# Yvonne StokesUniversity of Adelaide · School of Mathematical Sciences

Yvonne Stokes

PhD The University of Adelaide

## About

82

Publications

5,894

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625

Citations

Citations since 2016

Introduction

Yvonne Stokes currently works at the School of Mathematical Sciences, University of Adelaide. Yvonne does research in Applied Mathematics. Current research projects are 'Suspension flows and particle focusing in curved geometries’, ‘Mathematics the key to modern glass and polymer fibre technology’, and ‘Enhanced sensitivity of electro spray ionization mass spectrometry’.

Additional affiliations

January 2014 - present

January 2004 - December 2013

Education

January 1995 - June 1998

January 1994 - November 1994

## Publications

Publications (82)

A general mathematical framework is presented for modelling the pulling of optical glass fibres in a draw tower. The only modelling assumption is that the fibres are slender; cross-sections along the fibre can have general shape, including the possibility of multiple holes or channels. A key result is to demonstrate how a so-called reduced time var...

Laminar helically-symmetric gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section is considered. We extend the work of Stokes et al. (2013) and Lee et al. (2014) to channels with arbitrary curvature and torsion or, equivalently, arbitrary curvature and slope. We use a non-orthogonal coordinate system and, remarka...

Purpose
The purpose of this paper is to extend the penalty concept to treat partial slip, free surface, contact and related boundary conditions in viscous flow simulation.
Design/methodology/approach
The penalty partial‐slip formulation is analysed and related to the classical Navier slip condition. The same penalty scheme also allows partial pene...

In flows of very viscous fluids, it is often justifiable to neglect inertia and solve the resulting creeping-flow or Stokes equations. For drops hanging beneath a fixed wall and extending under gravity from an initial rest state, an inevitable consequence of neglect of inertia and surface tension is that the drop formally becomes infinite in length...

In vitro maturation-whereby an oocyte is harvested from an ovary just before full maturation, matured in the laboratory, fertilized, and then transplanted back to the uterus-has important benefits over, but is significantly less successful than, traditional in vitro fertilization. Inadequate in vitro nutrient environments are believed to be a prime...

Particles suspended in fluid flow through a closed duct can focus to specific stable locations in the duct cross-section due to hydrodynamic forces arising from the inertia of the disturbed fluid. Such particle focusing is exploited in biomedical and industrial technologies to separate particles by size. In curved ducts, the particle focusing is a...

Mathematical modelling is used to examine the unsteady problem of heating and pulling an axisymmetric cylindrical glass tube with an over-pressure applied within the tube to form tapers with a near uniform bore and small wall thickness at the tip. To allow for the dependence of viscosity on temperature, a prescribed axially varying viscosity is ass...

Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues...

We examine the effect of Dean number on the inertial focusing of spherical particles suspended in flow through curved microfluidic ducts. Previous modelling of particle migration in curved ducts assumed the flow rate was small enough that a leading order approximation of the background flow with respect to the Dean number produces a reasonable mode...

Microchannels are well-known in microfluidic applications for the control and separation of microdroplets and cells. Often the objects in the flow experience inertial effects, resulting in dynamics that is a departure from the underlying channel flow dynamics. This paper considers small neutrally buoyant spherical particles suspended in flow throug...

Mathematical modelling is used to examine the unsteady problem of heating and pulling an axisymmetric cylindrical glass tube with an over-pressure applied within the tube to form tapers with a near uniform bore and small wall thickness at the tip. To allow for the dependence of viscosity on temperature, a prescribed axially varying viscosity is ass...

Biological tissues are composed of cells surrounded by the extracellular matrix (ECM). The ECM can be thought of as a fibrous polymer network, acting as a natural scaffolding to provide mechanical support to the cells. Reciprocal mechanical and chemical interactions between the cells and the ECM are crucial in regulating the development of tissues...

Particles suspended in a fluid flow through a curved duct can focus to specific locations within the duct cross-section. This particle focusing is a result of a balance between two dominant forces acting on the particle: (i) the inertial lift force arising from small but non-negligible inertia of the fluid, and (ii) the secondary drag force due to...

Particles suspended in fluid flow through a curved duct focus to stable equilibrium positions in the duct cross-section due to the balance of two dominant forces: (i) inertial lift force - arising from the inertia of the fluid, and (ii) secondary drag force - resulting from cross-sectional vortices induced by the curvature of the duct. Such particl...

In a previous study, we compared experiments on drawing of axisymmetric tubular optical fibres to a mathematical model of this process. The model and experiments generally agreed closely. However, for some preforms and operational conditions, the internal channel of the drawn fibre was larger than predicted by the model. We have further investigate...

