Sedimentation curve

After point B, the sedimentation curve has a decreasing negative slope, reflecting the increasing concentration of solids at the interface. Line OD represents the locus of points... 

A second PMMA latex was prepared, with 3% acrylic acid (Stage II), in an effort to match the surface acid concentration of the standard acrylic latex. The acid location results in Table II show that the surface acid of this latex was indeed close to that of the standard acrylic. The sedimentation curve for this latex is shown in Figure 6 in which an apparent expansion maximum of about 60 A... 

Figure 2. Sedimentation curves of polystyrene latexes with nominal diameters of 0.45 and 0.765 urn disk centrifuged at 4000 rpm in 20 mL of spin fluid with gradients of (a) 0/4%, (b) 0/3%, (c) 0/2% sucrose. Reproduced with permission from Ref. 3. Copyright 1985, Academic Press.

With practice much may be learned from the shape of the sedimentation curves shown in Figure 17. Thus, a curve with a rapidly changing slope indicates a poly-dispersed sample, while a curve approaching a straight line indicates mono-dispersion. Two samples have approximately the same particle-size distribution when their slopes at corresponding times are the same. The curves are also valuable since they give a graphical comparison of the density. The relative densities of various materials sized in this manner are in accordance with the point of ordinate interception. 

Graphical Determination of Size-Frequency Curves—The usual sedimentation curves may be said to be historical in the sense that they picture the state of the suspension at any time t. However, by graphical means we may obtain the distribution function F(d) which gives the relation between the percentage weights of the suspended material and the corresponding diameters. Let be the particular sedimentation parameter observed. Note that... 

Thus, by taking t and t2 as close together as desired we obtain the shape of the sedimentation curve at any point between t and t2. Since we are interested in the second derivative of this function, let us take dQ/dt, set it equal to and plot values of against /. Then... 

In use the light beam and photoelectric cell may be moved up or down along the axis of the sedimentation tube. Thus, the time required to obtain a sedimentation curve of the suspension may be shortened considerably. By adjustment of the lamp and photoelectric cell to any level it is not necessary to wait for small particles to settle to a given level. If a level has been chosen to which particles less than d units in size have settled at a given time, then... 

FIG. 5 Sedimentation curve recorded for a latex particle (radius a = 1.5 /iin). r represents the particle height in the cell. One can observe the hydrodynamic slowing... 

Brown and Skrebowski [37] first suggested the use of x-rays for particle size analysis and this resulted in the ICl x-ray sedimentometer [38,39]. In this instrument, a system is used in which the difference in intensity of an x-ray beam that has passed through the suspension in one half of a twin sedimentation tank, and the intensity of a reference beam which has passed through an equal thickness of clear liquid in the other half, produces an inbalance in the current produced in a differential ionization chamber. This eliminates errors due to the instability of the total output of the source, but assumes a good stability in the beam direction. Since this is not the case, the instrument suffers from zero drift that affects the results. The 18 keV radiation is produced by a water-cooled x-ray tube and monitored by the ionization chamber. This chamber measures the difference in x-ray intensity in the form of an electric current that is amplified and displayed on a pen recorder. The intensity is taken as directly proportional to the powder concentration in the beam. The sedimentation curve is converted to a cumulative percentage frequency using this proportionality and Stokes equation. 

One problem associated with this technique is that the sediment consists both of oversize (greater than Stokes diameter) and undersize particles so that the sedimentation curve of amount settled P) against time (r) has to be differentiated to yield the weight (W) larger than Stokes diameter. Several balance systems, based on this equation, have been deseribed. 

Floe distributions are calculated from a sedimentation curve. Together with the experimental set-up and procedure, the calculation of the floe diameters and the evaluation of the methodology are given. 

To study the sedimentation behaviour of Fe203, 0,25 % vol. pigment was mixed with 10 ml. of water or aqueous solution of EHEC. Dispersion was predispersed for 15 min using a laboratory stirrer (700 rpm), then ultrasonically treated and placed into glass cylinders with scale divisions, and the movement of the interface between the solid phase and the pure dispersion medium was monitored. Sedimentation curves were constructed as a dependence of sedimentation volume Vsed (ml) on sedimentation time (min, logarithmical coordinates). 

Figure 1. Sedimentation curves for Ti02 pigment in absence and in presence of EHEC.

