Oliver Harlen
University of Leeds, Mathematics, Faculty Member
ABSTRACTThe “pom-pom” model of McLeish and Larson (J. Rheol. 42, 81, 1998) provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. The Edwards-de Gennes tube concept is used to derive a... more
ABSTRACTThe “pom-pom” model of McLeish and Larson (J. Rheol. 42, 81, 1998) provides a simple molecular theory for the nonlinear rheology of long chain branched polymer melts. The Edwards-de Gennes tube concept is used to derive a constitutive equation for a simple branched molecule composed of two star polymers linked by a single backbone chain. A feature of this model is that the backbone section of tube can stretch up to maximum length given by the maximum entropic drag-force from the arms, after which the star arms are withdrawn into the backbone tube. This produces a sharp transition in the extensional viscosity at this maximum stretch. This unphysical feature results from an over-simplification of the behaviour near the branch points.In this paper we introduce a simple treatment of the coupling between relaxed and unrelaxed polymer segments at branch-points. This allows for localised displacements of branch-point within a quadratic potential before maximum extension is reached. Displacing the branch-point reduces the length of arm outside the tube and so reduces in the drag on the star arms. This smoothes out the sharp transitions in extensional viscosity in the original “pom-pom” model at the cost of introducing an extra unknown parameter.This modification improves the prediction of the nonlinear rheology of H-polymers whose molecular structure is known. Alternatively, for polymers of unknown structure such as commercial Low Density Polyethylene, the model parameters may be fitted from linear viscoelastic and uniaxial extension data, to provide predictions for the behaviour in transient nonlinear shear and planar extension. By including local branch-point displacement we find improved agreement with the data for Low-Density Polyethylene.
Research Interests:
Research Interests:
Research Interests:
Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liquids. Questions remain as to the role of surfactants on the inkjet printing process at the microsecond timescale. Here, numerical and... more
Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liquids. Questions remain as to the role of surfactants on the inkjet printing process at the microsecond timescale. Here, numerical and experimental results demonstrating the effects of surfactants on jet break-up and drop formation at the scales relevant to drop-on-demand inkjet printing are presented. The rapid expansion of the free surface during the fast jetting process results in a depletion of surfactants along the air–liquid interface, resulting in surface tension gradients. During ejection, surfactants are concentrated toward the head of the droplet, while the trailing ligament is found to be almost devoid of surfactants. As a consequence, the initial evolution and pinch-off of the jet from the nozzle are found to be very similar to that of pure water, even though the equilibrium surface tension of the surfactant solution is lower by a factor of two. However, particularly for stron...
Research Interests:
As inkjet technology develops to produce smaller droplets, substrate features such as accidental scratches or manufacturing defects can potentially affect the outcome of printing, particularly for printed electronics where continuous... more
As inkjet technology develops to produce smaller droplets, substrate features such as accidental scratches or manufacturing defects can potentially affect the outcome of printing, particularly for printed electronics where continuous tracks are required. Here, the deposition of micro-droplets onto a scratch of commensurate size is studied. The scratch is considered as a groove of rectangular cross-section, with rectangular side ridges representing material displaced from the substrate, and seven equilibrium morphologies are identified as a result of inertial spreading, contact-line pinning, imbibition into the scratch and capillary flow. A regime map is constructed in terms of scratch depth and width, and theoretical estimates of the regime boundaries are developed by adapting droplet spreading laws for flat surfaces to account for liquid entering the scratches. Good agreement is seen with numerical results obtained using a graphical processing unit-accelerated three-dimensional mul...
