Showing papers in "Chemical Engineering in 1956"

On the Viscosity of Suspensions

Abstract: The presence of a set of rigid particles in a Newtonian liquid raises the viscosity of the liquid to a value ηs which is higher than the viscosity η0 of the liquid itself. The nondimensional ratio ηs/η0, which is known as the relative viscosity ηr of the suspension, might be a function of the fraction of the total volume of the suspension φv comprizing the particles.The most widely known expression for ηr, first obtained by Einstein, has the form of the equation 1. But this equation does not agree with the experimental results except for the case in which the concentration is very dilute. So many theoretical relationships, derived by Guth, Simha, Vand, Brinkman and others, for higher concentration, however, do not agree with the observed data in the range higher than 8-10 volume percentage, either. Now, Robinson considered that the specific viscosity in higher concentration was not only proportional to the volume fraction of solid, but to the reciprocal of free liquid volume fraction, and obtained the empirical equation in Table 1.Taking into account this consideration by Robinson and the observation by Bingham that the particles in the same stratum had the same velocity and did not change their mutual distances, the following theoretical relationship for the relative viscosity of general suspension system has been derived by the authors.(16)'where, d is the effective average diameter of particles, Sr is the volume specific surface, φv is the volume concentration and φvc is the limiting concentration at the full-packed state, where steady flow can occur without any deformation, fracture or grinding of particles.From this formula, the physical meanings of the two empirical constants k and S' in Robinson's equation can be explained as follows:in which, k is a function of particle shape, whose value becomes 3 for spherical particles, φvc, the limiting concentration, may be a function of particle shape and its size distribution.In a special case when the suspended particles are spherical and have equal size, the obtained formula becomes as follows, provided the value of φvc is assumed to be equal to 0.52, which is the volume fraction of solid in cubic packing of spheres of equal size.This formula agrees quite well with the observed values given by different writers over a wide range of concentration as shown in Figure 4. Figure 6 indicates the systematic variation of relative viscosity with changes in the relative fraction of large and small spheres in the suspensions. The plotted data are the experimental values by Eveson, Ward and Whitmore for the suspensions consisting of methyl methacrylate polymer spheres in an aqueous lead nitrate-plus-glycerol solution. The real lines are the theoretical results calculated by means of the equation (16)', using Furnas chart, Figure 5, for φvc. According to the equation 16, when 1/ηsp is plotted against 1/φv on condition that and 1/φv are constants, the graphs must be linear, and its intercepts are equal to 2/d·Sr and 1/φvc respectively. All the data reported were examined and they proved to agree approximately with this consideration as shown in Figs. 9-15. It is especially interesting to note that in Figure 14, the value of φvc is approximately equal to the concentration of the cake produced in the centrifuge.

Behaviours of Gairome-Clay Slurries at Constant Pressure Filtration

Abstract: In the papers previously published by several other authors5), 7), the average specific resistance ofcakeatconstant pressure filtration, αf, was represented as a function of a single variable, that is, the filtration pressure p0. According to the results of our constant-pressure-filtration experiments with the so-called ceramic slurries, the ignition-plug slurry was the only case where αf was a function of a single variable p0, and αf of all other slurries was not so simple. In this paper we report the various filtration characteristics of Gairome-Clay slurries.Summaries of the results were as follows:i) e vs. ps data obtained from the compression measurements by using a consolidometer are plott- ed in Fig. 1. (e) was a function of ps only, and was not influenced by the slurry concentrations. (k·S02)vs. e data from permeability measurements are plotted semilogarithmically in Fig. 2, resulting in approximate empirical equations (2). m-values predicted by equation (3) were found to be a function of p0 only, as shown in Fig. 3, and αapp-values predicted by equation (4) to be a function of s as well as of p0.ii) (Δθ/ΔV)vs. V relation at constant-pressure filtration with Gairome-Clay slurry, indicated a curve, which approached asymptotically to a straight line as V increased.iii) The relation of (K·S20)app·s vs. s, of each constant-pressure filtration, showed also a curve.iv) Applying the predicted m-values to the constant-pressure filtration results, the following empirical equations of αf were obtained.whereaad (dimensionless)Therefore, the average specific resistance, αf, of the Gairome-Clay cake at constant pressure filt- ration could be represented as the sum of the term (αapp) -including variables p0 and s only-, and the correction term (αcorr) -including variables p0, s and V.The term (αcorr) in the empirical equation of αf indicates the influence of degree of particle flocculation, depending on the slurry concentrations; while the term (αapp) in the expression of αf shows the occurrence of cake disflocculation due to the filtrate flow, in other words, the existence of a kind of scouring effect.

