ORCID Profile
0000-0001-5236-1850
Current Organisation
University Of Strathclyde
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Publisher: Springer Science and Business Media LLC
Date: 2008
DOI: 10.1140/EPJE/I2007-10262-8
Abstract: A single film (typical of a film in a foam) moving in a confined geometry (i.e. confined between closely spaced top and bottom plates) is analysed via the viscous froth model. In the first instance the film is considered to be straight (as viewed from above the top plate) but is not flat. Instead it is curved (with a circular arc cross-section) in the direction across the confining plates. This curvature leads to a maximal possible steady propagation velocity for the film, which is characterised by the curved film meeting the top and bottom plates tangentially. Next the film is considered to propagate in a channel (i.e. between top and bottom plates and sidewalls, with the sidewall separation exceeding that of the top and bottom plates). The film is now curved along as well as across the top and bottom plates. Curvature along the plates arises from viscous drag forces on the channel sidewall boundaries. The maximum steady propagation velocity is unchanged, but can now also be associated with films meeting channel sidewalls tangentially, a situation which should be readily observable if the film is viewed from above the top plate. Observed from above, however, the film need not appear as an arc of a circle. Instead the film may be relatively straight along much of its length, with curvature pushed into boundary layers at the sidewalls.
Publisher: IOP Publishing
Date: 22-01-2010
Publisher: Elsevier BV
Date: 05-2011
Publisher: AIP Publishing
Date: 03-2014
DOI: 10.1063/1.4868039
Abstract: The stability of a thread of fluid deposited on a flat solid substrate is studied numerically by means of the Finite Element Method in combination with an Arbitrary Lagrangian-Eulerian technique. A good agreement is observed when our results are compared with predictions of linear stability analysis obtained by other authors. Moreover, we also analysed the influence of inertia for different contact angles and found that inertia strongly affects the growth rate of the instability when contact angles are large. By contrast, the wave number of the fastest growing mode does not show important variations with inertia. The numerical technique allows us to follow the evolution of the free surface instability until comparatively late stages, where the filament begins to break into droplets. The rupture pattern observed for several cases shows that the number of principal droplets agrees reasonably well with an estimation based on the fastest growing modes.
Publisher: Elsevier BV
Date: 07-2020
Publisher: AIP Publishing
Date: 06-1998
DOI: 10.1063/1.869656
Abstract: A temperature gradient is applied along a fluid filled slot. A basic state is considered where the slot is subject to thermocapillary forces and vertical mean gravity, each of which produces a parallel flow and a vertical advected temperature gradient, and is also subject to streamwise mean gravity, which will make the applied temperature stratification either stable or unstable. When this basic state is perturbed by jitter imposed in the spanwise direction, normal to the plane of the basic flow, the resulting fluid motion is three dimensional. The flow and temperature fields are found to have a simple functional dependence on streamwise and spanwise coordinates, but retain a complicated dependence on vertical coordinate. Perturbation equations describing the vertical variation of these fields are derived when the jitter is weak. At first order in the spanwise jitter, there is a time periodic spanwise-streamwise circulation around the slot. As this circulation also advects heat, it produces spanwise temperature gradients, enabling thermocapillarity and vertical gravity to generate subsidiary spanwise flows. At next order in the weak spanwise jitter, parallel streamwise flows are encountered, along with streamwise and vertical temperature gradients. In most parameter regimes these are opposed to the flow and temperature fields in the basic state. A thorough parametric investigation is performed where the weak spanwise jitter equations are solved, assuming for simplicity that streamwise gravity is absent. This leads to comparatively simple polynomial solutions in vertical coordinate for the various fields. A large number of parameters can still affect the solutions, however, and a detailed parametric investigation is performed. Interesting behavior is found at small Biot number, with trapping of heat producing large temperatures in the slot and large subsidiary flows. The spanwise to streamwise aspect ratio is another influential parameter, since geometric constraints encountered at extreme values of this ratio suppress certain velocity components of the flow and enhance others, thereby suppressing or enhancing temperature advection. These advected temperature fields themselves produce subsidiary velocities and subsidiary temperatures, which can exhibit a subtle and often counterintuitive dependence on the spanwise-streamwise aspect ratio.
Publisher: Elsevier BV
Date: 10-2019
Publisher: AIP Publishing
Date: 06-1998
DOI: 10.1063/1.869655
Abstract: A temperature gradient is applied along a fluid filled slot with a flat upper interface, establishing flow via thermocapillarity and/or buoyancy. There is a known parallel flow along the slot, in which the fluid velocity varies vertically, and there is a known convected temperature profile. This parallel flow is then subjected to gravitational modulation or “jitter” which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, analytic solutions for velocity and temperature profiles are obtained for jitter of arbitrary litude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direction generates vorticity due to coupling with the applied horizontal temperature gradient. This alternately cooperates or competes with the steady basic flow over a cycle of the modulation, but does not qualitatively change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected temperature gradients and so is important when the basic flow is sufficiently strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarity alone, by vertical gravity alone or by a mixture of thermocapillarity and vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycle between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal thermal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular litudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Rayleigh-Bénard cells.
