Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem （BVP） of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition （or w ---- 0） along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the partic- ular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.

Experimental investigations of granular shape effects on the generation of electrostatic charge

In solid processing systems, electrostatic problems are commonly observed for granules of various shapes. However, a complete understanding of the basic dependence of electrostatic charge generation on particle shape has yet to be established. This observation motivated the present study on examining the effect of granular shape on electrostatics. In this study, polyvinyl chloride （PVC） granules （diameter 1.1-4.1 ram, in the shape of a triangle or trapezium） were first discharged to remove any residual charges and sub- sequently their electrostatic charging characteristics were studied by allowing a granule to slide along a pipe wall. Several factors such as granular front-facing angle, length-ratio, sliding area, sliding orienta- tion, sliding times, and relative humidity were considered when studying their effects on the electrostatic charging of granules. It was found that triangular granules with smaller front-facing angles tended to generate more electrostatic charge. The amount of electrostatic charge increased with granular length- ratio and sliding area but decreased with humidity. In addition, granular sliding in the orientation of the front-facing angle （for triangular granules） or the short side （for trapezoidal granules） generated more electrostatic charge than that in the orientation of the long side. For both granule shapes, the elec- trostatic charge increased with granular sliding times and reached a saturated state after around 8-9 sliding movements. The saturated electrostatic charge increased with either granular length ratio or sliding area.