On the Measurement of Flow Patterns of Liquid in a Mixing Tank, Applying Radio Isotope

Abstract: Using Radio Isotope as a means of measuring liquid velocity, flow patterns of liquid in a mixing tank were studied.The gist of this method was as follows: A set of device, consisting of a miniature GM counter shielded in an aluminium tube and a steel ball (dia. 5-7mm), containing an appropriate amount of 60Co, and hung with platinum wire (dia. 30 micron), was immersed in a mixing tank. In order to compute the liquid velocity by using Eq. (1), the transposition of the ball from P to P', expected from the balance of moments around A, presented in Fig. 3, was determined with fairly good accuracy, by measuring the intensity of gamma radiation. Paying no less attentions to the stability of GM counter and the preparation of a calibrated curve as shown in Fig. 2, the measurement of liquid velocity in each of the experiments was made.Experimental conditions were as follows:Tank diameter: 28cmLiquid used: waterLiquid depth: 26cmImpeller used: paddle type: length 12cmwidth 1.6cmDimensions of baffle plates employed to study the flow pattern under fully baffled condition were:width 3cmlength 30cm; number of plates 4Since the liquid used was water, the flow patterns thus studied pertain to those of so-called turbulent flow region.Experimental results are shown in Figs. 4, 5, 6 and 7. In these Figures, marked differences between flow patterns when baffled and those when unbaffled are revealed: decrease of tangential velocity and marked appearance of vertical velocity was noted in fully baffled agitation.Further, the turbulent state which has been defined by the interrelation between the Power number and the Reynolds number in agitation was experimentally described as the following: Flow patterns are independent of rotational speed of impeller (See Figs. 6 and 7).In the last section, some considerations on the relationship between flow pattern and power consumption in agitation are given.

Effects of Liquid Viscosity and other Factors on Flow Patterns of Paddle Type Impeller

Abstract: Effects of liquid viscosity on flow patterns were experimentally studied and so far as flow patterns of paddle type impeller were concerned, more concrete explanations were given on the correlation between NP and Re, which is considered to be an over-all reflection of flow pattern. In the second place, the relation between flow patterns and scale-up was studicd, followed by the study concerning those of geometrically dissimilar impellers.Experimental conditions were as follows:Experiment 1: (effect of liquid viscosity)Tank diameter: 28cmLiquid (water and glycerine solution) viscosity: 1-108c.p.Liquid depth: 13cm; Paddle (L=12cm, W=1.6cm)Experiment 2: (scale-up)Tank diameter: 15.5-50.0cmLiquid (water) depth: approximately equal to tank dia. Geometrical ratios relating to paddles, tanks (including baffle plates) and so on were the same as those in Ex. 1.Experiment 3: (geometrical dissimilarity)Tank diameter: 28cmLiquid (water) depth: 26cmPaddles: dimensions employed are shown in Table 1.The procedure of measuring liquid velocity reported here is the same as that which was reported in the previous paper.1)The effect of liquid viscosity on flow patterns is apparent as shown in Fig. 6 (c), in which the pattern is no longer independent of rotational speed of the impeller. This figure corresponds to that of the experimental region (c) described in Fig. 5. Flow patterns expected from the curves in Fig. 5 are checked in Figs. 6 and 7.Figs. 8 and 9 show flow patterns in geometrically similar mixing systems. Each figure indicates that the pattern remains unchanged, irrespective of dimensions of apparatuses and rotational speed of impellers, so far as the turbulent state is concerned, provided the depression of liquid surface when unbaffled is not taken into consideration.Flow patterns, particularly tangential velocity distributions in Fig. 4, indicate marked differences among geometrically dissimilar impellers, but a rather simple correlation between C* and Re* was observed as presented in Fig. 10, covering a considerably wide range of experimental conditions.The procedure through which the correlation was made is also described in the previous paper1).

