# (262d) Evaltuation of Particle Interaction for a Gas-Solid Suspending System

#### AIChE Spring Meeting and Global Congress on Process Safety

#### 2006

#### 2006 Spring Meeting & 2nd Global Congress on Process Safety

#### Fifth World Congress on Particle Technology

#### Measurements and Analysis of Slightly Consolidated and Fluidized Powders

#### Thursday, April 27, 2006 - 2:00pm to 2:20pm

In some particle handling processes, particles move as assemblage and sometimes can be treated as continuum. And at such a situation, the rheological characteristics of particles or powder are important to clarify its fluidity. In a liquid-solid suspending system, the rheological properties are well researched by many scientists and engineers, and one of the key topics to understand the property is ?Particle interaction?. Particle interaction causes the particle agglomeration or dispersion, and then the viscosity of suspension increase compared to that at the complete dispersion condition. However, in a gas-solid suspending system, that is for example ordinary particle transport system with airflow or particle mixing equipment, the particle interaction have not been clarified well. And the fluidity of powder is evaluated by traditional parameter, such as the angle of repose, measured under a stationary state. We have proposed the model to predict the inter-particle bonding energy as a parameter of particle interaction and number of particles included in a cluster, which is agglomerated particle assemblage, for a liquid-solid suspending system. In this model, we took notice of the number of particles in a cluster to evaluate particle agglomeration under shear flow. And then we assumed that it increased by Brownian or shear coagulations and reduced by shear break up, and these effects on number of particle in a cluster were balanced under a steady state. If the particles formed cluster, the liquid contained in void of cluster could not flow freely and then apparent liquid volume fraction reduced. Thus, particle agglomeration will cause the increase of apparent suspension viscosity due to the increase of solid volume fraction. Conversely, some rheological data will provide us the information of particle interaction and agglomeration. Thus, we attempted to apply the concept of this prediction model to a gas-solid suspending system and clarify the difference of particle interaction among three kinds of particle. First, in the process to apply this model to a gas-solid suspending system, we have to establish the method to measure the viscosity of a gas-solid suspension. We used FT-4 powder rheometer, in which a twisted blade and motor with torque meter were installed, and could measure the torque exerted on the blade, which rotated and descended in a powder layer with aeration. Under the assumption of laminar powder flow, the viscosity of powder layer shows proportional to the torque and inversely proportional to the blade tip velocity. And by using the result of viscosity known Newtonian fluid, the variation of viscosity could be calculated from the torque and rotating speed of the blade with some different solid volume fraction controlled by airflow rate. The volume of powder layer was 25ml and 160ml, and the rotating speed of blade was adjusted from 5 to 100mm/s as blade tip velocity. As a test particle, we used silica, talc, CaCO3 and crystal cellulose powder. Silica particle is spherical and mono dispersed, and Talc, CaCO3 and crystal cellulose are non-spherical and have multi modal particle size distribution. Each particle has the mean diameter of about 2 micrometers and the specific gravity of around 2. At the same airflow rate, silica and CaCO3 show almost the same solid volume fraction, but Talc and crystal cellulose show a comparable small value. For each test particle, the viscosity of powder layer indicated that the apparent viscosity reduced as the shear rate increased, which is a shear thinning phenomena. This infers that at a low shear rate region particles are agglomerated and large cluster causes a large apparent viscosity, but at a high shear rate region particle agglomerations are broken up and powder layer becomes easy to flow. Next, we applied our proposed prediction model to a gas-solid suspending system by using the rheological data of these test particles shown above. In the process to predict the number of particle included in a cluster, we repeated the assumption of number of particles in a cluster and calculation of the corresponding apparent viscosity until the viscosity difference between calculation and experiment. Then, we need some viscosity estimation model, which is the relationship between number of particle in a cluster, solid volume fraction and suspension viscosity, and we applied Simha's cell model with some modifications. Simha's cell model was based on the Einstein's equation and the relative viscosity, that is the ration of suspension viscosity to dispersant viscosity, was defined as a function of apparent solid volume fraction and maximum packing fraction. Though dispersant is liquid for a liquid-solid suspension, it should not be adequate to treat dispersant as gas for a gas-solid suspension because the viscosity of suspension is mainly affected by the particle interaction and the effect of gas viscosity is small. And more the effect of gravity on the particle interaction cannot be neglected. Therefore we introduced a hypothetical dispersant viscosity, which can be calculated from the extrapolation of viscosity data. In our proposed model, once the number of particles in cluster can be decided with the corresponding rheological data, that is shear rate and apparent viscosity, the inter-particle bonding energy can be estimated. By the use of this inter-particle bonding energy, we can estimate the apparent viscosity corresponding to any shear rate and any solid volume fraction. And the apparent viscosity at the same condition will be one of the parameters to evaluate the fluidity. Comparing these four test particles, Talc indicated the worst and crystal cellulose do the best. From the angle of repose, however, these two particles show almost the same value. On the other hand, the silica particle shows the largest angle of repose, however, comparable good fluidity by this analysis. Because silica particle have a spherical shape and mono-dispersed size distribution, the particle will be easy to pile as a high corn and show a large angle of repose. These results infer that this simple evaluation under powder-fluidized region will give us a new insight of powder fluidity.

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