Publisher: Elsevier BV
Date: 11-2023
Publisher: Elsevier BV
Date: 05-2015
Publisher: The Royal Society
Date: 2021
Abstract: The pressure-driven growth model has been employed to study a propagating foam front in the foam-improved oil recovery process. A first-order solution of the model proves the existence of a concave corner on the front, which initially migrates downwards at a well defined speed that differs from the speed of front material points. At later times, however, it remains unclear how the concave corner moves and interacts with points on the front either side of it, specifically whether material points are extracted from the corner or consumed by it. To address these questions, a second-order solution is proposed, perturbing the aforementioned first-order solution. However, the perturbation is challenging to develop, owing to the nature of the first-order solution, which is a similarity solution that exhibits strong spatio-temporal non-uniformities. The second-order solution indicates that the corner’s vertical velocity component decreases as the front migrates and that points initially extracted from the front are subsequently consumed by it. Overall, the perturbation approach developed herein demonstrates how early-time similarity solutions exhibiting strong spatio-temporal non-uniformities break down as time proceeds.
Publisher: Cambridge University Press (CUP)
Date: 15-10-2002
DOI: 10.1017/S0022112002002045
Abstract: A shallow fluid-filled cavity with a longitudinal applied temperature gradient is subjected to spanwise accelerations ( g -jitter) representing the space-based microgravity environment. A simplified slot model is introduced to describe the buoyancy-driven flow and advected temperature fields produced in the cavity. Numerical solutions indicate that boundary layer behaviour can manifest itself in the limit of strong g -jitter (large Rayleigh number Ra ). However, boundary layer thicknesses do not obey the conventional Ra −1/4 scaling that typically arises in free thermal convection problems. This anomalous scaling results from the three-dimensional complexity of the flow and advected temperature fields, which are not themselves produced by a single fixed applied temperature change. Three different regimes are identified at large Rayleigh number characterized by the shapes of the advected temperature profiles. These regimes are selected according to the values of the Biot number Bi and an aspect ratio parameter. Simple models are presented of the boundary layer behaviour which reproduce, in each regime, the numerically predicted scalings for boundary layer thickness and advected temperature. These models give a succinct overall picture of the slot behaviour in the buoyancy-dominated limit.
Publisher: The Royal Society
Date: 12-2018
Abstract: A mathematical model formulated as a system of Hamilton–Jacobi equations describes implicitly the propagation of a foam–liquid front in an oil reservoir, as the zero-level set of the solution variable. The conceptual model is based on the ‘pressure-driven growth’ model in Lagrangian coordinates. The Eulerian mathematical model is solved numerically, where the marching is done via a finite volume scheme with an upwind flux. Periodic reinitialization ensures a more accurate implicit representation of the front. The numerical level set contour values are initially formed to coincide with an early time asymptotic analytical solution of the pressure-driven growth model. Via the simulation of the Eulerian numerical model, numerical data are obtained from which graphical representations are generated for the location of the propagating front, the angle that the front normal makes with respect to the horizontal and the front curvature, all of which are compared with the Lagrangian model predictions. By making this comparison, it is possible to confirm the existence of a concavity in the front shape at small times, which physically corresponds to an abrupt reorientation of the front over a limited length scale.
Publisher: Informa UK Limited
Date: 21-12-2007
Publisher: Springer Science and Business Media LLC
Date: 09-2000
Publisher: Elsevier BV
Date: 08-2021
Publisher: Springer Science and Business Media LLC
Date: 2018
DOI: 10.1140/EPJE/I2018-11618-7
Abstract: The pressure-driven growth model for advance of a foam front through an oil reservoir during foam improved oil recovery is considered: specifically the limit of strong heterogeneity in the reservoir permeability is treated, such that permeability variation with depth more than outweighs the tendency of the net pressure driving the front to decay with depth. This means that the fastest moving part of the front is not at the top of the solution domain, but rather somewhere in the interior. Moreover the location of the foam front on the top boundary of the system can no longer be specified as a boundary condition, but instead must be determined as part of the solution of the problem. Numerical solutions obtained from the pressure-driven growth model under these circumstances are compared with approximate analytic solutions. An early-time approximate solution is found to break down remarkably quickly (far more quickly than breakdown would occur in the analogous homogeneous system). Numerical solutions agree much better with local quasi-static solutions centred about local maxima in the front shape, each local maximum corresponding to a depth within the reservoir at which a high permeability stratum is found. These in idual local solutions meet together at sharp concave corners to cover the entire depth of the foam front. As time continues to progress however, the system evolves towards a long-time, global quasi-static solution, corresponding to the fastest moving of the aforementioned local maxima. Additional key features of the predicted front shapes are elucidated. The foam front is found to meet the top boundary obliquely despite an established convention in pressure-driven growth that the front and top boundary should meet at right angles. In addition, at each sharp concave corner, discontinuous jumps are predicted in the path length that material points travel to reach either side of the corner. Moreover the long-time, global quasi-static solution is found to admit smooth concavities, as opposed to the aforementioned sharp concave corners, which only tend to be prominent earlier on.