On the Method of Calculating Effectiveness Factor of the Porous Catalyst in Any Reaction

Abstract: The method of Calculating effectiveness factor of the porous catalyst, which factor depends upon the diffusibility of reactants or products insid catalyst as well as on the pure chemical reaction, had formerly been developed to the first order reaction or to a few other cases. Whereupon the authors have tried and succeeded in extending its application to the cases in general in which chemical reaction rates are given and equations are presented as a function of constitution. As an example, the calculation method for ammonia synthesis is illustrated.

Pumping action of the impeller in a mixing tank

Abstract: Flow Patterns of the paddle, the turbine and the propeller are intuitively said to be peripheral, radial and axial, respectively. Among them, the flow patters of a paddle type impeller were reported previously.1), 2) The introduction of the concept, "discharge rate of liquid from the turbine and the propeller", into the field of agitation, assimilating these impellers with those of turbine and propeller pumps, is considered to be helpful to the better understanding and simplification of the complicated phenomena, even apart, for the time being, from the concrete determination of interrelation between the "discharge rate" and the effect of mixing.Since the direct application of many theoretical and practical analyses of pumps is apparently difficult in general, flow patterns of the turbine and the propeller impellers, together with the determination of power consumption, were studied, in this paper, following the same procedure as was described before1).Prior to the experiment, theoretical considerations were given to the relationship between the power consumed and its flow pattern concerning the pitched paddle, for convenience sake. (See. Eqs. 1-10) Except for the introduction of lift, the way of reasoning is the same as was reported in the paper referred above.ExperimentFlat blade turbines and a marine propeller together with its "modification" which were used in this series of experiments are described in Fig. 2, their specifications being tabulated in Table 1. Tank dimension and other experimental conditions (liquid: water) were the same as were described in the previous paper1).Experimental Result and DiscussionExemplifications of experimental results are shown in Figs. 3-5, concerning the turbine, the marine propeller and the "pitched paddle, " respectively. It is apparent from these figures that flow patterns of the turbine and the propeller are characterized as radial and axial, respectively, in the region adjacent to the impellers.Analyses of these experimental results, whose procedures are exemplified in Tables 2 and 3 are plotted in Fig. 6. It is seen, in this figure, that the lift seems most powerful in the case of the marine propeller, with the tendency to decrease as the pitched angle θ0 approaches π/2.Last of all, the estimation of discharge rate from the turbine was discussed. The discharge rate Q' as quoted in Fig. 7, relating to the flat blade turbine (nB=4) is the only data5) ever published. However, the discharge rate Q which is defined in Eq. (11) may be different, in general, from Q' defined by Rushton et al. Therefore, by securing the data of power consumption of this flat blade turbine, (See Fig. 8), ω' was estimated by the trial and error method, using Fig. 6. And then, Q was calculated, using Eq. (12). Power was experimentally determined under the same experimental condition as was precisely described in the original paper5).On the other hand, using the vector angle at the blade periphery which is recorded in the paper5), ω' was estimated and then, Q was computed, following the same procedure just mentioned above.Comparison of Q, or ω' calculated through different procedures, …in short, ω' in the latter case…estimated by using the flow pattern data determined by optical observation, and that in the former case…estimated through the power determination and the use of Fig. 6 shows a good agreement in the range of the experimental condition.