Particle neutrally buoyant

The flow patterns for single phase, Newtonian and non-Newtonian liquids in tanks agitated by various types of impeller have been repotted in the literature.1 3 27 38 39) The experimental techniques which have been employed include the introduction of tracer liquids, neutrally buoyant particles or hydrogen bubbles, and measurement of local velocities by means of Pitot tubes, laser-doppler anemometers, and so on. The salient features of the flow patterns encountered with propellers and disc turbines are shown in Figures 7.9 and 7.10. 

This technique is invasive however, the particle can be designed to be neutrally buoyant so that it well represents the flow of the phase of interest. An array of detectors is positioned around the reactor vessel. Calibration must be performed by positioning the particle in the vessel at a number of known locations and recording each of the detector counts. During actual measurements, the y-ray emissions from the particle are monitored over many hours as it moves freely in the system maintained at steady state. Least-squares regression methods can be applied to evaluate the temporal position of the particle and thus velocity field [13, 14]. This technique offers modest spatial resolutions of 2-5 mm and sampling frequencies up to 25 Hz. 

Neutrally buoyant particle with/8 = 0.16 Hz. (b) Neutrally buoyant particle with/8 = 0.80 Hz. (c) Heavy particle with/g =... 

Electrolyte mixing is necessary to maintain the particles in suspension, unless the particles are neutrally buoyant, and to transport the particles to the surface of the electrode. The hydrodynamics of the electrodeposition system control the rate, direction, and force with which the suspended particles contact the electrode surface. Bringing the particles in contact with the electrode is a necessary step for the incorporation of particles into the metal matrix, although particle-electrode contact does not guarantee incorporation of the particle. Of course, an increase in flow can increase the plating rate as the thickness of the diffusion layer at the electrode surface decreases. 

The fate of dissolved Fe from MOR vents has been investigated at the Rainbow plume from the mid-Atlantic Ridge. Plume particles were sampled from the buoyant part of the Rainbow plume, proximal to the vent, as well as particles from neutrally buoyant portions of the plume that were more distal from the vent (Severmann et al. 2003). Particles from the buoyant part of the plume have positive 5 Fe values (up to +1.2%o), whereas in the neutrally buoyant sections of the plume, the particles have a near-constant 8 Fe value of -0.2%o that matches the Fe isotope composition of the vent fluid. The high 5 Fe values of plume particles that were proximal to the vent probably reflect oxidation processes. In the neutrally-buoyant plume, all aqueous Fe(ll) had been oxidized and it appears that there was no net loss in Fe because the neutrally buoyant plume particles have the same isotopic composition as the vent fluid. Moreover, metalliferous sediments sampled below the plume match the isotopic composition of the plume particles. The implication of these data is that for at least one plume, the Fe isotope composition of the vent fluid matches that of the plume particles. The Rainbow vent fluid, however, has an unusually high Fe to S ratio and hence it is uncertain if these results can be extrapolated to other plumes that originated fi om vent fluids that had lower Fe to S ratios. 

Much of the work on particle rotation at low Rqq follows from the early work of Jeffery (J2) who considered a rigid, neutrally buoyant spheroid subject to the uniform shear field defined by Eq. (10-30). Jeffery showed that the particle center moves with the velocity which the continuous fluid would have at that point in the absence of the particle, while the axis of the spheroid undergoes rotation in one of a family of periodic orbits with angular velocities... 

To visualize the flow for PIV purposes, the measured fluid flow has to be seeded with particles, which need to be neutrally buoyant and small with respect to the flow phenomena studied (e.g., Raffel et al., 2007). For different sorts of visualized flow, seeding particles could be quite different. 

The effectiveness of deep-bed filters in removing suspended particles is measured by die value of die filter coefficient which in turn is related to the capture efficiency of a single characteristic grain of the bed. Capture efficiencies are evaluated in the present paper for nil cases of practical importance in which London forces and convective-diffusion serve to transport particles to the surface of a spherical collector immersed in a creeping How field. Gravitational forces are considered in some cases, but the general results apply mainly to submicron or neutrally buoyant particles suspended in a viscous fluid such as water. Results obtained by linearly superimposing the in-... 

