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Adhesion model to predict the behavior of wet material

Having trouble with wet, sticky material in your production process? With Rocky DEM, you can predict the behavior of such materials with ease. Rocky provides several advanced and validated physics models that accurately capture the behavior of sticky materials in a variety of manufacturing settings.

The success of DEM is based on how accurately the forces acting on each particle are captured. For macroscopic bulk particle systems, inertial forces are the most important. Thus, forces like weight and friction are accounted for in every DEM simulation. But as we decrease the particle size, van der Waals (VDW) forces also become very important. For wet particles in contact, the liquid bridge between them exerts an attractive capillary force and a viscous dissipative force that must also be accounted for; additional models are needed to capture these effects.

As capillary and VDW forces are attractive and act along the line connecting the center of the contacting particles, these are added to the normal force. Once a particle is in close vicinity to another particle or boundary, the adhesive force model is activated. This activation distance is provided by the user as an adhesive distance.

How Rocky DEM addresses adhesive forces

Multiple adhesive models are implemented in Rocky. A brief overview is provided below:

Constant adhesive model: In this model, the user is required to input a force fraction constant, which is multiplied with the weight of the smaller particle of the contact pair. If the force fraction is 1, it means the adhesive force will be equal to the gravity force on the particle. This model is very good for most cases where the adhesive force is not related to contact stresses. This is true of most substances, like fine pharmaceutical powder or wet rocks, and has been used successfully across many industries. The animation below shows a simulation of an auger conveyor transferring wet barley from a conveyor belt.

To use this model, the user should calibrate the force fraction using a simple test like angle of repose, shear cell, etc. (Figure 1).

Angle of repose test used to calibrate the constant adhesive force model for modeling flow of wet granulated powder.
Figure 1: Angle of repose test used to calibrate the constant adhesive force model for modeling flow of wet granulated powder.

Linear adhesive model: For cases where the adhesive force is a function of the contact stresses. This model is good for cases with stress consolidation, such as the adhesion of powders to the weight of the overlying bed in a hopper, and hardening of snow upon squeezing. This adhesive increases proportionally to the sum of this distance and the actual particles’ overlap. The coefficient of proportionality is defined as the stiffness fraction and is a user input.

Figure 2 shows a force-overlap plot of a particle collision with a wall for both dry and adhesive impacts. It is evident that the larger the contact overlap, the larger the attractive force, thus allowing an accurate model to represent the stress consolidation of granular materials.

Force-overlap plot for the linear adhesive model
Figure 2: Force-overlap plot for the linear adhesive model. Increasing the stiffness ratio increases the attractive force and the overlap to model stress consolidation.

Using this model, Rocky predicted the flow of wet ore on a transfer chute.

Leeds adhesive force model: Similar to the linear adhesive model, this model simulates the elasto-plastic-adhesive behavior of particles. The relationship of adhesive force to particle overlap is described using a stepwise function taken from Pasha et .al. (2014).

JKR adhesive force model: This model is based on the widely accepted JKR theory (1971) for adhesive elastic spheres which relates the surface energy of a material to the adhesive force. The surface energy is a thermodynamic material property which can be experimentally determined using a variety of material characterization techniques. Thus, in theory the user input for this model does not need calibration, unlike with other models. Following its theoretical origins, this model is only compatible with the Hertzian contact model.

Liquid bridge model: Rocky has recently introduced this model in which the capillary and viscous forces due to the liquid bridge can be captured. The formation and breakage of the liquid bridge would be decided based on the quantity and material properties (surface tension, viscosity) of the liquid and dynamic process conditions (distance between particles, etc.). This model is based on the one proposed by Mikami, Kamiya, and Horiyo (1998) and is very useful for cases where liquid is added to make particles wet, such as coating of pharmaceutical tablets, wet granulation of fine powders, and so on. An example is shown in the animation below.

References :

Pasha, M., Dogbe, S., Hare, C., Hassanpour, A., and Ghadiri, M. (2014). A linear model of elasto-plastic and adhesive contact deformation. Granular Matter, 16:151–162

Johnson, K. L., Kendal, K., and Roberts, A. D. (1971). Surface energy and the contact of elastic solids. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 324:301–313

Mikami,T., Kamiya,H., Horiyo,M. (1998). Numerical simulation of cohesive powder behavior in a fluidized bed. Chemical Engineering Science, 53(10): 1927-1940

Saurabh Sarkar

Applications Engineer, Rocky DEM

Dr. Saurabh Sarkar is an Applications Engineer for the Rocky DEM Business Unit. Prior to joining ESSS, Dr. Sarkar worked as an Adjunct Faculty at Rutgers University and an on-site Consultant at Sunovion Pharmaceuticals where he supported drug formulation and process development activities. He obtained his Ph.D. in Pharmaceutics from the University of Connecticut where his focus was understanding and optimization of different pharmaceutical unit operations using DEM and CFD tools in projects with multiple industrial and government collaborators. He is a Senior Member of the AIChE and serves as an expert reviewer for several journals.

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