Figure 6. Sedimentation curves for Fe 203 pigment in 1% wt. aqueous solution of EHEC by different duration of the ultrasonic treatment.

Figures 5 and 6 show sedimentation curves for aqueous dispersions of Ti02 and Fe203, respectively, in the presence of 1 % solution of EHEC at different times of ultrasonic treatment. It is seen from the figures that the optimum time of treatment for obtaining the most stable dispersions is 2 minutes. An increase in the time of ultrasonic treatment leads to a considerable reduction in the system stability. It can be shown that EHEC, being an insufficiently flexible polymer, undergoes mechanodestruction, which weakens its stabilizing effect on the system.

Fig. V-34. The influence of diffusion on the Fig. V-35. The effect of diffusion on boundary position during the centrifugation of the shape of sedimentation curves system containing monodispersed particles plotted in c - AR / At coordinates...

To obtain the q(r) / Pmm curve from sedimentation curve, c (R, A/=const.), one can plot the relative concentration, c/c0, as a function of particle radius obtained from particle displacement, AR, that occurred over the time, At, using eq. (V.53). If the diffusion rate is negligibly small, the c = c (AR / AO curves match each other at all times, At. The latter allows one to separate sedimentation and diffusion in polydisperse systems as well. To... 

Fig. VIII-15. Change in shape of sedimentation curves caused by coagulation...

The two terms in the right side of equation 35 are indicated on a typical sedimentation curve as shown in Figure 32. Both equations 35 and 36 can be used to find M(f). The most obvious method is to tabulate t and P(t) and thereby derive dP(t), dt, and finally M(t) (cumulative oversize percentage) versus Dp(t) (equation 32). Equation 36 is recommended in suspensions of particles having a wide size distribution. 

Homogeneous Suspension Method. Equation 38 still applies however, at time t, all particles of size greater than Dp(t) will have settled out radially to a distance Rr2. Conversion of the sedimentation curve into a cumulative curve is not as simple in this case as for gravitational sedimentation. Difficulties involved in evaluating the sedimentation curve in centrifugal fields may be overcome by assuming a constant... 

Pig. 23. Sedimentation curves of L-myosin and actomyosin. Points O,pure, homogeneous L-myosin V, denatured, homogeneous L-myosin A, components from mixtures of pure and denatured L-myosin 4 homogeneous natural actomyosins -(-, natural actomyosins with two components a, actomyosin from actin and L-myosin. Curve 1 L-myosin curve la, denatured L-myosin of Sjo = 15 curves 2, 3, and 4 actomyosin. The broken curve 2 is extrapolated by means of the... 

Comparison of the sedimentation curves in Figures 8 and 10 showed that the sludge at the 500 1 dilution settled more slowly than all samples except for those taken by Morel et al. (22). The filterable solids concentration at the 500 1 dilution was 50 mg/L. Morel s 10 1 dilution of effluent/NaCl should have had a solids concentration of 25-30 mg/L. 

In particular, coefficients a, b and xo in (2.3) and also error degree under approximation of experimental sedimentation curves under BaS04 suspension synthesis (see 2.2.6) are presented in Table 2.3. 

Microscopic analysis of received suspensions showed that particles of BaS04 posses pronounced anisometry (they represent sticks with length-to-diameter ratio about 4, that explains the sigmoid shape of sedimentation curves with extreme) (Fig. 5.19). At the initial moment of sedimentation the rotation of stick-shaped particles is possible, that determines additional resistance to sedimentation proceeding (analogously to viscosity increase) and slowing down of rate of deposition accumulation. Moreover, at free precipitation particles of spherical form are oriented in movement direction in that way to create maximum resistance to movement. This also reduces the precipitation rate of solid particles in liquid and embarrasses the definition of their actual sizes. In this connection, equivalent radius re (radius of spherical particle precipitating with the same rate) was determined by results of sedimentation analysis. 

It is obvious from the shape of sedimentation curves (Fig. 5.19) that at rise of mixing rate they shift to the region of particles with smaller sizes (higher sedimentation times), i.e. under increase of turbulence level of mixing decrase of average particles radius in reaction zone occurs. 

With the aim of estimation of polydispersity degree of resulted suspensions by sedimentation curve (Fig. 5.19) weight-average and numerical-average rn particles radiuses were calculated ... 

In order to estimate the polydispersity degree of the synthesised suspensions, the average weight and average numeric radii r of particles were calculated along the sedimentation curve ... 

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