This brief section provides a historical and practical overview of useful empiricisms employed in suspension theories, including a few useful formulas. Early investigators were mainly concerned with the measurement and correlation of two fundamentally important, but apparently unrelated, quantities (i) The effective viscosity fi of sheared suspensions of neutrally buoyant particles and (ii) the sedimentation speed us of suspensions of non-neutrally buoyant particles. Upon appropriate normalization, both were regarded as being functions only of the volumetric solids concentration ... 

In the present rheological context, lattice deformation may be regarded as arising from the transport of neutrally buoyant lattice points suspended within a macroscopically homogeneous linear shear flow. The local vector velocity field v at a general (interstitial or particle interior) point R of such a spatially periodic suspension can be shown to be of the form... 

This generic formula permits averages to be calculated for any pertinent suspension property /. When time-independent external forces F(e) and torques N(e) act on each of the suspended particles, Eq. (7.14), together with the net force- and torque-free conditions characterizing the neutrally buoyant... 

B. Solid, neutrally buoyant particles, continuous phase coefficient JVS = AA = 2 + 0.471V04 E> d tank/ Graphical comparisons are in Ref. 88, p. 116. [E] Use log mean concentration difference. Density unimportant if particles are close to neutrally buoyant. Also used for drops. Geometric effect (tiimp/titank) is usually unimportant. Ref. 102 gives a variety of references on correlations. [E] E = energy dissipation rate per unit mass fluid PgC AT = TT, P = power, F c V [88] p. 115 [102] p. 132 [152] p. 523... 

C. Solid, neutrally buoyant particles, continuous phase coefficient... 

E] Use log mean concentration difference. Density unimportant if particles are close to neutrally buoyant. 

Segre and Silberberg [131, 132] showed experimentally that neutrally buoyant particles would migrate to, and concentrate at approximately 60% of the pipe radius in laminar flow. They used small tubes and relatively large particles. 

In order to determine the mean turbulent approach velocity of bubbles causing bubble-bubble collisions, a series of questionable assumptions were made by Luo and Svendsen [74]. First, in accordance with earlier work on fluid particle coalescence the colliding bubbles were assumed to take the velocity of the turbulent fluid eddies having the same size as the bubbles [16, 92]. Luo and Svendsen [74] further assumed that the turbulent eddies in liquid flows may have approximately the same velocity as neutrally buoyant droplets in the same flow. Utilizing the experimental results obtained in an investigation on turbulent motion of neutrally buoyant droplets in stirred tanks reported by Kuboi et al [53, 54], the mean square droplet velocity was expressed by ... 

The / coefficient vaiue in the dropiet rms veiocity reiation (9.31) obtained by Kuboi et al [53, 54] is accidentally about the same as the C r ( )C fc value in the Kolmogorov structure function relation (9.14), that is / C 2.0. However, it was commented by Kuboi et al [53, 54] that the comparison of these relations cannot be very decisive, in view of the fact that there is a large difference between the processes and kind of fluid used to obtain these relations. Kuboi et al [53, 54] also investigated the particle-fluid density difference effect producing non-neutrally buoyant particle flows and concluded that the parameter value discussed above is very sensitive to the density ratio. Therefore, the application of the above relation as an approximation for the bubble velocity is highly questionable. 

Problem 3-14. Design of a Cross-Flow Filter. In cross-flow filtration, a pressure drop G forces fluid containing neutrally buoyant particles to flow between two porous plates. There is also a transverse flow that forces the particles to collect on one of the plates. A key design question is how one determines the length of the filter. 

Let us then consider a suspension of identical, neutrally buoyant solid spheres of radius a. We are interested in circumstances in which the length scale of the suspension at the particle scale (that is, the particle radius) is very small compared with the characteristic dimension L of the flow domain so that the suspension can be modeled as a continuum with properties that differ from the suspending fluid because of the presence of the particles. Our goal is to obtain an a priori prediction of the macroscopic rheological properties when the suspension is extremely dilute, a problem first considered by Einstein (1905) as part of... 

H. Brenner, Dynamics of neutrally buoyant particles in low Reynolds number flows, Prog. Pleat Mass Transfer 6,509-74 (1972) J. HappelandH. Brenner, Low Reynolds Number Hydrodynamics (Noordhoff, Leyden, The Netherlands, 1973). 

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