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Rapid advances in experimental biophysical techniques are generating a wealth of information about the mechanical operation of the cellular cytoskeleton and its motors. However, each of these tools typically provides only a limited piece... more
Rapid advances in experimental biophysical techniques are generating a wealth of information about the mechanical operation of the cellular cytoskeleton and its motors. However, each of these tools typically provides only a limited piece of a highly complex puzzle. There is a need to develop new computational tools that can integrate these data together into a central model. Here we discuss the experimental advances alongside the computational tools, and propose how these could be developed to successfully combine the emerging structural and dynamic experimental data on cytoskeletal motors. We consider examples of both single motors and arrays of motors within a biological cell
Research Interests:
Research Interests:
KOBRA is a coarse-grained algorithm for parameterising and simulating slender proteins using Kirchoff rods.
Research Interests:
Research Interests:
The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of... more
The jetting of dilute polymer solutions in drop-on-demand printing is investigated. A quantitative model is presented which predicts three different regimes of behaviour depending upon the jet Weissenberg number Wi and extensibility of the polymer molecules. In regime I (Wi L) the chains remain fully extended in the thinning ligament. The maximum polymer concentration at which a jet of a certain speed can be formed scales with molecular weight to the power of (1-3ν), (1-6ν) and -2ν in the three regimes respectively, where ν is the solvent quality coefficient. Experimental data obtained with solutions of mono-disperse polystyrene in diethyl phthalate with molecular weights between 24 - 488 kDa, previous numerical simulations of this system, and previously published data for this and another linear polymer in a variety of “good” solvents, all show good agreement with the scaling predictions of the model
Research Interests:
... heat flux-r. Jt**", For the case of a spherical droplet, a solution for the fields ip, i/i, y?'and!/>'may be found as a... more
... heat flux-r. Jt**", For the case of a spherical droplet, a solution for the fields ip, i/i, y?'and!/>'may be found as a Rayleigh series expansion ... T or r We rewrite the boundary conditions (10) to (13) as -&+<,),16) or eiKacose+ e'* V+ e"'V= p (y+ 0),(17) eiKaco'e+ eiKa $)+ rvtai/;= I ...
Research Interests:
ABSTRACT PEDOT:PSS is commonly inkjet printed in aqueous solutions with surfactant additives for improved electrical properties in organic electronics applications. These shear thinning complex fluids have been found to DoD jet... more
ABSTRACT PEDOT:PSS is commonly inkjet printed in aqueous solutions with surfactant additives for improved electrical properties in organic electronics applications. These shear thinning complex fluids have been found to DoD jet surprisingly well over a wide range of drive voltages and drop speeds, behaving rather like Newtonian fluids with far (ten times) lower viscosities than measured at low shear-rate. As ∼ 1 wt% PEDOT:PSS solutions showed little evidence for satellite production even at high jet speeds this would suggest that the fluid has regained high viscosity levels, in order to slow the necking rate, on timescales ≪ 100 μs and much faster than accessible to conventional mechanical testing means.Experimental work on the break-up of Newtonian ligaments was recently extended to DoD-scale ligaments, and supports the interpretation that the PEDOT:PSS ligaments attain higher viscosity during flight than during the jet emergence from the print head nozzle, although such rapid recovery timescales for PEDOT:PSS were not predicted from its measured rheology.Our recent work has focused on oscillating drop (OD) techniques for determination of properties of DoD (50 μm) scale aqueous PEDOT:PSS solutions (with and without surfactants) and on a larger (3mm) dispensing scale for more general shear thinning fluids. Imaging studies by one of us (SW) evaluated diffraction effects on OD analyses.The small effects of weak elasticity on the drop oscillations, as assessed theoretically by Khismatullin and Nadim (2001), have been exploited to provide new limits to the recovery time for aqueous PEDOT:PSS based on the fluid viscosity deduced from measured rheology and OD decay rate. These limits are consistent with recent numerical simulations of shear thinning fluid jetting.