We model the process of wet chemical etching of the external surface of a single-bore microstructured silicon dioxide fiber in hydrofluoric acid (HFA) while water is pumped through the internal channel to prevent etching of it. The model uses the Stokes flow for the velocity throughout the system and the advection–diffusion equation for the concent...

We consider the role of heating and cooling in the steady drawing of a long and thin viscous thread with an arbitrary number of internal holes of arbitrary shape. The internal holes and the external boundary evolve as a result of the axial drawing and surface-tension effects. The heating and cooling affects the evolution of the thread because both...

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable e...

Particle-laden flows in helical channels are of interest for their applications in spiral particle separators used in the mining and mineral processing industries. In this paper, we extend the previous work of Lee, Stokes, and Bertozzi [“Behaviour of a particle-laden flow in a spiral channel,” Phys. Fluids 26, 043302 (2014)] by studying thin-film f...

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable e...

Particle-laden flows in helical channels are of interest for their applications in spiral particle separators used in the mining and mineral processing industries. In this paper, we extend the previous work of Lee, Stokes, Bertozzi (2013) by studying thin-film flows of mono-disperse particle-laden fluid in helically-wound channels of arbitrary cent...

This paper reviews the development of an efficient mathematical model for the drawing of optical fibres using extensional flow theory which is applicable for fibres of arbitrary geometry. The model is comprised of a 1D axial stretching problem describing the change in area of the cross-section from preform to fibre coupled with a 2D cross-plane pro...

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 mode...

We consider the steady, pressure driven flow of a viscous fluid through a microfluidic device having the geometry of a planar spiral duct with a slowly varying curvature and height smaller than width. For this problem, it is convenient to express the Navier–Stokes equations in terms of a non-orthogonal coordinate system. Then, after applying approp...

There are many fluid flow problems involving geometries for which a nonorthogonal curvilinear coordinate system may be the most suitable. To the authors’ knowledge, the Navier–Stokes equations for an incompressible fluid formulated in terms of an arbitrary nonorthogonal curvilinear coordinate system have not been given explicitly in the literature...

The classical Joukowsky formula for the head jump associated with a sudden flow stoppage is an engineering rule of thumb that helps estimate peak surge pressures in pipelines. However, the Joukowsky formula does not take account of friction. Although this is usually of little concern for short pipelines, the effects of pipe friction can cause signi...

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 efficient...

We consider the steady, gravity-driven flow of a thin film of viscous fluid down a helically wound shallow channel of arbitrary cross-sectional shape with arbitrary torsion and curvature. This extends our previous work [D. J. Arnold et al., “Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature,” J. Fluid Mech. 7...

We model the drawing of a six-hole microstructured optical fibre with a combination of asymptotic techniques and a new efficient numerical method, and compare this to a previous set of experiments and finite element simulations. The new approach accurately models the deformation of the inner channels and predicts cross-sectional fibre geometries wh...

We examine the extension of an axisymmetric viscous thread that is pulled at both ends with a prescribed speed such that the effects of inertia are initially small. After neglecting surface tension, we derive a particularly convenient form of the long-wavelength equations that describe long and thin threads. Two generic classes of initial thread sh...

Motivated 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 th...

A series of six experiments drawing tubular fibres are compared to some recent mathematical modelling of this fabrication process. The importance of fibre tension in determining the internal geometry of the fibre is demonstrated, confirming a key prediction of the models. There is evidence of self-pressurisation of the internal channel, where an ad...

The use of channel pressurisation in drawing microstructured optical fibres (MOFs) potentially allows for fine control of the internal structure of the fibre. By applying extra pressure inside the channels it is possible to counteract the effect of surface tension which would otherwise act to close the channels in the fibre as it is drawn. This pap...

A mathematical model is presented describing the deformation, under the combined effects of surface tension and draw tension, of an array of channels in the drawing of a broad class of slender viscous fibres. The process is relevant to the fabrication of microstructured optical fibres, also known as MOFs or holey fibres, where the pattern of channe...

Oocyte in vitro maturation (IVM) is an important assisted reproductive technology and research tool. The adoption of IVM into routine clinical practice has been hindered by its significantly lower success rates compared to conventional in vitro fertilization (IVF). Cyclic AMP (cAMP) modulation and follicle-stimulating hormone (FSH), independently,...

Spiral gravity separators are devices used in mineral processing to separate particles based on their specific gravity or size. The spiral geometry allows for the simultane- ous application of gravitational and centripetal forces on the particles, which leads to segregation of particles. However, this segregation mechanism is not fundamentally unde...

Gravity assisted miscible CO2 injection into oil reservoirs is an efficient method of enhancing oil recovery. CO2 injection into aquifers for sequestration purposes is another application of miscible displacement under gravity control. This paper reports pore scale simulation studies to determine the role of different parameters on the frontal stab...

