises from a large difference in the number of water molecules that makes fragmentation an activated process as in the ion evaporation mechanism (IEM). This finding is in agreement with the predictions of Labowsky et al. [Anal. Chim. Acta 2000, 406, 105-118] for charged aqueous drops. The size of the daughter droplets is larger than the prediction of Born's theory by 0.1 to 0.15 nm. The nature and the dynamics of the intermediate states of the fragmentation process characterized by a bridge formed between the mother droplet and the evaporating ion or thorned structures where the ion sits on the tip are important for the outcome of the size-distribution of the fragments, while they are is missing in Born's theory.

An analytical treatment for the sedimentation rate of disordered suspensions is presented in the context of a resistance problem. From the calculation it is confirmed that the lubrication effect is important in contrast to the suggestion by Brady and Durlofsky (Phys.Fluids 31, 717 (1988)

An improvement of the Stokesian Dynamics method for many-particle systems is presented. A direct calculation of the hydrodynamic interaction is used rather than imposing periodic boundary conditions. The two major difficulties concern the accuracy and the speed of calculations. The accuracy discussed in this work is not concerned with the lubrication correction but, rather, focuses on the multipole expansion which until now has only been formulated up to the so-called FTS version or the first order of force moments. This is improved systematically by a real-space multipole expansion with force moments and velocity moments evaluated at the centre of the particles, where the velocity moments are calculated through the velocity derivatives; the introduction of the velocity derivatives makes the formulation and its extensions straightforward. The reduction of the moments into irreducible form is achieved by the Cartesian irreducible tensor. The reduction is essential to form a well-defined linear set of equations as a generalized mobility problem. The order of truncation is not limited in principle, and explicit calculations of two-body problems are shown with order up to 7. The calculating speed is improved by a conjugate-gradient-type iterative method which consists of a dot-product between the generalized mobility matrix and the force moments as a trial value in each iteration. This provides an O(N2) scheme where N is the number of particles in the system. Further improvement is achieved by the fast multipole method for the calculation of the generalized mobility problem in each iteration, and an O(N) scheme for the non-adaptive version is obtained. Real problems are studied on systems with N = 400 000 particles. For mobility problems the number of iterations is constant and an O(N) performance is achieved; however for resistance problems the number of iterations increases as almost N1/2 with a high accuracy of 10−6 and the total cost seems to be O(N3/2).

It is shown that the method of reflections in resistance form ͑with truncated multipoles͒ is one of many possible iterative methods to obtain the inverse of the mobility matrix ͑with the same truncation͒ in low-Reynolds-number hydrodynamics. Although the method of reflections in the mobility form is guaranteed to converge, it is found that in the resistance form the method may fail to converge. This breakdown is overcome by conjugate-gradient-type iterative methods, and the implications of the iterative method for low-Reynolds-number hydrodynamics are discussed.

A numerical simulation of a gas-fluidized bed is performed without introduction of any empirical parameters. Realistic bubbles and slugs are observed in our simulation. It is found that the convective motion of particles is important for the bubbling phase and there is no convection in the slugging phase.From the simulation results, non-Gaussian distributions are found in the particle velocities and the relation between the deviation from Gaussian and the local density of particles is suggested. It is also shown that the power spectra of particle velocities obey power laws. A brief explanation on the relationship between the simulation results and the Kolmogorov scaling argument is discussed.