Flow visualisation and modelling of solid soap extrusion

Abstract

Ram extrusion of a solid granular soap was studied using three geometrically identical but differently-scaled extruders. The experimental design revealed deviation from the Benbow and Bridgwater (1993) extrusion model due to nonideal, scale-dependent effects. Typically these effects, linked to the shear rate in the extruder, are absorbed into the model's material pseudo-properties. The data were able to be represented using the Basterfield et al. (2005) model for extrusion flow which does include a shear rate as a variable. Flow visualisation in conjunction with fluid dynamics-based simulations showed, however, that the assumptions underlying the Basterfield et al. model are not appropriate for soap extrusion, despite the good agreement of the model with the experimental extrusion data. This highlights a need for care in interpretation of extrusion data, in that the limited information gathered about any given experiment, typically just the extrusion pressure, can lead to the generation of spurious parameters if the wrong model is applied.

Rheology of human faeces and pathophysiology of defaecation

“…The physical relationship between the minimum yield stress σmin necessary for passage though the geometric model and the principal geometric parameters is given by , where Da is the diameter of the residual anal canal, Dr is the diameter of the rectum, and P is a uniformly applied pressure acting on the walls and the proximal lumen of the rectal canal. In fact the expression is multiplied by a coefficient that depends on the shape of the passage zone from the rectum to the anus [35,36].To estimate the total pressure required for the stool to flow by the anus, it is necessary to add the pressure to overcome the friction of the stools against the wall of the anus. This contribution is much smaller than that required to deform the stool during the passage from the rectum to the anus.…”

“…Given that faecal material can deform into the constriction represented by our model only if the yield stress is lower than a threshold [35,36,38] and that this threshold depends on the geometry (diameters, length, angle) and the applied pressure, plotting the relationship between the minimal yield stress smin and Da /Dr shows that as Da/Dr decreases, the minimal yield stress smin for which evacuation is possible, decreases over several orders of magnitude ( Fig. 1-c).…”

Linking fresh paste microstructure, rheology and extrusion characteristics of cementitious binders for 3D printing

“…Analysis of extrusion flow of non‐Newtonian fluids such as cement pastes is rather complex because of the effects of paste properties on the flow field, and slip along the die walls . In this study, a variant of the Benbow‐Bridgwater model, which employs a plasticity approach to analyze extrusion rheology data of dense ceramic suspensions, is used to model the extrusion behavior of the printable cementitious binders.…”

“…Since the die of the extruder used here is a frustum of a cone rather than a cylinder, instead of directly calculating the extrusion pressures P 1 and P 2 , the corresponding forces are used. The total force was plotted as a function of L d / D d ratios for different velocities (similar to a Bagley plot) . Extrapolating the linear relationship between L d / D d and the extrusion force for different velocities back to the Y ‐axis gives the force at L d / D d = 0, which corresponds to the force required to converge the paste into the die entry ( F 1 ).…”

“…It can be easily noticed from Figure that τ w is different for the two die sizes used—the larger the L d / D d ratio, the higher the wall shear. This is because the wall slip of cement paste is pressure‐dependent, as has been observed for other similar systems . It is conceivable that the increased extrusion pressures in smaller diameter dies will increase τ W due to higher degrees of particle‐wall contact.…”