Spherical collectors

From the standpoint of collector design and performance, the most important size-related property of a dust particfe is its dynamic behavior. Particles larger than 100 [Lm are readily collectible by simple inertial or gravitational methods. For particles under 100 Im, the range of principal difficulty in dust collection, the resistance to motion in a gas is viscous (see Sec. 6, Thud and Particle Mechanics ), and for such particles, the most useful size specification is commonly the Stokes settling diameter, which is the diameter of the spherical particle of the same density that has the same terminal velocity in viscous flow as the particle in question. It is yet more convenient in many circumstances to use the aerodynamic diameter, which is the diameter of the particle of unit density (1 g/cm ) that has the same terminal settling velocity. Use of the aerodynamic diameter permits direct comparisons of the dynamic behavior of particles that are actually of different sizes, shapes, and densities [Raabe, J. Air Pollut. Control As.soc., 26, 856 (1976)]. 

Also, Schier s experiments revealed the necessity to consider the directional influence of the walls of the filter bed on the bed porosity e. This effect is very important especially for small sized beds that are usually used in laboratories for investigations. For beds made of spherically shaped collectors several correlations exist describing the e(y/dc) function where y denotes the distance from the wall in the radial direction. However, for relative large bed diameters DB/dc ranging from 5 to 25 it proved to be sufficient to use an averaged e in Eq. (3.2.5), as proposed by Jeschar [6],... 

He et al. (2002) used an off-line HPLC/CE method to map cancer cell extracts. Frozen ovarian cancer cells (containing 107 cells) were reconstituted in 300 pL of deionized water and placed in an ultrasonic bath to lyse the cells. Then the suspension was centrifuged and the solubilized proteins were collected for HPLC fractionation. The HPLC separation was carried out on an instrument equipped with a RP C-4 column, 250 mm x 4.6 mm, packed with 5-pm spherical silica particles. Extracted proteins were dissolved in 300 pL of DI water, and lOOpL was injected onto the column at a flow rate of 1 mL/min. Buffer A was 0.1% TEA in water and buffer B was 0.1% TFA in acetonitrile. A two-step gradient, 15-30% B in 15 min followed by 30-70% B in 105 min, was used. The column effluent was sampled every minute into a 96-well microtiter plate with the aid of an automatic fraction collector. After collection, the fractions were dried at room temperature under vacuum. The sample in each well was reconstituted before the CE analysis with 10 pL deionized water. The... 

In the general case, when arbitrary interaction profiles prevail, the particle deposition rate must be obtained by solving the complete transport equations. The first numerical solution of the complete convective diffusional transport equations, including London-van der Waals attraction, gravity, Brownian diffusion and the complete hydrodynamical interactions, was obtained for a spherical collector [89]. Soon after, numerical solutions were obtained for a panoplea of other collector geometries... 

On opproocbing o collecting body (fiber or liquid drop led, 0 porltcle corned along by ihe gos stream tends lo follow the stream but moy strike the obstruction becouse of iis inertia Solid lines represent the fluid streamlines around a body of diometer and the dotted lines represent the paths of particles that initially followed the fluid streamlines. X is the distance between the limiting sireomlines A and B The fraction of particles initially preseni in o volume swepi by the body thoi is removed by inertial interception is represented by the quontity X/Db for o cylindrical collector and (X/Db)2 for a spherical collector... 

Fig. 12. Spherical condenser for measurements of the photoelectron kinetic energy distribution from solids. 1—sample 2—LiF window 3—shutter 4—container of the monochromator exit slit 5—exit slit 6—electron collector 7—fluorescent layer 8—electrostatic screen photomultiplier for intensity measurements of the u.v. light on the left.

When particles experience a mean curvilinear motion and also have Brownian agitation, they are deposited on obstacles by both mechanisms. For very small particles of radii less than 0.1 /xm, Brownian motion dominates particle collection on surfaces. For larger particles, inertial forces dominate. An example of the difference in collection efficiency for spherical collectors of different size is shown in Fig. 3 for different particle diameters and aerosol flow velocity. 

The separator and flusher are steel enameled cylindrical apparatuses with flat lids, spherical bottoms and siphons, through which water is continuously withdrawn into collector 14. Additional flushing of silanol is carried out in apparatuses 10 and 12 by sending water into diffusers mounted... 

The rate of deposition is calculated for a spherical, cylindrical, or rotating disc collector the dimensionless rate of deposition was found to be a function of a single dimensionless group B, involving the rate constant, characteristic velocity, diffusion coefficient, and (except in the case of a disc) the collector size. 

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-... 

The objectives of the present paper are to (1) compute the rate of deposition of particles onto a spherical collector in a creeping flow field for all situations in which London forces and convective-diffusion act as transport mechanisms, (2) identify limiting behaviors according to the relative values of the characteristic parameters for each mechanism, (3) establish the physical conditions in which each of the limiting cases is valid, and (4) test the accuracy of the additivity rule. 

By performing a radial force balance, Spieiman and Fitzpatrick (1973) determined the radial velocity of a particle attracted to a spherical collector by Loudon forces when particle inertia and Brownian motion are... 

Fig. 2. Colloidal particle suspended in a fluid creeping over the surface of a spherical collector.

Fig. 3- Cose 1. Sherwood numbers computed for the convective-diffusion of particles of finite sine to the surface of a spherical collector by neglecting interaction forces. The dashed line is the Levich-LighthilJ equation (19) which is valid when a diffusion boundary-layer exists and the particles are infinitesimal.

Fig. 6. Sherwood numbers computed for the transport of finite particles to a spherical collector under the combined action of convective-diffusion and London forces. Values of the aspect ratio are (a) ft - 104, (b) ft — 105, (c) ft =- 10s, and (d) ft = 10. For each aspect ratio, the value of A/kT was taken (upper curves to lower curves) as ID2, 1, 10 2 and 10 4. Dashed lines represent the Levich-Lighthill equation (19), while the dotted curves represent Sherwood numbers deduced from Figure 4 which ignores the transport from diffusion.

A true test of the significance of different forces computed between similar pairs of surfaces (e.g., those pairs in Fig. 1) is whether these different forces lead to different rates of deposition. Toward this end, the rate of deposition of spherical hydrosol particles onto a rotating disk collector... 

A spherical vacuum chamber several hundred meters in radius, capable of achieving a vacuum less than 10-15 atm and operating at 10 9 atm might be possible, but would be very expensive. Heating the system to more than 2000K only adds spice to the problem. If the system were built and, in the one-meter cube center, SiO molecules were introduced at 104 cm-3, then condensed to make 10 nm grains ( 105 SiO molecules per grain) that are allowed to settle onto a 10 m square collection plate, and if this experiment were repeated 10 times, then the collector would... 

N. Single Spherical Collector Efficiencies. Four collection mechanisms are considered in the present analysis inertial impaction, interception. Brownian movement and Coulombic forces. Although in our previous analysis the electrical forces were considered to be of the induced nature (13), there is evidence that it is the Coulombic forces which dominate the electrical interactions between the particle and collector (, ], 22). Taking the net effect as the simple summation of each collection mechanism results in the single spherical collector efficiency equation. 

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