(231b) Systems Approach to Solution of Caking Problems

Powder handling industries often find that their processing lines are disrupted by the presence of lumps of materials which in turn results in revenue losses. It is virtually impossible to look at this lumping or caking pheonomena using a single modeling tool as the problem in itself is multifacted and elaborate involving the porosity, permeability, shape and surface properties of the material. Little or no discussion in the literature looks at this wide spectrum of phenomena that act as ingredients to this problem. Available literature involves modeling that uses the bulk property of materials largely ignoring the physical attributes of individual powder. The authors have developed a multifacteted approach that involves various physical and chamical properties of various materials inorder to arrive at an elaborate model for caking. Moisture migration into the bulk with varying atmospheric temperature is simulated by Finite Difference methods. The droplet evolution on the surface is studied using the thin film equation and a Monte Carlo method.

Since most of the literature dealt with experiments in caking [1,2,3], a more rigorous approach that deals with individual mechanisms is used in this technique. An X-ray mirotomograph was used to create the real shape of the particle bed. The algorithms were implimented on this real structure. Essentially the technique is divided into three major components. (1)Moisture migration into the bulk with varying atmospheric temperature is simulated by Finite Difference methods. (2) The distribution of moisture on the surface is then found using a Monte Carlo approach. (3) The quantity of material that dissolves in the droplets is found out using the solubility of the material involved that also provides information on the final strength of the material.

Diffusivity equation is discretised to account for variations in Diffusivity inside the bulk.

A similar approach is used to find the temperature distribution inside the bulk. Once the final volume of liquid is found on the surface of the material, the thin film equation is used to find the height of the resultant droplet. The droplet evolution on the surface is studied using a Monte Carlo method. The droplets on the surface of the particles are discretised and moved randomly to minimize the energy. The results are discussed as below.

(a) Finite Difference method for moisture distribution inside the bulk bed

 Migration of moisture into the particle bed is studied by using the actual structure scanned using X-ray micro tomography. Finite Difference method, with varying diffusivity is implemented on the digitized structure to obtain an in-depth understanding into this mechanism. This technique gives a detailed map of moisture distribution inside the structure of the particle. The effect of presence of deliquescent materials inside the bulk is also evident. The quantity of liquid available on the surface of the particle is mapped using this technique. (b) Surface moisture evolution using Monte Carlo method

On the surface, thin film equations are solved to provide the film thickness data. A Monte Carlo surface energy minimization method is solved to predict the evolution of liquid film. The method is first tested on flat surfaces and the results show excellent match. It is then tested over particle surfaces. The results of the Monte Carlo simulations provide an insight into the volume distribution of moisture on the surface. This helps in calculating exactly how much moisture is formed between particle surfaces contributing to the final strength of the bulk.

(a)(b)

Figure 1 Actual X-ray Micro Tomography image used for the moisture migration simulation. (b) Moisture map inside the powder bed (red for high concentration and blue for low. The dark blue color shows the moisture adsorbed on to the particle surface)

                        (a)                                            (b)                                            (c)

Figure 2 Liquid droplet breakup from the surface of a hydrophobic particle (a) particle covered completely with liquid (b) Initial holes observed on the liquid layer (c) Final configuration of droplets on the particle CONCLUSIONS

A new model for caking is proposed that includes a detailed treatment of individual moisture penetration mechanism in detail. The volume of moisture on the surface of each particle is first calculated using DEM. A Monte Carlo method is then used to find the final distribution of droplet. It is shown that the moisture on the surface of the particle are distributed as surface droplets and pendules at contact points between particles FUTURE WORK

Experiments are planned to find the solubility of different components involved in the simulations. In order to validate the model, shear tests are planned using controlled amount of moisture inside the bulk. Validation of the moisture distribution on the surface will be performed by Magnetic Resonance Imaging (MRI).  

REFERENCE

1)      Chemical Engineer's Handbook (ed. Perry, R.H.; Green, D.W.) 1997

2)      Rogé B., Mathlouthi M. 2003. Caking of white crystalline sugar. International Sugar Journal 105(1251): 128

3)      Leaper M.C., Berry R.J, Bradley M.S.A., Bridle I., Reed A.R., Abou-Chakra H and Tüzün U. Measuring the tensile strength of caked sugar produced from humidity cycling Proceedings of the I MECH E Part E Journal of Process Mechanical Engineering, 1 April 2003, vol. 217, no. 1, pp. 41-47(7)