Modelling of paste flows subject to liquid phase migration

Abstract

SUMMARYParticulate pastes undergoing extrusion can exhibit differential velocities between the solid and liquid phases, termed liquid phase migration (LPM). This is observed experimentally but understanding and predictive capacity for paste and extruder design is limited. Most models for LPM feature one-dimensional analyses. Here, a two-dimensional finite element model based on soil mechanics approaches (modified Cam-Clay) was developed where the liquid and the solids skeleton are treated separately. Adaptive remeshing routines were developed to overcome the significant mesh distortion arising from the large strains inherent in extrusion.Material data to evaluate the model's behaviour were taken from the literature. The predictive capacity of the model is evaluated for different ram velocities and die entry angles (smooth walls). Results are compared with experimental findings in the literature and good qualitative agreement is found.Key results are plots of pressure contributions and extrudate liquid fraction against ram displacement, and maps of permeability, liquid velocity and voids ratio. Pore liquid pressure always dominates extrusion pressure.The relationship between extrusion geometry, ram speed and LPM is complex. Overall, for a given geometry, higher ram speeds give less migration. Pastes flowing into conical entry dies give different voids ratio distributions and do not feature static zones.

Critical review: Injectability of calcium phosphate pastes and cements

“…The quality of extrudate and paste in the barrel were analysed, post and also during extrusion [134,140,[166][167][168][169]. Like the study by Bohner and Baroud [78], several studies have taken a theoretical approach in an attempt to gain a deeper understanding of the phase separation process and identify the mechanism and extent by which different methods may reduce phase separation [150,151,170,171]. As a result, the understanding of phase separation during extrusion of these pastes is more advanced compared to the extrusion of CPC.…”

Shaping ceramics by plastic processing

“…This approach is hindered by computational complexity as current computing power limits us to simplified systems with significantly fewer particles than in practice so it is unlikely to be of practical use in the short term. An alternative approach is to modify soil mechanics models to accommodate the large strains experienced during extrusion and this has been demonstrated by Patel et al 84 : the shortcoming is the need to generate material parameters but its power lies in being able to predict phase separation or difference in solid/liquid concentrations.…”

“…Testing of formulations propensity for phase migration can be performed by capillary extrusion 85 and squeeze flow 86 : linking the results to performance in complex geometries is not straightforward. Extrusion has been analysed by critical state theory 87 to develop threshold criteria and this is now being applied to detailed simulations 84 to link formulation, die geometry and operation to design out phase migration.…”

Linking particle properties to dense suspension extrusion flow characteristics using discrete element simulations

“…Simultaneously, the flow entering the die along the extruder axis (near to y = 0) undergoes almost pure extension, as shown by the positive ∂V x /∂x, maintaining the incom-pressibility of the material so that a relative permeating liquid flow can be neglected. This stretching of the paste entering the die may be indicative of the above mentioned suction effect [30,31,33] that is responsible for drawing liquid out of slower flowing die entry corners into the main extruding flow. These velocity gradients serve to offer a thorough qualitative description of the main deformational flow at the die entry at steady state.…”