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...

This is a review of thin-body and slender-body theories, with indications of some new applications. Topics discussed include bodies with near-constant surface pressure, subsonic and supersonic aerodynamics, ship hydrodynamics, slender bodies in Stokes flow, slender footings in elastic media, and slender moonpools. Mathematical features of the thin-...

Microstructured optical fibres can be designed for a wide range of applications. Extrusion of a preform and drawing to form a fibre is a promising fabrication process for mass production. The effects of flow during fabrication on fibre structure needs to be understood. We propose a modelling methodology suitable for complex structure and focus on f...

We apply recent results for gravity driven slurries to the model of a spiral concentrator in the case of a monodisperse particle slurry. We use a thin film approximation to derive an equilibrium profile for the particle concentration and fluid thickness. Our results explain observations seen in laboratory experiments and commercial products.

This paper presents both visualization and flow simulation of glass micromodel experiments which are performed to visualize the gravity dominated miscible gas displacement process. This approach enables to simulate the exact porous pattern on which the micromodel experiments are performed.
At first, a porous pattern for experiments was constructed...

A viscous micropump is a device such that a cylindrical rotor is eccentrically placed in a channel, and when the rotor is forced to rotate the viscous resistance between the small and large gaps between the cylinder and the channel walls generate a net flow along the channel. Assuming that the gaps between the cylinder and the channel walls are sma...

This is a review of thin-body and slender-body theories, with indications of some
new applications. Topics discussed include bodies with near-constant surface pressure,
subsonic and supersonic aerodynamics, ship hydrodynamics, slender bodies in Stokes
flow, slender footings in elastic media, and slender moonpools. Mathematical features
of the thin-...

This paper presents both visualization and flow simulation of glass micromodel experiments which are performed to visualize the gravity dominated miscible gas displacement process. This approach enables to simulate the exact porous pattern on which the micromodel experiments are performed.
At first, a porous pattern for experiments was constructed...

Motivated by a desire to understand better the operation of spiral
gravity separators, we consider flow of small depth down a helically
wound channel of small torsion and rectangular cross section. The small
fluid depth makes experimental investigation difficult, so that
mathematical modelling and theoretical and computational studies are of
great...

In vitro maturation (IVM) of mammalian oocytes provides an alternative to traditional in vitro fertilization techniques for clinical treatment of infertility or animal breeding. IVM involves the collection of oocytes from the ovary prior to ovulation, with maturation occurring in a laboratory environment. The success of IVM is highly sensitive to t...

The extensional flow and break-up of fluids has long interested many authors. A slender viscous fluid drop falling under gravity
from beneath a horizontal surface is examined. After reviewing previous work which has neglected surface tension, a one-dimensional
model which describes the evolution of such a drop, beginning with a prescribed initial d...

This paper presents both visualization and flow simulation of glass micromodel experiments which are performed to visualize the gravity dominated miscible gas displacement process. This approach enables to simulate the exact porous pattern on which the micromodel experiments are performed. At first, a porous pattern for experiments was constructed...

The ability of an oocyte to successfully mature is highly dependent on intrafollicular conditions, including the size and structure of the follicle. Here we present a mathematical model of oxygen transport in the antral follicle. We relate mean oxygen concentration in follicular fluid of bovine follicles to the concentration in the immediate vicini...

An optical fibre is made by stretching, or “drawing”, a glass or polymer preform in a drawing tower. Extrusion through dies has re- ceived much recent attention as a suitable method for manufacture of preforms of complex shape and novel material composition. How- ever, the preforms are subject to bending during extrusion, so that the final preform...

Oxygen diffusion through oil is important in the culture of oocytes and embryos. A diffusion coefficient two orders of magnitude smaller than that of oxygen in water has been thought possible, and this has led to concerns of anoxia in cultures. Using an assay for determining the oxygen consumption rate of embryos and oocytes, along with a mathemati...

With the advent of microscale and nanoscale devices, the Navier-slip boundary condition as a macroscale model of fluid behaviour at a solid wall has seen renewed interest. The penalty concept and variational formulation are extended here to treat partial slip, free surface, contact and related boundary conditions for boundaries of general shape in...

With the advent of microscale and nanoscale devices, the Navier-slip boundary condition as a macroscale model of fluid behaviour at a solid wall has seen renewed interest. The penalty concept and variational formulation are extended here to treat partial slip and related boundary conditions in viscous flow simulation. An analysis of the penalty par...

We develop a one-dimensional Eulerian model suitable for analyzing the behavior of viscous fluid drops falling from rest from an upper boundary. The method allows examination of development and behavior from early time, when a drop and filament begin to form, out to large times when the bulk of the fluid forms a drop at the bottom of a long thin fi...