Research Interests:
This work looks at the sensitivity of large amplitude oscillatory shear (LAOS) to micro-scale structure of long chain branched polymer melts. Fourier Transform Rheology is used in combination with LAOS to extract the odd harmonic... more
This work looks at the sensitivity of large amplitude oscillatory shear (LAOS) to micro-scale structure of long chain branched polymer melts. Fourier Transform Rheology is used in combination with LAOS to extract the odd harmonic contributions within the stress response of a material under oscillation for shear strains of up to unity. This work focusses on the third harmonics and experimental measurements of three long chain branched (LCB) polyethylene samples which are compared to the Pompom constitutive model. The polyethylenes consist of two LCB-HDPEs which have well quantified low levels of branching, and one highly branched commercial LDPE. The Pompom model is a constitutive model which is parametrised by various aspects of molecular detail. The Pompom model can capture the rheology of industrial branched resins using a multi-mode approach, with each Pompom mode consisting of two linear parameters and two non-linear parameters. Typically, the non-linear parameters are fitted us...
Research Interests:
Research Interests:
ABSTRACT The ultrasonic characterization of emulsions relies principally upon the theory of thermoacoustic scattering. For a single spherical particle of radius a suspended in a homogeneous medium, the theory provides an exactly soluble... more
ABSTRACT The ultrasonic characterization of emulsions relies principally upon the theory of thermoacoustic scattering. For a single spherical particle of radius a suspended in a homogeneous medium, the theory provides an exactly soluble solution to the scattering problem. Unfortunately, direct computations with this solution are often ill-conditioned for certain ranges of the acoustic wave number K and thermal wave number L. Recently the authors have developed a low frequency (i.e., |Ka|,|La|≪1) approach to the theory based on a potential theory technique. This low frequency theory is rapidly convergent and overcomes computation ill-conditioning. In this paper, we pursue the single particle theory and consider the region in which |Ka|≪1 and |La|≫1, i.e., the high frequency range of the thermal wavelength. To achieve this, we employ the geometric theory of diffraction. We show that the high frequency solution agrees well with both the experimental measurements and the exact solution in the region where |Ka|≪1 and |La|≫1. As in the low frequency case, the high frequency solution may be applied to arbitrary scattering domains.
Research Interests:
... The coupling between the thermal and acoustic fields varies with frequency according to the ratio of Fr to Ft in (7). For the case of a spherical droplet, a solution for the fields (o, b, p', and... more
... The coupling between the thermal and acoustic fields varies with frequency according to the ratio of Fr to Ft in (7). For the case of a spherical droplet, a solution for the fields (o, b, p', and O' may be found as a Rayleigh series expansion in ... (23) F (eiKacose + eiKa%) + FteiLa4 = F ...
Research Interests:
Research Interests:
Research Interests:
Research Interests: Mathematics, Applied Mathematics, Computer Science, Ultrasound, Low Frequency, and 8 moreApplied Mathematics and Computational Science, Diffraction, Wavelength, Numerical Analysis and Computational Mathematics, Rayleigh Scattering, Electrical And Electronic Engineering, Helmholtz Equation, and Helmholtz Free Energy
Research Interests:
The sedimentation of a small dense sphere through a suspension of neutrally buoyant fibres is investigated via a numerical simulation technique that includes both fibre fibre contact forces and long-range hydrodynamic interactions. In... more
The sedimentation of a small dense sphere through a suspension of neutrally buoyant fibres is investigated via a numerical simulation technique that includes both fibre fibre contact forces and long-range hydrodynamic interactions. In situations where the diameter of the sphere is smaller than the length of the fibres, calculations that exclude the effect of contacts between fibres severely underestimate the
Research Interests:
Research Interests:
Advances in structural biology, such as cryo-electron microscopy (cryo-EM) have allowed for a number of sophisticated protein complexes to be characterized. However, often only a static snapshot of a protein complex is visualized despite... more
Advances in structural biology, such as cryo-electron microscopy (cryo-EM) have allowed for a number of sophisticated protein complexes to be characterized. However, often only a static snapshot of a protein complex is visualized despite the fact that conformational change is frequently inherent to biological function, as is the case for molecular motors. Computer simulations provide valuable insights into the different conformations available to a particular system that are not accessible using conventional structural techniques. For larger proteins and protein complexes, where a fully atomistic description would be computationally prohibitive, coarse-grained simulation techniques such as Elastic Network Modeling (ENM) are often employed, whereby each atom or group of atoms is linked by a set of springs whose properties can be customized according to the system of interest. Here we compare ENM with a recently proposed continuum model known as Fluctuating Finite Element Analysis (FF...
