Viscosity critical particle diameter

Example Determine the dimensions of a simple settling chamber required to remove 50 ft size particles under the following conditions Gas capacity, q = 2400 mVhr Particle density, Pp = 2400 kg/m Gas temperature, t = 20 °C Gas density, p = 1.2 kg/m Gas viscosity, ft = 1.8x 10 N-s/m. The solution is as follows. The settling regime for the particles must be determined first. Hence, the critical particle diameter is computed first ... 

Dpmin = critical particle diameter p = gas viscosity B, = inlet duct width... 

Fig. 7. Effect of liquid viscosity on lower critical particle diameter solid-liquid fluidized beds [a = 3.0, Cy = /(e), pl = 1000 kg/m ].

Fig. 11. Effect of density difference at various liquid viscosities on particle Reynolds number evaluation at lower critical particle diameter, (a) Solid-liquid fluidized beds [a = 3.0, Cv = f(s), pi = 1000 kg/m ]. (b) Gas-solid fluidized beds [a = 3.0, Cy = /(e), po = 1 kg/m ]. (c) Unified stability map of particle Reynolds number vs density difference for different values of transition hold-up solid-liquid fluidized beds [a = 3.0, Cy = f(s), p-l = 1 mPas, pi = 1000 kg/m ].

Eq. (8) shows the dependency of the critical thickness with mass m, radius rp, and velocity v0 of the inert particles coated with plastic and with the viscosity of the material that coats the sand fi. For the experimental conditions (total mass of sand, 30 g mass of plastic in the feed, 1 g sand particle diameter, between 0.6 and 1.2 mm sand density 2600 kg m-3, average velocity of the particles in the annular zones, 0.25ms-1 [7], the critical thickness predicted by Eq. (8) is 250 p,m. In this calculation, the viscosity of the plastic has been taken at its fusion temperature, 16 poises, because it is in the initial step of fusion when the stickiness of the plastic is maximum point. 

From the above correlation, it is clear that the critical stirrer speed Nc mainly depends on the geometry of the stirrer d, and the vessel (H/dx), the type of stirrer, the density (pL) and viscosity (vL) of the liquid, the solids mass ratio ps = mj(ms + mL), and the particle diameter (dp) and density (pp). On the basis of a dimensional analysis, one gets the dimensionless relation... 

Physical properties of the fluid such as density, viscosity, and particle density and the model parameters such as dispersion coefficient and virtual mass coefficient have a substantial effect on the critical diameter. These effects are discussed systematically in the following paragraphs. 

To keep the particles in suspension, the flow should be at least 0.15m/sec faster than either 1) the critical deposition velocity of the coarsest particles, or 2) the laminar/turbulent flow transition velocity. The flow rate should also be kept below approximately 3 m/sec to minimize pipe wear. The critical deposition velocity is the fluid flow rate that will just keep the coarsest particles suspended, and is dependent on the particle diameter, the effective slurry density, and the slurry viscosity. It is best determined experimentally by slurry loop testing, and for typical slurries it will lie in the range from 1 m/s to 4.5 m/sec. Many empirical models exist for estimating the value of the deposition velocity, such as the following relations, which are valid over the ranges of slurry characteristics typical for coal slurries ... 

The critical stirrer speed n mainly depends on geometry of stirrer (d) and vessel (H/D), type of stirrer, density ( l) and viscosity (Vl) of the liquid, solids mass ratio vPg=ms/(mg+mL)> particle diameter (dp) and other properties of the system. 

Solid Suspension. Characteristic dissolution times increase by an order of magnitude if suspension does not occur. There exists a critical agitation speed for suspension, Nm- This critical suspension speed depends on the densities of the solid and liquid. A well-known correlation for suspension appears in equation (16), where is the solution viscosity, ps is the density of solid, pi, is the density of liquid, g is gravity, dp is the particle diameter, w is the weight percent solids and di is the impeller diameter (67). The critical agitation speed for high density... 

Taylor s work with Newtonian liquids showed that elongation of a droplet is favoured by low interfacial tension, larger particle diameter, matrix viscosity and high shear rates. Flumerfelt [17], using non-Newtonian fluids, showed that in a simple shear field, a spherical drop becomes ellipsoidal with the major axis and inclined at about 45° from perpendicular to the shear field. Depending on relative viscosities, a critical shear rate was reached in which the droplet broke up into smaller droplets. A minimum size was eventually reached below which break-up could not be achieved regardless of shear rate. 

Roll-mill for Dispersive Mixing A laboratory roll-mill with 5-in diameter rolls and 0.05 in minimum clearance between the rolls is used for dispersive mixing of carbon black agglomerates in LDPE. Calculate the roll speed needed to break up 5 of the particles per pass, assuming that the critical shear stress needed for breakup is that obtained in Problem 7.12 in the narrow clearance, and that the amount of polymer on the rolls is 50% above the minimum. Assume the same constant viscosity as in Problem 7.7. 

The speed of a chromatographic separation is fixed by the particle size, the stationary phase characteristics, the available pressure, the solvent viscosity, the solute diffusivity, the a values of the critical pair, and extracolumn dispersion. One way to achieve faster separations is to reduce the particle size of the stationary phase. However, if material of smaller diameter is packed into a conventional size column, the backpressure will become prohibitively high. Thus, in a compromise between speed and optimum performance, narrow (<2 mm) columns packed with small 3-5 ju.m diameter particles have been developed. 

To avoid major fouling and clogging problems, the nature of the feed to be treated has to be considered when hollow fiber modules are used. In the case of lumen to shell filtration, the inside diameter of the fiber is supposed to be at least 10 times the diameter of the largest species present in the feed. However, when the permeate flows from shell fo lumen, concentration and viscosity of the feed and the density of hollow fiber membrane per module may be critical parameters in the design process. Specific aeration or mixing requirements are necessary to keep the feed particles in suspension, and to avoid the clogging of the membrane module. 

Critical parameters Viscosity Solid content Droplet diameter Diffusion rate of particles, tp Vapour pressure Temperature Evaporation rate, tE... 

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