Publisher: American Chemical Society (ACS)
Date: 20-12-2019
Publisher: Elsevier BV
Date: 06-2011
Publisher: Elsevier BV
Date: 02-2004
Publisher: Springer Science and Business Media LLC
Date: 04-2016
DOI: 10.1140/EPJE/I2016-16042-5
Abstract: The pressure-driven growth model is considered, describing the motion of a foam front through an oil reservoir during foam improved oil recovery, foam being formed as gas advances into an initially liquid-filled reservoir. In the model, the foam front is represented by a set of so-called "material points" that track the advance of gas into the liquid-filled region. According to the model, the shape of the foam front is prone to develop concave sharply curved concavities, where the orientation of the front changes rapidly over a small spatial distance: these are referred to as "concave corners". These concave corners need to be propagated differently from the material points on the foam front itself. Typically the corner must move faster than those material points, otherwise spurious numerical artifacts develop in the computed shape of the front. A propagation rule or "speed up" rule is derived for the concave corners, which is shown to be sensitive to the level of anisotropy in the permeability of the reservoir and also sensitive to the orientation of the corners themselves. In particular if a corner in an anisotropic reservoir were to be propagated according to an isotropic speed up rule, this might not be sufficient to suppress spurious numerical artifacts, at least for certain orientations of the corner. On the other hand, systems that are both heterogeneous and anisotropic tend to be well behaved numerically, regardless of whether one uses the isotropic or anisotropic speed up rule for corners. This comes about because, in the heterogeneous and anisotropic case, the orientation of the corner is such that the "correct" anisotropic speed is just very slightly less than the "incorrect" isotropic one. The anisotropic rule does however manage to keep the corner very slightly sharper than the isotropic rule does.
Publisher: Elsevier BV
Date: 03-2017
DOI: 10.1016/J.JCIS.2016.12.015
Abstract: Foams demonstrate great potential for displacing fluids in porous media which is applicable to a variety of subsurface operations such as the enhanced oil recovery and soil remediation. The application of foam in these processes is due to its unique ability to reduce gas mobility by increasing its effective viscosity and to ert gas to un-swept low permeability zones in porous media. The presence of oil in porous media is detrimental to the stability of foams which can influence its success as a displacing fluid. In the present work, we have conducted a systematic series of experiments using a well-characterised porous medium manufactured by 3D printing technique to evaluate the influence of oil on the dynamics of foam displacement under different boundary conditions. The effects of the type of oil, foam quality and foam flow rate were investigated. Our results reveal that generation of stable foam is delayed in the presence of light oil in the porous medium compared to heavy oil. Additionally, it was observed that the dynamics of oil entrapment was dictated by the stability of foam in the presence of oil. Furthermore, foams with high gas fraction appeared to be less stable in the presence of oil lowering its recovery efficiency. Pore-scale inspection of foam-oil dynamics during displacement revealed formation of a less stable front as the foam quality increased, leading to less oil recovery. This study extends the physical understanding of oil displacement by foam in porous media and provides new physical insights regarding the parameters influencing this process.
Publisher: Informa UK Limited
Date: 06-2003
Publisher: Elsevier BV
Date: 05-2015
Publisher: ASME International
Date: 02-2012
DOI: 10.1115/1.4005668
Abstract: The printing of a thin line of liquid onto a moving flat solid substrate was studied numerically. For a fixed value of the Capillary number, the window of steady state deposition was explored in terms of the substrate-nozzle gap and flow rate parameter space for two nozzle configurations: a nozzle pointing vertically at the plate and a nozzle slightly tilted towards the substrate motion direction. A lower limit for the flow rate was found, below which no steady state solutions could be obtained. This minimum flow rate increases as the nozzle stand-off and the nozzle tilting do. Solutions near this lower flow rate boundary were stable under a flow rate perturbation. The process was also studied experimentally and the measurements were compared with the corresponding numerical simulations, giving a fairly good agreement, except in the advancing front deposition region.