Research Interests:
ABSTRACT In many polymer processing applications filler particles such as glass beads are added to the polymer matrix. To study the rheology of such multiphase systems we perform direct simulations of the motion of the suspended particles... more
ABSTRACT In many polymer processing applications filler particles such as glass beads are added to the polymer matrix. To study the rheology of such multiphase systems we perform direct simulations of the motion of the suspended particles when subjected to an external linear flow, such as simple shear or planar extensional flow. The method uses a Lagrangian finite element grid that deforms with fluid combined with a quotient representation of the periodic computational domain. For shear flow we show that one can predict the viscometric properties of the suspension for shear thining fluid by using a simple shifting model. For planar extensional flow it is found that adding particle suppressed the extend of strain hardening in strongly strain-hardening fluids.
Research Interests:
ABSTRACT This paper describes a novel numerical method for simulating time-dependent flows of viscoelastic fluids. The method uses Lagrangian finite elements that move with the fluid, and is particularly well suited to problems involving... more
ABSTRACT This paper describes a novel numerical method for simulating time-dependent flows of viscoelastic fluids. The method uses Lagrangian finite elements that move with the fluid, and is particularly well suited to problems involving liquid-air interfaces, such as those found in many coating applications. This method is used study the stretching of a viscoelastic filament.
Research Interests:
A novel numerical method for simulating time-dependent flow of viscoelastic fluids derived from dumbbell models is described. The constitutive equation is solved in a co-deforming frame, where the natural time-derivative is the... more
A novel numerical method for simulating time-dependent flow of viscoelastic fluids derived from dumbbell models is described. The constitutive equation is solved in a co-deforming frame, where the natural time-derivative is the upper-convected derivative. Mesh reconnection is achieved using a variant of Delaunay triangulation. The velocity and pressure are found via a finite element solution of the momentum equations. The
Research Interests:
Research Interests:
ABSTRACT The phenomenon of the negative wake behind a sphere sedimenting through a viscoelastic fluid is investigated. It is shown that there are two competing viscoelastic forces at work in this flow. The relaxation downstream of shear... more
ABSTRACT The phenomenon of the negative wake behind a sphere sedimenting through a viscoelastic fluid is investigated. It is shown that there are two competing viscoelastic forces at work in this flow. The relaxation downstream of shear stresses generated near the side of the sphere drives a flow directed away from the sphere, giving rise to a negative wake. This force is opposed by the extensional stresses generated in the extensional flow at the rear of the sphere, which drives a flow towards the sphere producing an extended wake. The parameter controlling the balance between these forces is the extensibility of the polymer, which limits the extensional viscosity, with high extensibility producing an extended wake and smaller values giving negative wakes.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
ABSTRACT The sedimentation of a small dense sphere through a suspension of neutrally buoyant fibres is investigated via a numerical simulation technique that includes both fibre–fibre contact forces and long-range hydrodynamic... more
ABSTRACT The sedimentation of a small dense sphere through a suspension of neutrally buoyant fibres is investigated via a numerical simulation technique that includes both fibre–fibre contact forces and long-range hydrodynamic interactions. In situations where the diameter of the sphere is smaller than the length of the fibres, calculations that exclude the effect of contacts between fibres severely underestimate the drag force on the sphere measured in experiments. By including fibre–fibre contacts in our simulations we are to able to account for this discrepancy, and also the strong dependence of the drag on the initial orientation of the fibres. At low and moderate values of nL3, where n is the number of fibres per unit volume and L the fibre length, hydrodynamic interactions are found to be important in moderating the effect of contacts between fibres.