Singularities at rims in three-dimensional fluid flow

Asymptotic solutions are presented for Stokes flow near circular rims in three-dimensional geometries. Using nonstandard toroidal coordinates, asymptotic analytical expressions are derived for different corner angles. In comparison to the two-dimensional case, an extra critical corner angle value is derived, below which the swirling behaviour of a particle is absent. Illustrations of the motion of a particle near a rim in a three-dimensional fluid flow are given for different corner angles

Mass transport in a partially covered fluid-filled cavity

A method of computing the concentration field of dissolved material inside an etch-hole is presented. Using a number of assumptions, approximate convection-diffusion equations are formulated, and analytical descriptions for the concentration in different parts of the domain are obtained. By coupling these descriptions the concentration field can be computed. The assumptions and the results are validated by comparison with solutions based on a finite-volume method. Results of the boundary-layer method are given for two characteristic etch-hole geometries. The described boundary-layer method is efficient in terms of computational time and memory, because it does not require the construction of a computational grid in the interior of the domain. This advantage will be exploited in a future paper where the method will be used to simulate wet-chemical etching

Determination of color-octet matrix elements from e^+e- process at low energies

We present an analysis of the preliminary experimental data of direct j/psi production in e^e- process at low energies. We find that the color-octet contributions are crucially important to the cross section at this energy region, and their inclusion produces a good description of the data. By fitting to the data, we extract the individual values of two color-octet matrix elements: \approx 1.1\times 10^{-2} GeV^3, <{\cal O}_8^{\psi}(^3P_0)> m_c^2\approx 7.4\times 10^{-3}GeV^3. We discuss the allowed range of the two matrix elements constrained by the theoretical uncertainties. We find that is poorly determined because it is sensitive to the variation of the choice of m_c, \alpha_s and <{\cal O}_1^{\psi}(^3S_1)>. However m_c^2 is quite stable (about (6-9)\times 10^{-3}GeV^3) when the parameters vary in reasonable ranges. The uncertainties due to large experimental errors are also discussed.Comment: 13 page, RevTex, 2 figures in postscript. To appear in Phys. Rev.

An accurate boundary-element method for Stokes flow in partially covered cavities

The two-dimensional flow of a viscous fluid over an etched hole is computed with a boundary-element method. The etch-hole geometry contains sharp corners at which the solution of the traction boundary-integral equation is singular. Therefore, only the regular part of the solution is computed with the boundary-element method, using a singularity-subtraction method, and the singular part of the solution is added. However, there are regions in which these regular and singular parts are of almost equal magnitude, but different in sign. To avoid the subtraction and addition of large quantities where quantities of smaller order are computed a domain-decomposition technique is introduced. We show that the accuracy indeed increases by the described techniques. After extrapolation the results for a rectangular geometry agree very well with results obtained earlier with a semi-analytical method. In a separate paper the results of the described boundary-element method will be used for the numerical simulation of wet-chemical etching. For such a simulation, also the stream function is required. Therefore, a new integral formulation is derived for the stream function in the form of a boundary integral over the velocity and shear-stress components. Finally we show some results for arbitrary etch holes

An accurate boundary-element method for Stokes flow in partially covered cavities

The two-dimensional flow of a viscous fluid over an etched hole is computed with a boundary-element method. The etch-hole geometry contains sharp corners at which the solution of the traction boundary-integral equation is singular. Therefore, only the regular part of the solution is computed with the boundary-element method, using a singularity-subtraction method, and the singular part of the solution is added. However, there are regions in which these regular and singular parts are of almost equal magnitude, but different in sign. To avoid the subtraction and addition of large quantities where quantities of smaller order are computed a domain-decomposition technique is introduced. We show that the accuracy indeed increases by the described techniques. After extrapolation the results for a rectangular geometry agree very well with results obtained earlier with a semi-analytical method. A new integral formulation is derived for the stream function in the form of a boundary integral over the velocity and shear-stress components. Finally we show some results for arbitrary etch holes

An accurate boundary-element method for Stokes flow in partially covered cavities

The two-dimensional flow of a viscous fluid over an etched hole is computed with a boundary-element method. The etch-hole geometry contains sharp corners at which the solution of the traction boundary-integral equation is singular. Therefore, only the regular part of the solution is computed with the boundary-element method, using a singularity-subtraction method, and the singular part of the solution is added. However, there are regions in which these regular and singular parts are of almost equal magnitude, but different in sign. To avoid the subtraction and addition of large quantities where quantities of smaller order are computed a domain-decomposition technique is introduced. We show that the accuracy indeed increases by the described techniques. After extrapolation the results for a rectangular geometry agree very well with results obtained earlier with a semi-analytical method. In a separate paper the results of the described boundary-element method will be used for the numerical simulation of wet-chemical etching. For such a simulation, also the stream function is required. Therefore, a new integral formulation is derived for the stream function in the form of a boundary integral over the velocity and shear-stress components. Finally we show some results for arbitrary etch holes

Low-Reynolds-number flow over partially covered cavities

We solve the problem of two-dimensional flow of a viscous fluid over a rectangular approximation of an etched hole. In the absence of inertia, the problem is solved by a technique involving the matching of biorthogonal infinite eigenfunction expansions in different parts of the domain. Truncated versions of these series are used to compute a finite number of unknown coefficients. In this way, the stream function and its derivatives can be determined in any arbitrary point. The accuracy of the results and the influence of the singularities at the mask-edge corners is discussed. The singularities result in a reduced convergence of the eigenfunction expansions on the interfaces of the different regions. However, accurate results can be computed for the interior points without using a lot of computational time and memory. These results can be used as a benchmark for other methods which will have to be used for geometries involving curved boundaries. The effect of hole size on the flow pattern is also discussed. These flow patterns have a strong influence on the etch rate in the different regions