Stokes settling

At finite concentration, tire settling rate is influenced by hydrodynamic interactions between tire particles. For purely repulsive particle interactions, settling is hindered. Attractive interactions encourage particles to settle as a group, which increases tire settling rate. For hard spheres, tire first-order correction to tire Stokes settling rate is given by [33]... 

The feed rate corresponding to this condition is related to the bowl geometry r, and /, the bowl angular speed, CO and the Stokes settling velocity. 

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)]. 

Continuou.s Centrifugal Sedimentation Theory The Stokes settling velocity of a spherical particle under centrifugal field is given... 

Dpo Initial diameter of drop, meter DpS/a Apparent Stokes settling diameter of floe, meters (18 ft u,J[kc g (pP - p)] 1/2 B Diffusion coefficient, meters2/sec Bp Diffusion coefficient for particles, of diameter Dp, meters2/sec Dpi Diffusion coefficient for particles of diameter >pl, meters2/sec Bp2 Diffusion coefficient for particles of diameter Dp2, meters2/sec e Natural logarithmic base, 2.718 E Potential or potential difference, V Ex Ionization potential, V... 

Equation (17.60) combines the formula for Stokes settling velocity, Vg, and that for the equivalent clarification area, r, also known as the comparison coefficient Q = (vs)CET). The vs term is... 

This is given by the Stokes number, St = [g(Pp — p)d2]/(18TiWf), which is a ratio between the Stokes settling velocity and the local velocity for the flowing suspension. 

The case of Stokes settling velocity is considered as an illustrative example. If we assume that the stationary settling velocity, Wg, of a small particle flowing into a liquid or gaseous medium is a function of its diameter, d, specific weight, gAp, and the viscosity of the gaseous or liquid medium, it follows that ... 

This relationship is commonly called the Stokes settling velocity and is applicable for Re = wodp/ri <1 and when particle interactions are not present during the settling process. 

Lerman A. L. and Dacey M. F. (1974) Stokes settling and chemical reactivity of suspended particles in natural waters. 

The Stokes settling radius of colloidal particles can be obtained from their sedimentation rate. An ultracentrifuge is used to increase the sedimentation rate, since colloidal particles settle very slowly under the influence of gravity alone. 

For particles having densities of approximately 1 g/cm3 and radii less than 1 /rm, gravitational settling often may be neglected, because it is usually slower than other removal processes the Stokes settling velocity for such particles is on the order of 10 m/day or less. Although such small particles... 

For the case of free sedimentation, a sphere with diameter cf, and density differing from that of the medium by A p moves at the Stokes settling velocity. 

The third group of terms on the right-hand side describes particle transport to the collector by gravity forces acting on the suspended particle. Hydrodynamic retardation is included. Here, Nc is a gravity number, that is, the ratio of the Stokes settling velocity of a suspended particle to the superficial or approach velocity of flow. 

Here nh np and nk are the number concentrations of particles of sizes i, j, and k in the epilimnion and nfc in is the number concentration of fc-size particles in river inflows. The term X(i,j)s incorporates most of the effects of physical processes on the rate at which particles of size i and j come into close proximity. The subscript S is used to indicate that Smoluchowski s approach (1917) to the kinetics of particle transport has been adopted. Smoluchowski did not consider hydro-dynamic retardation in his early analysis, and it has not been included here in Mi,j)s. A more rigorous approach is possible (Valiolis and List, 1984a, b). The term a(i J)s incorporates chemical factors that retard the kinetics of aggregation between particles of size i and j and also those aspects of the kinetics of particle transport that are not included in Smoluchowski s analysis. The Stokes settling velocity of a particle of size k is denoted as vk the mean depth of the epilimnion is zc qin and qoul refer to river flows into and out of the lake expressed as volume of water per unit of lake surface area and time (the sum of such inflows or outflows is also termed the areal hydraulic loading of the lake). The symbol W refers to all processes of production or destruction of particles in the epilimnion it can include a variety of chemical and biological processes. 

Problem 9-21. Nonlinear Microrheology. A common way to measure the viscosity of a liquid is to drop a heavy spherical ball into a large tank of the fluid and measure the steady speed with which the ball descends. When the ball is only slightly more dense than the liquid, the Reynolds number based on the ball s fall speed will be small, and the viscosity can be determined from the Stokes settling velocity Ustokes = [(2/9)Apa2g//r], where Ap is the density difference between the ball and the fluid, a is the ball radius, g is the acceleration of gravity, and /i is the fluid viscosity. 

Question Determine the effective viscosity jieff from the force balance (3) by relating U to the external force of gravity from the Stokes settling velocity... 

If the velocity of a spherical particle in Stokes settling is always codirected with the gravity force, even for homogeneous axisymmetric particles the velocity is directed vertically if and only if the vertical coincides with one of the principal axes of the translational tensor K. If the angle between the symmetry axis and the vertical is [Pg.85]

Sonshine, R. M., and Brenner, H., The Stokes translation of two or more particles along the axis of an infinitely long circular cylinderi Appl. Sci. Res., Ser. A (in press) see also Sonshine, R. M., The Stokes settling of one or more particles along the axis of finite and infinitely long circular cylinders. Ph.D. Dissertation, New York University, New York, 1966. 

The flux is the Stokes settling velocity of a spherical particle times the number of particles in that size interval. In the expression, g is the gravitational acceleration, v the kinetic viscosity, and pp and pt the particle and fluid densities. The time unit is indicated by [t]. 

The third coagulation mechanism, differential sedimentation, occurs when a particle falling at its terminal settling velocity collides with a slower settling particle. This is represented as a cross-sectional area of collision multiplied by the difference in Stokes settling velocities of the colliding particles... 

Brun-Cottan, J. C. Stokes Settling and Dissolution Rate Model for Marine... 

Here, the subscript k denotes particles with a particular volume and within a particular box, w is the Stokes settling velocity of the particle, z is the depth of each box, and m is the number of the box (Figure 7). The first two terms on the right-hand side of Equation 16, similar to those in Equation 13, describe the flocculation process within each box. The... 

Table 9.3 Some terminal (stokes) settling velocities atmospheric aerosols of liquid droplets.

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