Publisher: Elsevier BV
Date: 05-2010
Publisher: Elsevier BV
Date: 08-2013
Publisher: Elsevier BV
Date: 09-2017
Publisher: Springer Science and Business Media LLC
Date: 18-02-2021
DOI: 10.1007/S11242-021-01562-W
Abstract: Liquid drainage within foam is generally described by the foam drainage equation which admits travelling wave solutions. Meanwhile, Richards’ equation has been used to describe liquid flow in unsaturated soil. Travelling wave solutions for Richards equation are also available using soil material property functions which have been developed by Van Genuchten. In order to compare and contrast these solutions, the travelling waves are expressed as dimensionless height, $$ {\\hat{\\xi }} $$ ξ ^ , versus moisture content, $$ \\varTheta $$ Θ . For low moisture content, $$ {{\\hat{\\xi }}} $$ ξ ^ exhibits an abrupt change away from the dry state in Richards equation compared to a much more gradual change in foam drainage. When moisture content nears saturation, $$ {\\hat{\\xi }} $$ ξ ^ reaches large values (i.e. $$ {\\hat{\\xi }} \\gg 1 $$ ξ ^ ≫ 1 ) for both Richards equation and foam drainage, implying a gradual approach of $$ \\varTheta $$ Θ towards the saturated state. The $$ {\\hat{\\xi }} $$ ξ ^ values in Richards equation tend, however, to be larger than those in the foam drainage equation, implying an even more gradual approach towards saturation. The reasons for the difference between foam drainage and Richards equation solutions are traced back to soil material properties and in particular a soil specific parameter “ m ” which is determined from the soil-water retention curve.
Publisher: American Chemical Society (ACS)
Date: 16-12-2022
Publisher: ASME International
Date: 09-1999
DOI: 10.1115/1.2823520
Abstract: A model is developed describing a novel ink jet printer driven by a piezoelectric component used to eject a fluid droplet through a rubber valve. The model is analyzed to address specific printer design issues. Rapid droplet production and efficient conversion of piezoelectric energy to droplet kinetic energy are ensured by suitable choices of the ejector geometry and the voltage step used to produce the droplet. A parameter regime is found in which a resonance prevents the valve from closing properly, and this particular regime must be avoided for correct printer operation. By choosing a suitable voltage signal after the production of an ink droplet, the device is returned rapidly to its initial or quiescent state.
Publisher: Elsevier BV
Date: 06-2011
Publisher: Cambridge University Press (CUP)
Date: 10-01-1995
DOI: 10.1017/S0022112095000176
Abstract: Care is needed with algorithms for computer simulations of the Brownian motion of complex systems, such as colloidal and macromolecular systems which have internal degrees of freedom describing changes in configuration. Problems can arise when the diffusivity or the inertia changes with the configuration of the system. There are some problems in replacing very stiff bonds by rigid constraints. These problems and their resolution are illustrated by some artificial models firstly in one dimension, then in the neighbourhood of an ellipse in two dimensions and finally for the trimer polymer molecule.
Publisher: Elsevier BV
Date: 07-2022
Publisher: Elsevier BV
Date: 09-2013
Publisher: The Royal Society
Date: 02-2022
Abstract: A charged oil droplet advancing into a charged capillary is considered, assuming the special case in which charges are opposite and equal. The droplet is surrounded by an aqueous phase that wets the capillary wall, such that a thin film adjacent to the wall is laid down as the droplet advances. Electro-osmotic conjoining pressures contrive to make the film even thinner than in an uncharged case. The pressure drop needed to drive the droplet along is examined. The pressure drop is dominated by capillarity but contains electro-osmotic and viscous corrections. The viscous correction is shown to be remarkably insensitive to the presence of electro-osmotic effects. The electro-osmotic pressure correction is negative, reflecting work done by the electro-osmotic conjoining pressure as film is laid down. The negative electro-osmotic correction to pressure drop can far exceed the positive viscous correction. As a result, in the presence of conjoining pressures, a droplet can be driven along a capillary channel with even less pressure drop than is seen for a static uncharged droplet.
Publisher: Elsevier BV
Date: 05-2014
Publisher: ASME International
Date: 2000
DOI: 10.1115/1.1852474
Abstract: Oscillatory incompressible fluid flow with a free surface occurs in an inkjet print head. Due to complex physical fluid behavior, numerical simulations have been a common approach to characterize the pressure and velocity development in time and space. However, the cost of a numerical approach is high in terms of computational time such that approximate analytic approaches have been developed. In this paper, an approximate analytic solution for a tapered nozzle section is described with a proper downstream boundary condition and the physical behavior of the meniscus deformation is modeled with a simple “window” theory.
