Venkataramana Runkana

Modeling flocculation of colloidal mineral suspensions using population balances

Abstract Flocculation as well as dispersion of mineral suspensions has become increasingly important in mineral processing as we have to deal with fine and ultrafine particles. Population balance models for flocculation of such suspensions are discussed in this paper. Models ranging from those based on pure aggregation and fragmentation to those based on simultaneous aggregation–fragmentation are presented in detail. The two important parameters in the population balance model are the collision frequency factor and the collision efficiency factor. Differences among collision frequency models for impermeable and permeable aggregates are described. The main drawback of existing flocculation models is the disregard of forces between mineral particle surfaces. The collision efficiency is usually assumed to be unity or employed as a fitting parameter in a majority of the models. An approach for incorporating the influence of surface forces in the presence of salts and polymers is outlined. Another important lacuna of flocculation models is the assumption of homogeneous flow structure or uniform fluid velocity gradient in stirred flocculation tanks. Short-cut procedures adopted in the literature to address heterogeneous fluid flow structure are summarized. It is also stressed that an integrated approach be followed to tackle practically relevant issues such as selective flocculation of mineral mixtures, dual polymer flocculation, dynamics of polymer/surfactant adsorption, polymer–surfactant interactions, surface precipitation of dissolved species and presence of air bubbles in the suspension.

Virtual indurator: A tool for simulation of induration of wet iron ore pellets on a moving grate

Pelletization of iron ore fines is an important step in an integrated steel plant. It essentially involves balling of fine powders on a rotating disk or drum to produce wet pellets and induration on a moving grate to produce fired pellets. The development of a user-friendly simulation tool, virtual indurator, for induration is presented here. The simulator is based on a phenomenological model of induration. The mean diameter and moisture content of wet pellets, composition and temperature of inlet gas, firing hood temperature profile, pellet bed and hearth layer heights, and furnace design parameters such as grate length are used as model inputs. The model predicts bed and gas temperature and composition profiles, burn-through point temperature and its location, etc. This simulator can be utilized for improving furnace productivity, for optimizing fuel costs and as an operator training simulator.

Balling and granulation kinetics revisited

Abstract Balling of finely comminuted solids by random coalescence and granulation of iron ore fines and other minerals by autolayering are two major size enlargement processes. The existing kinetic model for random coalescence does not take into account the strong dependence of coordination number on the size distribution of agglomerating entities. We present a coordination number based coalescence model, which mimics the underlying physical process more realistically. Simulations show that in spite of highly diverse model structures, random and coordination coalescence models give remarkably similar results. Only static models of autolayering are available presently. These map the input size distribution of feed solids into steady state or terminal size distribution of granules, with little or no information on the path traversed by the process. We propose a continuous-time dynamic model of autolayering within the population balance framework. The model, which is based on the proportionate growth postulate of autolayering, agrees reasonably well with experimental data.

Modeling drug release through stimuli responsive polymer hydrogels

There is a rising interest in stimuli-responsive hydrogels to achieve controlled and self-regulated drug delivery. Stimuli responsive polymer hydrogels with their ability to swell/de-swell under varying pH conditions present themselves as a potential candidate for controlled drug delivery. It is important to develop a mechanistic understanding of the underlying phenomena that will help suggest ways to control the drug release from a polymer hydrogel. We present a mathematical model that couples Nernst-Planck, Poisson and force balance equations to incorporate diffusion of ionic species and drug along with deformation of hydrogel under osmotic pressure. The model can be used to simulate swelling behaviour of the hydrogel along with the kinetics of drug release. It has been validated with published experimental data for swelling of polyhydroxyl methacrylate-co-methacrylic acid (pHEMA-co-MA) gels and release kinetics of Phenylpropanolamine from these gels. Effect of formulation parameters such as polymer concentration and cross-linker concentration has also been evaluated. The model can be used to reduce the number of exploratory experiments required during design of a drug delivery system.