Translation and rotation of a porous spheroid in a spheroidal container

The flow problem of an incompressible axisymmetrical quasisteady translation and steady rotation of a porous spheroid in a concentric spheroidal container are studied analytically. The same small departure from a sphere is considered for each spheroidal surface. In the limit of small Reynolds number, the Brinkman equation for the flow inside the porous region and the Stokes equation for the outside region in their stream functions formulations and velocity components, which are proportional to the translational and angular velocities, respectively, are used. Explicit expressions are obtained for both inside and outside flow fields to the first order in a small parameter characterizing the deformation of the spheroidal surface from the spherical shape. The hydrodynamic drag force and couple exerted on the porous spheroid are obtained for the special cases of prolate and oblate spheroids in closed forms. The dependence of the normalized wall-corrected translational and rotational mobilities on permeability for a porous spheroid in an unbounded medium and for a solid spheroid in a cell on the particle volume fraction is discussed numerically and graphically for various values of the deformation parameter. In the limiting cases, the analytical solutions describing the drag force and torque or mobilities for a porous spheroid in the spheroidal vessel reduce to those for a solid sphere and for a porous sphere in a spherical cell.

Cluster Origin of the Solubility of Single-Wall Carbon Nanotubes

The possibility of the existence of single-wall carbon nanotubes (SWNT) in organic solvents, in the form of clusters containing a number of SWNTs, is discussed. A theory is developed based on a bundletmodel for clusters, which enables describing the distribution function of clusters by size. Comparison of the calculated values of solubility with experimental data would permit obtaining energetic parameters characterizing the interaction of an SWNT with its surrounding in a solid phase or solution. Fullerenes and SWNTs are unique objects, whose behavior in many physical situations is characterized by remarkable peculiarities. Peculiarities in solutions show up in that fullerenes and SWNTs represent the only soluble forms of carbon, what is primary related to the originality in the molecular structure of fullerenes and SWNTs. The fullerene molecule is a virtually uniform closed spherical or spheroidal surface, having no sharp ridges or dents. Similarly, an SWNT is a smooth cylindrical unit. Both structures give rise to the relatively weak interaction between the neighbouring molecules in a crystal, and promote effective interaction of the molecules with those of a solvent. Another peculiarity in solutions is related to their tendency to form clusters, consisting of a number of fullerene molecules or SWNTs. The energy of interaction of a fullerene molecule or SWNT with solvent molecules is proportional to the surface of the former molecule, and roughly independent of the relative orientation of solvent molecules. A unified treatment is proposed in the framework of the bundlet model of a cluster, in accordance with which the free energy of an SWNT involved in a cluster consists of two components: a volume one proportional to the number of molecules n in a cluster and a surface one proportional to n1/2.

Numerical Approach to Far Field Acoustic Wave Propagation from a Prolate Spheroidal Surface

A method is described for calculating the far field, transient, three-dimensional pressure field generated by acoustic waves emanating from a prolate spheroidal surface. The pressure field is expanded in a series of spherical harmonics, which leads to a system of linear, tridiagonal, one dimensional wave equations that can be integrated efficiently by numerical techniques based on the method of characteristics. Integrals involving orthogonal functions are approximated by a numerically robust scheme where exact orthogonality is obtained (in the absence of round-off errors) in terms of weighted sums over a discrete variable.