Publisher: Springer Science and Business Media LLC
Date: 08-2002
DOI: 10.1140/EPJE/I2002-10042-0
Abstract: Foam drainage is considered in a froth flotation tank with a sloping weir. The drainage is shown to be gravity dominated in most of the foam, except for thin boundary layers at the base of the froth, and along the sloping weir. The mathematical reason for the boundary layers is that capillary suction is a much weaker effect than gravity, but cannot be ignored altogether, because it represents a singular perturbation. The relative weakness of capillary suction with respect to gravity is represented by a key dimensionless parameter, denoted K, which satisfies K<<1. The volumetric flow at any point along the weir boundary layer is the accumulation of all liquid that has rained onto the weir above the point in question: typically, this flow is linear in distance measured downward from the weir lip. All liquid raining onto the weir is ultimately returned to the pulp phase as a high-speed jet. The jet velocity scales with the (2/3) power of distance from the weir lip, and is O(K(-2/3)) times larger than the typical velocity in the gravity-dominated flow in the bulk of the flotation tank. The liquid volume fraction in the jet is likewise O(K(-2/3)) larger than that in the bulk. Across the jet, the foam exhibits a known profile of liquid fraction vs. distance from the weir: this is known as the equilibrium profile. The foam requires a distance equivalent to O(K(4/3)) weir lengths to dry out significantly from the wetness value on the weir, but a larger O(K) distance to fall back to a wetness comparable with that in the bulk of the froth.
Publisher: Elsevier BV
Date: 11-2018
Publisher: Elsevier BV
Date: 22-05-190728634
Publisher: Cambridge University Press (CUP)
Date: 20-06-2014
DOI: 10.1017/JFM.2014.287
Abstract: During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.
Publisher: Elsevier BV
Date: 10-2013
Publisher: Elsevier BV
Date: 12-2016
Publisher: Elsevier BV
Date: 12-2023
Publisher: Elsevier BV
Date: 02-2016
Publisher: Cambridge University Press (CUP)
Date: 05-09-2017
DOI: 10.1017/JFM.2017.541
Abstract: The pressure-driven growth model is used to determine the shape of a foam front propagating into an oil reservoir. It is shown that the front, idealised as a curve separating surfactant solution downstream from gas upstream, can be sub ided into two regions: a lower region (approximately parabolic in shape and consisting primarily of material points which have been on the foam front continuously since time zero) and an upper region (consisting of material points which have been newly injected onto the foam front from the top boundary). Various conjectures are presented for the shape of the upper region. A formulation which assumes that the bottom of the upper region is oriented in the same direction as the top of the lower region is shown to fail, as (despite the orientations being aligned) there is a mismatch in location: the upper and lower regions fail to intersect. Alternative formulations are developed which allow the upper region to curve sufficiently so as to intersect the lower region. These formulations imply that the lower and upper regions (whilst in idually being of a convex shape as seen from downstream) actually meet in a concave corner, contradicting the conventional hypothesis in the literature that the front is wholly convex. The shape of the upper region as predicted here and the presence of the concave corner are independently verified via numerical simulation data.
Publisher: Elsevier BV
Date: 07-2023
Publisher: Elsevier BV
Date: 09-2009
Publisher: The Royal Society
Date: 07-2023
Abstract: A two-dimensional foam system comprised of three bubbles is studied via dynamic simulations with the viscous froth model. The bubbles are arranged in a staircase configuration and move along a channel due to an imposed driving back pressure. Depending on the bubble size relative to channel size, the three-bubble system can undergo topological transformations (as for a simpler staircase structure, known as the simple lens) or it can reach a geometrically invariant migrating state (as for an infinite staircase structure). A methodology used previously determined the system evolution up to the first topological transformation, but evolution beyond this was not studied before. To address this, unsteady state three-bubble simulations are realized here, extending beyond the first transformation. For sufficiently high imposed back pressures, a sequence of topological transformations occurs before a steadily migrating shape is reached, typically in a topology such that an equal number of films connect to both channel walls.
Publisher: Elsevier BV
Date: 09-2015
Publisher: Elsevier BV
Date: 04-2008
Publisher: Society of Rheology
Date: 05-2012
DOI: 10.1122/1.3687442
Publisher: Elsevier BV
Date: 11-2023
Publisher: Canadian Science Publishing
Date: 10-2001
DOI: 10.1139/P01-114
Abstract: Plateau's rule states that bubble lamellae in a foam meet at equal angles. Attempts to rationalize this rule via a naive "force along a tangent line" argument employing vertex variables are shown to fail, since they do not properly account for bubble volume constraints. Indeed Plateau's rule appears to make a foam system overdetermined, in the sense that there seem to be more constraints than available variables. The resolution of this paradox is that the angle constraints of Plateau's rule cannot be regarded as all independent. This is explained in detail for the two-bubble system in two dimensions. By exploiting just pressure-curvature relations and geometry, it is shown that the lamella joining the two bubbles is obliged to subtend precisely the angle needed to satisfy Plateau's rule and minimize energy. Speculations are offered for a many bubble foam. PACS Nos.: 68.10Cr, 68.15+e
Publisher: Elsevier BV
Date: 07-2019
Publisher: Elsevier BV
Date: 04-2016
Publisher: American Association of Physics Teachers (AAPT)
Date: 02-2001
DOI: 10.1119/1.1289211
Abstract: A large particle moves through a sea of small particles. On the microscale, all particle collisions are elastic. However, on the macroscale, where only the large particle is properly resolved, dissipative forces and fluctuating random forces are observed. These forces are connected by a fluctuation–dissipation theorem proved in two different ways, first via statistical mechanics, and second from fundamental classical mechanical principles of momentum and energy conservation. The novel classical mechanics proof elucidates the relation between micro- and macroscale behaviors, and offers new insights into the physics behind the fluctuation–dissipation result.
