Surface pressure distribution potential flow

Actual shapes of fluid particles deviate from the idealized shape which leads to Eqs. (8-15) and (8-16). Surface pressure distributions derived from observed shapes (W2) are shown in Fig. 8.3 for spherical-cap bubbles at high Re. It is seen that the pressure variation is well described by Eq. (8-15) for 0 < 0 < while the potential flow pressure distribution, Eq. (1-32), gives good agreement up to about 30° from the nose. 

Fig. 5.28 Distribution of dimensionless modified pressure at surface of spheres at Re = 100, compared with potential flow distribution. (A) Potential flow (p, — Px)/ipU = 1 — 2.25sin fl (B) Rigid sphere (L5) (C) Water drop in air k = 55, y = 790 (L9) (D) Gas bubble k — y 0 (H6).

The effectiveness of a given plasma-assisted surface treatment depends primarily on the nature of the feed gas, and on a number of externally controllable parameters pressure, power, gas flow rate, frequency of the electrical energy used to excite the discharge, reactor geometry, etc. These "external variables, in turn, affect the "internal" plasma parameters which control the overall processes, namely the electron density ne, the average electron energy , the electron energy distribution function f(E), and the plasma potential... 

These are known as the boundary-layer equations. There is one further simplification that we can always introduce. In particular, if we integrate (10 35), we see that the pressure distribution in the boundary layer is a function of x only. Thus the pressure gradient in the boundary layer (dp/dx) is also independent of Y and must have the same form as the pressure gradient in the outer potential flow, evaluated in the limit as we approach the body surface, namely,... 

To illustrate the idea of potential flow and how to use it to calculate forces, let us calculate the pressure distribution on the surface of a cylinder which is immersed in a flow perpendicular to it. If this is a very long cylinder, then there will be negligible change in the flow in the direction of the cylinder s axis, and so the flow will be practically two-dimensional. To find the flow field, we must make a judicious combination of a steady flow, a source, and a sink. Consider first a source and a sink with equal flow rates located some distance A apart on the X axis See Fig. 10.16. The flow between them is given by... 

The appearance of flow visualization methods [61, 62, 63, 64] has made possible the study of two-phase flows in flow field channels. These methods should be perfected considering the potential measurement artifacts introduced by the transparent element (change in thermal and current distribution, and flow field channel surface properties). Mathematical representations of the pressure drop in presence of two-phase flow will be needed to modify existing stack reactant flow distribution models [65]. 

Factors that could potentially affect microbial retention include filter type, eg, structure, base polymer, surface modification chemistry, pore size distribution, and thickness fluid components, eg, formulation, surfactants, and additives sterilization conditions, eg, temperature, pressure, and time fluid properties, eg, pH, viscosity, osmolarity, and ionic strength and process conditions, eg, temperature, pressure differential, flow rate, and time. 

Fig. 9 Velocity contours for different heterogeneous zeta potential distributions in electro-pressure-driven flows, (a) Symmetrical arrangement of surface potential and (b) interlaced arrangement of surface potential...

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