Centrifugal force driven flow

We have discussed in Section 3.1.2.7 (equation (3.1.51)) that when a solvent/liquid rotates in a centrifugal field with an angular velocity y (radian/s), the hydrostatic pressure P in the liquid increases radially outward  

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At the rotating-disk electrode (RDE Fig. 4.6), it is the solid electrode and not the liqnid that is driven bnt from a hydrodynamic point of view this difference is nnim-portant. Liquid flows, which in the figure are shown by arrows, are generated in the solution when the electrode is rotated around its vertical axis. The liquid flow impinges on the electrode in the center of the rotating disk, then is diverted by centrifugal forces to the periphery. 

Figure 17.4 shows a centrifugal pump, driven by a steam turbine. The correct operating speed for the pump and turbine is that speed that puts the process-control valve in a mostly open, but still controllable, position. As we slow the turbine to force open the process-control valve, the turbine s governor valve will close. Steam flow to the turbine will decline in accordance with fan laws ... 

Often bubbles are generated at the electrode surface (e.g., when the reaction being studied is the hydrogen evolution reaction) or reach it from the bulk of the solution, from the gas used to deaerate it, or from degassing of the solvent. A bubble trapped at the surface of the RDE is driven toward its center by centrifugal force. This phenomenon can cause major errors in measurement because (a) part of the surface of the electrode is blocked and (b) the hydrodynamic flow in the vicinity of the electrode can be greatly distorted. 

The phenomenon of Dean vortices was first observed by Dean in a curved tube. The fluid in the central part is driven toward the external wall by the centrifugal force, which gives rise to a secondary flow. This results in the inward movement of the fluid near the wall and the outward movement of the fluid near the center (Fig. 3A,B). Curved tubes may be classified as torus, bends, helical coils (with a constant curvature), and spirals (with a variable curvature). Fig. 4 shows the helical coiled, spiral, and bend tubes. The hydrodynamics in a coiled tube can be characterized by a dimensionless number named after Dean and is defined as ... 

Thus the presence of a small amount of curvature of the tube axis is seen to produce a significant departure in the nature of the flow even at the leading-order correction, 0(a/R). The motion is no longer simply in the axial direction, but there is also motion in the cross-sectional plane. This motion, superposed upon the primary axial flow, is known as a secondary flow. A sketch of the streamlines for the secondary flow, given by contours of constant f, is shown in Fig. 4-5. The motion at the center of the tube is from the inside to the outside, driven essentially by the centrifugal force exerted on the fluid as it traverses the curved path followed by the tube axis. The return flow nearest the tube walls at the top and bottom is necessary to satisfy continuity. 

The generation of a stable and controllable fluid flow in microfluidic devices is a major issue, and a lot of research work has been put into optimizing the flow driving methods. Not only conventional methods (derived from macroscopic applications) like pressure-driven and electroosmotic flows have been scaled down, but also novel methods like shear-driven flows (SDF) have been introduced. There are several problems associated with the conventional flow driving methods pressure-driven flows suffer from pressure drop limitations, while electroosmotic flows suffer from Joule heating, fluctuations of flow velocity, and double-layer overlap [1]. Therefore, other approaches to evade these problems and limitations have been proposed (centrifugal forces, magnetohydrodynamic forces, etc.). 

At higher Reynolds numbers (>10" ), the impeller causes high flow velocities, which leads to the effect that solid particles with higher densities than the liquid are driven outward due to centrifugal forces. Due to this phenomenon, the flow pattern around the impeller as well as the power number Ne does not differ from one-phase operation, as long as the solids concentration remains smaller than 10 wt%. 

Due to the similarity of the flow profiles, most of these passive, continuous-flow schemes can, in principle, also be adopted for centrifugally driven flows. In addition, the availability of the Coriolis pseudo force/c (4) offers an intrinsic means for the generation transversal flow components, even in straight radial channels exhibiting a constant cross section (Fig. 8). Due to the scaling of forces //c (13), the Coriolis-force induced mixing is... 

The centrifugaUy driven flow rate Q (9) is governed by the mean radial position r [r< - -r>] (5) of the hquid volume and the frequency of rotation co. In typical assay protocols, a metered volume such as a reagent or a wash buffer is driven from an upstream chamber by the centrifugal force through a stationary phase such as a biosensitive layer immobilized on the channel wall, aggregated beads or a membrane. 

The centrifugal force may be imposed by virtue of the flow of the slurry, as in a hydrocyclone, or by means of mechanically driven rotation, as in the sedimenting centrifuge. 

In a rotating flow, the BBOT equations therefore describe a centrifugation movement of a small particle, the characteristics of which ate driven by rather simple mechanisms. The duration of the transient regime before equilibrium between the centrifugal forcing term and the friction is very short. The centrifugation process is described approximately by ... 

The separation takes place in the centrifugal field of soheavy particles are forced to the outer wall (HW cleaners) whereas the fight ones are driven to the center (LW cleaners). The flow streams where the heavy or fight particles are accumulated are separated from the cleaned stock stream. The flow in a hydrocyclone is a three-dimensional two-phase flow. The circumferential component generates the centrifugal force, the axial component moves the solid particles towards the cleaner outlet and the radial component of the suspension flow proceeds from the outside towards the center and vice versa. 

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