Publisher: Springer Science and Business Media LLC
Date: 06-2015
DOI: 10.1140/EPJE/I2015-15067-6
Abstract: A model, called pressure-driven growth, is analysed for propagation of a foam front through an oil reservoir during improved oil recovery using foam. Numerical simulations of the model predict, not only the distance over which the foam front propagates, but also the instantaneous front shape. A particular case is studied here in which the pressure used to drive the foam along is suddenly increased at a certain point in time. This transiently produces a concave front shape (seen from the domain ahead of the front): such concavities are known to be delicate to handle numerically. As time proceeds however, the front evolves back towards a convex shape, and this can be predicted by a long-time asymptotic analysis of the model. The increase in driving pressure is shown to be beneficial to the improved oil recovery process, because it gives a more uniform sweep of the oil reservoir by the foam.
Publisher: Elsevier BV
Date: 2023
Publisher: Cambridge University Press (CUP)
Date: 18-03-2019
DOI: 10.1017/JFM.2019.126
Abstract: A model developed by Wilmott et al. ( J. Fluid Mech. , vol. 841, 2018, pp. 310–350) for the advance of a charged oil droplet along a charged capillary pore is considered. The oil droplet is surrounded by an aqueous phase filling the pore, and the model considers a uniformly curved capillary static droplet front plus an aqueous thin film separating the body of the oil droplet from the capillary wall, with these two regions being joined by a transition region. The methodology follows a classical asymptotic approach proposed by Bretherton ( J. Fluid Mech. , vol. 10, 1961, pp. 166–188) but incorporates additional electro-osmotic effects (specifically an electro-osmotic disjoining tension) due to the charged surfaces. A number of dimensionless parameters control the model’s behaviour, of which the most important is denoted $\\unicode[STIX]{x1D712}^{\\prime }$ and represents the ratio between the ‘nominal’ thickness of the aqueous film (as determined neglecting any electrostatic effects) and the Debye length within the film, which is sensitive to ion concentrations and hence to salinity. When $\\unicode[STIX]{x1D712}^{\\prime }$ is large, electro-osmotic effects are screened and Bretherton’s classical results are recovered. However as $\\unicode[STIX]{x1D712}^{\\prime }$ decreases, electro-osmotic effects come into play and the film becomes much thicker than Bretherton’s prediction to ensure that screening effects are not altogether lost, and also there is a noticeable increase in the pressure needed to drive the droplet front along. These results apply with minor variations in the case of singly charged surfaces (charge on either oil or on the capillary wall), oil and wall surfaces with like charges, or oil and wall surfaces with opposite but unequal charges. However in the case of opposite and equal charges, the system’s behaviour changes dramatically. There is now a conjoining electro-osmotic pressure rather than a disjoining tension, the film becomes thinner than the analogous Bretherton film, and the pressure needed to drive the droplet front along decreases. Surprisingly in this case, for sufficiently small $\\unicode[STIX]{x1D712}^{\\prime }$ , the work done by the conjoining pressure can exceed the work done against viscous dissipation, meaning the pressure required to drive the droplet front is not just smaller than in Bretherton’s predictions but also slightly less than would be estimated based on capillary forces alone. Although the main effect of reducing salinity is to increase Debye length and hence reduce $\\unicode[STIX]{x1D712}^{\\prime }$ , salinity also affects surface charges. A situation is explored whereby reducing salinity affects charges, producing a switch from disjoining tensions to conjoining pressures and back again: this leads to a non-monotonic response in film thickness and pressure required to drive the droplet front along.
