No abstract

A finite-difference scheme is used to solve the Navier-Stokes equations for the steady flow inside and outside viscous spheres in a fluid of different properties. Hence, the hydrodynamic force and the steady-state drag coefficient of the spheres are obtained. The Reynolds numbers of the computations range between 0.5 and 1000 and the viscosity ratio ranges between 0 (inviscid bubble) and infinity (solid particle). Unlike the numerical schemes previously implemented in similar studies (uniform grid in a stretched coordinate system) the present method introduces a two-layer concept for the computational domain outside the sphere. The first layer is a very thin one [ORe−1/2] and is positioned at the interface of the sphere. The second layer is based on an exponential function and covers the rest of the domain. The need for such a double-layered domain arises from the observation that at intermediate and large Reynolds numbers a very thin boundary layer appears at the fluid-fluid interface. The computations yield the friction and the form drag of the sphere. It is found that with the present scheme, one is able to obtain results for the drag coefficient up to 1000 with relatively low computational power. It is also observed that both the Reynolds number and the viscosity ratio play a major role on the value of the hydrodynamic force and the drag coefficient. The results show that, if all other conditions are the same, there is a negligible effect of the density ratio on the drag coefficient of viscous spheres.

No abstract

Raman backscattering studies for a series of cubic SiC (3C-SiC) single-crystal films grown on (100)Si by way of chemical vapor deposition (CVD) with SiC film thicknesses dSiC from 600 Å to 17 μm are performed. Raman spectra of samples with dSiC>4 μm show a sharp and strong feature which obeys the selection rule for the 3C-SiC LO(Γ) phonon line. The Raman signals from the SiC film and the Si substrate show the same polarization behavior which confirms that the crystalline orientations of the Si substrate and 3C-SiC film are the same. Although there is a big lattice mismatch of 20% between 3C-SiC and Si the observed Raman shifts between 3C-SiC/Si and free 3C-SiC films are ≤2 cm−1 and reflect strains of 0.1%–0.2% in films thicker than 4 μm. Some interesting enhancements of Si and 3C-SiC Raman signals are reported. The Si 522 cm−1 phonon from a Si wafer is enhanced in intensity by a factor of 2–3 due to a CVD overlayer of cubic SiC. Furthermore, the 3C-SiC longitudinal optical phonon at the Γ point, LO(Γ), from SiC/Si samples is enhanced by a factor of 2 or 3 following the removal of the Si substrate. The strict selection rules are no longer obeyed in this case. The former is possibly due to the electric-field-induced inelastic scattering from the SiC/Si heterojunction. The latter is explained by the multiple reflection in free 3C-SiC films. Our theoretical analysis shows that if the cross section for forward scattering is about one order of magnitude larger than that for backscattering, this enhancement will appear. The forward scattering has different selection rules from the back scattering and thus could lead to the appearance of the forbidden transverse optical phonon and the depolarization of the 3C-SiC Raman phonons from the SiC free films. The variation of the Raman spectrum with incident power has also been studied. The Raman cross section for 3C-SiC is estimated by a new method. The wavelength shifts of 3C-SiC LO(Γ) phonons taken from SiC/Si or free films are measured and explained.

No abstract