Gravitational extension of a fluid cylinder with internal structure

First published online 3 February 2016Motivated by the fabrication of microstructured optical fibres, a model is presented for the extension under gravity of a slender fluid cylinder with internal structure. It is shown that the general problem decouples into a two-dimensional surface-tension-driven Stokes flow that governs the transverse shape and an axial problem that depends upon the transverse flow. The problem and its solution differ from those obtained for fibre drawing, because the problem is unsteady and the fibre tension depends on axial position. Solutions both with and without surface tension are developed and compared, which show that the relative importance of surface tension depends upon both the parameter values and the geometry under consideration. The model is compared with experimental data and is shown to be in good agreement. These results also show that surface-tension effects are essential to accurately describing the cross-sectional shape.Hayden Tronnolone, Yvonne M. Stokes, Herbert Tze Cheung Foo and Heike Ebendorff-Heideprie

Thin-film flow in helically wound rectangular channels with small torsion

Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters

Pinch-off masses of very viscous fluids extruded from dies of arbitrary shape

The extrusion of slender very viscous fluid cylinders from dies of arbitrary geometry is modeled to approximate the mass of the first drop to pinch off. The model neglects inertia, which, although important to the dynamics near pinch-off, does not have a significant impact on the drop mass. Extrudate swell is also assumed to be negligible. The model is able to compute the pinch-off mass for fluid cylinders with cross-sectional geometries of any connectivity. By way of illustration, pinch-off masses are computed for epicycloidal cross sections, two touching circular rods, and circular cylinders with a single circular hole placed both centrally and off-centre. It is shown that the drop mass may be controlled by altering either the extrusion conditions or the die geometryHayden Tronnolonea and Yvonne M. Stoke

Extrusion of fluid cylinders of arbitrary shape with surface tension and gravity

A model is developed for the extrusion in the direction of gravity of a slender fluid cylinder from a die of arbitrary shape. Both gravity and surface tension act to stretch and deform the geometry. The model allows for an arbitrary but prescribed viscosity profile, while the effects of extrudate swell are neglected. The solution is found efficiently through the use of a carefully selected axial Lagrangian coordinate and a transformation to a reduced-time variable. Comparisons between the model and extruded glass microstructured optical fibre preforms show that surface tension has a significant effect on the geometry but the model does not capture all of the behaviour observed in practice. Experimental observations are used in conjunction with the model to argue that some deformation, due neither to surface tension nor gravity, occurs in or near the die exit. Methods are considered to overcome deformation due to surface tension.Hayden Tronnolone, Yvonne M. Stokes and Heike Ebendorff-Heideprie

Characterising shape patterns using features derived from best-fitting ellipsoids

Available online 15 June 2018A method is developed to characterise highly irregular shape patterns, especially those appearing in biomedical settings. A collection of best-fitting ellipsoids is found using principal component analysis, and features are defined based on these ellipsoids in four different ways. The method is defined in a general setting, but is illustrated using two-dimensional images of dimorphic yeast exhibiting pseudohyphal growth, three-dimensional images of cancellous bone and three-dimensional images of marbling in beef. Classifiers successfully distinguish between the yeast colonies with a mean classification accuracy of 0.843 (SD=0.021), and between cancellous bone from rats in different experimental groups with a mean classification accuracy of 0.745 (SD=0.024). A strong correlation (R2=0.797) is found between marbling ratio and a shape feature. Key aspects of the method are that local shape patterns, including orientation, are learned automatically from the data, and the method applies to objects that are irregular in shape to the point where landmark points cannot be identified between samples.Amelia Gontar, Hayden Tronnolone, Benjamin J. Binder, Murk J. Bottem

Towards understanding of geometrical structure in microstructured optical fibres

http://www.ictam2012.org/?p=269

Modelling uniaxial non-uniform yeast colony growth: comparing an agent-based model and continuum approximations

Available online 20 April 2021Biological experiments have shown that yeast can be restricted to grow in a uniaxial direction, vertically upwards from an agar plate to form a colony. The growth occurs as a consequence of cell proliferation driven by a nutrient supply at the base of the colony, and the height of the colony has been observed to increase linearly with time. Within the colony the nutrient concentration is non-constant and yeast cells throughout the colony will therefore not have equal access to nutrient, resulting in non-uniform growth. In this work, an agent based model is developed to predict the microscopic spatial distribution of labelled cells within the colony when the probability of cell proliferation can vary in space and time. We also describe a method for determining the average trajectories or pathlines of labelled cells within a colony growing in a uniaxial direction, enabling us to connect the microscopic and macroscopic behaviours of the system. We present results for six cases, which involve different assumptions for the presence or absence of a quiescent region (where no cell proliferation occurs), the size of the proliferative region, and the spatial variation of proliferation rates within the proliferative region. These six cases are designed to provide qualitative insight into likely growth scenarios whilst remaining amenable to analysis. We compare our macroscopic results to experimental observations of uniaxial colony growth for two cases where only a fixed number of cells at the base of the colony can proliferate. The model predicts that the height of the colony will increase linearly with time in both these cases, which is consistent with experimental observations. However, our model shows how different functional forms for the spatial dependence of the proliferation rate can be distinguished by tracking the pathlines of cells at different positions in the colony. More generally, our methodology can be applied to other biological systems exhibiting uniaxial growth, providing a framework for classifying or determining regions of uniform and non-uniform growth.Anthony J. Gallo, Hayden Tronnolone, J. Edward F. Green, Benjamin J. Binde

Quantifying the dominant growth mechanisms of dimorphic yeast using a lattice-based model

A mathematical model is presented for the growth of yeast that incorporates both dimorphic behaviour and nutrient diffusion. The budding patterns observed in the standard and pseudohyphal growth modes are represented by a bias in the direction of cell proliferation. A set of spatial indices is developed to quantify the morphology and compare the relative importance of the directional bias to nutrient concentration and diffusivity on colony shape. It is found that there are three different growth modes: uniform growth, diffusion-limited growth (DLG) and an intermediate region in which the bias determines the morphology. The dimorphic transition due to nutrient limitation is investigated by relating the directional bias to the nutrient concentration, and this is shown to replicate the behaviour observed in vivo Comparisons are made with experimental data, from which it is found that the model captures many of the observed features. Both DLG and pseudohyphal growth are found to be capable of generating observed experimental morphologies.Hayden Tronnolone, Jennifer M. Gardner, Joanna F. Sundstrom, Vladimir Jiranek, Stephen G. Oliver and Benjamin J. Binde