Publisher: Elsevier BV
Date: 08-2005
Publisher: Elsevier BV
Date: 08-2005
Publisher: Springer Science and Business Media LLC
Date: 14-03-2023
DOI: 10.1007/S11242-023-01925-5
Abstract: With a view towards modelling the foam improved oil recovery process, fractional flow theory is used to study the dynamics of a foam as it propagates in a porous medium that is initially filled with liquid. In particular, a case is studied whereby, at a certain time, the net pressure driving the foam is decreased below the hydrostatic pressure at depth, leading to a local change in the flow direction. This is known as flow reversal. In both forward and reverse flow, the boundary between foamed gas and liquid is found as a discontinuous jump in liquid saturation. Over a certain thickness in the neighbourhood of this discontinuity, foam is finely textured, and the mobility of foamed gas drops by orders of magnitude relative to either pure gas or pure liquid. In reverse flow, however, the foam mobility itself and also the thickness over which low mobilities apply might differ from the forward flow case. Fractional flow theory reveals that the thickness of the low mobility region, and hence the resistance to motion that it presents, increases directly proportional to the distance travelled. Previous studies recognised this, but assumed the thickness of this region to be just a small fraction of the distance travelled by the discontinuity. Here, however, we demonstrate that the extent of the low mobility region, in both forward and reverse flow, accounts for a considerable fraction of the distance travelled by the foam, despite what was assumed in previous works.
Publisher: AIP Publishing
Date: 08-1998
DOI: 10.1063/1.869707
Abstract: A slot with applied temperature stratification is considered when mean gravity is directed along its length and weak quasistatic jitter is applied in the spanwise direction, but when there is no component of gravity in the vertical. The behavior of the slot is governed by a number of factors: The sense of the mean gravity with respect to the applied stratification, the spanwise and lengthwise Rayleigh numbers, the Prandtl and Biot numbers, and the spanwise–lengthwise aspect ratio of the slot. A perturbation expansion of the governing equations is performed for weak spanwise jitter. At the first order of perturbation there is a circulation around the slot, producing an advected temperature field with spanwise gradients. At second order there are inflows or outflows in both the spanwise and lengthwise directions, along with a vertical redistribution of fluid. There is also a temperature field with lengthwise gradients, which typically competes with the applied temperature gradient. Equations are derived governing the vertical structure of all these fields and are solved in terms of a set of special basis functions. A parametric study is performed for the solutions. When lengthwise buoyancy forces are absent (the lengthwise Rayleigh number is zero), it is comparatively easy to deduce the required fields. However, finite lengthwise Rayleigh numbers couple the momentum and thermal equations thereby affecting the structure of the fields. Interesting behavior is predicted for small Biot numbers, when convected heat is effectively trapped in the slot: Infinitessimal flows can produce finite advected temperatures. The limits of small Biot number and small lengthwise Rayleigh number are found to be noninterchangeable. At large lengthwise Rayleigh number, boundary layers occur for stable applied stratification and layered cellular structures occur for unstable stratification. For the stable case at moderately small Biot number, the temperature jump across the boundary layer is small compared with the depth independent temperature in the bulk. Then by exploiting the boundary layer nature of the solutions, it becomes simple to predict the bulk fluid temperatures, interfacial heat fluxes and the circulations associated with the buoyant flows. Turning to the unstably stratified case, it is demonstrated that runaways can occur at first order in the spanwise jitter, and these correspond to resonant excitation of three-dimensional, stationary, long wave Rayleigh–Bénard modes. It is demonstrated how the Biot number and the spanwise–lengthwise aspect ratio of the slot influence the lengthwise Rayleigh number at which these resonances occur. There is in addition a set of two-dimensional Rayleigh–Bénard modes, which can potentially become excited at second order. When the Biot number and the spanwise–lengthwise aspect ratio are not too large, the Rayleigh numbers corresponding to the two sets of modes are nearly coincident. The second-order system will then be strongly forced near resonance, causing it to have a disproportionately large response.
Publisher: The Royal Society
Date: 06-2022
Abstract: A model developed by Bussonnière & Cantat [ 1 ] is considered for film-to-film surfactant transport around a meniscus within a foam, with the transport rate dependent upon film-to-film tension difference. The model is applied to the case of a five-film device, in which motors are used to compress two peripheral films on one side of a central film and to stretch another two peripheral films on the central film’s other side. Moreover, it is considered that large amounts of compression or stretch are imposed on peripheral films, and also that compression or stretch might be imposed at high velocities (relative to a characteristic velocity associated with physico-chemical properties of the foam films themselves). The actual strain that results on elements within each film might differ from the imposed strain, with the instantaneous film length coupled to the actual strain determining the amount of surfactant currently on each film (and hence also the amount of surfactant that has transferred either from or onto films). Quite distinct surfactant transport behaviour is predicted for the stretched film compared with the compressed one. In particular, when a film is stretched sufficiently at high enough velocity, surfactant flux onto it is predicted to become extremely ‘plastic’, increasing significantly.
