Order In Number Density Research Articles

Structure Properties in a Bidisperse Ferrofluid in the Absence of an External Magnetic Field

The structure properties of a ferrofluid modeled by a bidisperse system of dipolar hardspheres are studied theoretically for the case of zero external field. Analytical expressions are providedfor the pair distribution function (PDF) and structure factor (SF) to within the first order in numberdensity and the second order in dipole-dipole interaction strength. The influence of the granulometriccomposition on the behavior of the PDF and the position of the first peak of the SF is analyzed.

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) − 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.

The hard-sphere fluid: New exact results with applications

A theorem for convolution integrals is proved and then applied to extend the “second zero-separation theorem” to the bridge functionb(r) and direct-correlation tail functionsd(r). This theorem allows us to exactly relate∂b(r)/∂r and∂d(r)/∂ratr=0 for the hard-sphere fluid to the “contact value” of the radial distribution functiong(r) atr=σ+. From this we obtain immediately the exact values of ∂b(r)/∂r and ∂d(r)/∂r atr=0 through second order in number density ρ. Using our results to compare the exact and Percus-Yevick (PY) bridge function, we find that they differ significantly. After obtaining the bridge function and tail function and their derivatives atr=0 andr=σ through, we suggest new approximations forb(0) andd(0) as well as an analytical integral-equation theory to improve the PY approximation in the pure hard-sphere fluid. The major deficiency of that approximation has been its poor assessment of the cavity function inside the hard-core region. Our theory remedies this defect in a way that yields ay(r) that is self-consistent with respct to the virial and compressibility relations and also the two zero-separation relations involvingy(r) and its spatial derivative atr=0.

Diffusion coefficients of interacting Brownian particles

Starting from a N-particle diffusion equation, the effective particle (self-) and concentration diffusion coefficients of interacting Brownian particles are studied theoretically. These two diffusion coefficients defined by distinct ways are different for interacting systems. By taking into account both potential and hydrodynamic interactions, the expression for the frequency-dependent particle diffusion coefficient exact to linear order in number density is derived. Detailed calculations of both diffusion coefficients are performed for model systems of hard spheres with a repulsive or an attractive long-range potential. The effects of potential and hydrodynamic interactions on these two diffusion coefficients are clarified. The velocity autocorrelation function is also calculated and non-Markovian behaviors are discussed.