Immature oocytes benefit from nutrient modification of the follicular environment by the surrounding cumulus mass. However, the oxygen concentration that the oocyte may be exposed to could be lower than the antral follicular concentration due to the metabolism of surrounding cumulus cells. Using metabolic data previously determined, we have develop...

Some optical surfaces are formed by gravity sagging of molten glass. A glass sheet supported on a ceramic former is heated; the glass becomes a very viscous fluid and sags under its own weight until the lower surface is in full contact with the former. The smooth upper free surface is the required optical surface. Its shape is dependent on the init...

Six patents were secured by E.H. Lanier from 1930 to 1933 for aero- plane designs that were intended to be exceptionally stable. A feature of five of these was a flow-induced “vacuum chamber” that it was thought provided superior stability and increased lift compared to typical wing designs. Initially this chamber was in the fuselage, but later des...

The study of flow in open helically-wound channels has application to many natural and industrial flows, including those in static spiral separators. The flow consists of a primary axial component and a secondary cross flow and, in spiral separators, the fluid depth is typically small making experimental investigation difficult. Mathematical models...

The study of flow in open helically-wound channels has application to many natural and industrial flows, including those in static spiral separators. The flow consists of a primary axial component and a secondary cross flow and, in spiral separators, the fluid depth is typically small making experimental investigation difficult. Mathematical models...

Smooth honey dripping from a spoon is an everyday example of a viscous fluid in a long filament-like extensional flow which may eventually break up into drops. Similar filament or drop forming flows are important in modern technologies including ink-jet printing, molten metal processing, polymer and glass fibre spinning, and for rheological measure...

To assess rotational deformity in a broken forearm, an orthopaedic surgeon needs to determine the amount of rotation of the radius from one or more two-dimensional x-rays of the fracture. This requires only simple first-year university mathematics — rotational transformations of ellipses plus a little differential calculus — which yields a general...

To achieve improvements in the design of spiral particle separators, used in the mineral processing industry, it is necessary to have a good understanding of the fluid flow in them and the factors that affect it. To this end, we are developing computational techniques for determining the flow in a spiral channel of general geometry, includ- ing the...

Inertia is often justifiably neglected in studies of very viscous fluid
flows. We consider its role in the fall of a very viscous fluid drop
hanging beneath a fixed wall and extending under gravity from an initial
rest state. An inevitable consequence of neglect of inertia is that the
drop formally becomes infinite in length at a finite crisis time...

We compute the flow in an open helical (or spiral) channel and must, as part of the solution process, find the free surface shape which is dependent on geometrical and flow parameters. We extend work on closed spiral flows to open spiral flows, seeking for helically symmetric solutions as a first step towards solving what could be a full three-dime...

Summary A finite drop of fluid with large viscosity µ and density ρ is initially at rest hanging under gravity g from the underside of a solid boundary. The initial configuration may be of a general boundary shape, with (vertical) maximum length L(0) = L0 and (horizontal) maximum width w0. The subsequent motion, drop length L(t) as a function of ti...

Both very viscous Newtonian flow and Maxwell viscoelastic models have been used in recent publications to compute the time scale over which glass windowpanes at ambient temperatures will flow perceptibly. We compare these two different methods and show them to be, despite first appearances, completely consistent. We also show that the time scale is...

The slumping of molten glass under gravity into a mould, so as to replicate the mould surface on the upper free surface of the glass, is used in the manufacture of some optical components for which the curvature of the upper free surface is critical. A finite-element simulation of the process based on the creeping-flow equations is described. In ad...

Glass has properties of a liquid. But do glass windows really flow over centuries becoming thicker at the bottom, as is commonly reported? Simple calculations show that the time $t$ taken for a windowpane of height $L_0$ to increase in thickness by $q$% due to gravity $g$ is given by
\[
t= \frac{4\mu}{\rho g L_0}\frac{q}{100}
\]
where the glass has...

A layer of very viscous liquid (e.g. tar, molten glass) spans a chasm between two vertical walls. The slow fall or slump of this initially-rectangular liquid bridge is analysed. A semi-analytical solution is obtained for the initial motion, for arbitrary thickness/width ratios. The formal limits of large and small thickness/width ratios are also in...

Formation of drops via extensional flow and break-off has been much studied (see the review article by Eggers [1]), motivated by a wide range of applications such as ink-jet printing, spinning and drawing of polymer or glass fibres, glass blowing and blow-moulding in the manufacture of containers, light bulbs and glass tubing, rheological measureme...

## Projects

Projects (3)

Particles suspended in a fluid flow through a curved duct can focus to equilibrium locations within the duct cross-section. This particle focusing is a result of a balance between two dominant forces acting on the particle: (