Publisher: Elsevier BV
Date: 12-2013
Publisher: The Royal Society
Date: 02-2022
Abstract: The viscous froth model is used to predict rheological behaviour of a two-dimensional (2D) liquid-foam system. The model incorporates three physical phenomena: the viscous drag force, the pressure difference across foam films and the surface tension acting along them with curvature. In the so-called infinite staircase structure, the system does not undergo topological bubble neighbour-exchange transformations for any imposed driving back pressure. Bubbles then flow out of the channel of transport in the same order in which they entered it. By contrast, in a simple single bubble staircase or so-called lens system, topological transformations do occur for high enough imposed back pressures. The three-bubble case interpolates between the infinite staircase and simple staircase/lens. To determine at which driving pressures and at which velocities topological transformations might occur, and how the bubble areas influence their occurrence, steady-state propagating three-bubble solutions are obtained for a range of bubble sizes and imposed back pressures. As an imposed back pressure increases quasi-statically from equilibrium, complex dynamics are exhibited as the systems undergo either topological transformations, reach saddle-node bifurcation points, or asymptote to a geometrically invariant structure which ceases to change as the back pressure is further increased.
Publisher: Springer Science and Business Media LLC
Date: 07-11-2022
Publisher: Elsevier BV
Date: 11-2007
Publisher: Acoustical Society of America (ASA)
Date: 27-08-2003
DOI: 10.1121/1.1603769
Abstract: A simple oscillatory, slightly compressible, fluid flow model in a thick-walled piezoelectric tube used in a drop-on-demand inkjet print head is developed from the point of view of fluid-structure interaction to take account of pressure wave propagation and pressure loading opposing wall motion. A frequency sweep is performed computationally using the model revealing the first acoustic fluid-structure resonance frequency and the influence of fluid viscosity. The validity of the model, with given information on the speed of sound in a fluid, is evaluated by comparing the theoretically predicted resonance frequency to the experimentally measured resonance frequency. In addition, the intrinsic speed of sound can be easily computed using the measured acoustic resonance frequency and this computed speed of sound agrees closely with speeds of sound reported in the literature.
Publisher: Elsevier BV
Date: 12-2013
Publisher: Springer Science and Business Media LLC
Date: 12-2001
Publisher: Elsevier BV
Date: 07-2009
Publisher: Elsevier BV
Date: 08-2004
Publisher: Informa UK Limited
Date: 06-2006
Publisher: Cambridge University Press (CUP)
Date: 10-02-1996
DOI: 10.1017/S0022112096001474
Abstract: Numerical simulations are employed to study the Brownian motion of a bead-rod polymer chain dissolved in a solvent. An investigation is conducted of the relaxation of the stress for an initially straight chain as it begins to coil. For a numerical time step δ t in the simulations, conventional formulae for the stress involve averaging large ± O (1/(δ t ) 1/2 ) contributions over many realizations, in order to yield an O (1) average. An alternative formula for the stress is derived which only contains O (1) contributions, thereby improving the quality of the statistics. For a chain consisting of n rods in a solvent at temperature T, the component of the bulk stress along the initial chain direction arising from tensions in the rods at the initial instant is $k\\hat{T}\\times n(\\frac{1}{3}n^2 + n +\\frac{2}{3})$ . Thus the bead-rod model yields results very different from other polymer models, such as the entropic spring of Flory (1969), which would assign an infinite stress to a fully aligned chain. For rods of length l and beads of friction factor $\\hat{\\zeta}$ the stress decays at first on $O(\\hat{\\zeta}\\hat{l}^2/k\\hat{T}\\times 1/n^2)$ time scales. On longer time scales, this behaviour gives way to a more gradual stress decay, characterized by an $O(k\\hat{T}\\times n)$ stress following a simple exponential decay with an $O(k\\hat{T}/\\hat{\\zeta}\\hat{l}^2\\times 1/n^2)$ rate. Matching these two limiting regimes, a power law decay in time t is found with stress $O(k\\hat{T}\\times n^2\\times (k\\hat{T}\\hat{t}/\\hat{\\zeta}\\hat{l}^2)^{-1/2})$ . The dominant physical processes occurring in these separate short, long and intermediate time regimes are identified.
Publisher: The Royal Society
Date: 08-11-2013
Abstract: The viscous froth model is used to study the evolution of a long and initially straight soap film which is sheared by moving its endpoint at a constant velocity in a direction perpendicular to the initial film orientation. Film elements are thereby set into motion as a result of the shear, and the film curves. The simple scenario described here enables an analysis of the transport of curvature along the film, which is important in foam rheology, in particular for energy-relaxing ‘topological transformations’. Curvature is shown to be transported diffusively along films, with an effective diffusivity scaling as the ratio of film tension to the viscous froth drag coefficient. Computed (finite-length) film shapes at different times are found to approximate well to the semi-infinite film and are observed to collapse with distances rescaled by the square root of time. The tangent to the film at the endpoint reorients so as to make a very small angle with the line along which the film endpoint is dragged, and this angle decays roughly exponentially in time. The computed results are described in terms of a simple asymptotic solution corresponding to an infinite film that initially contains a right-angled corner.
Publisher: Elsevier BV
Date: 02-2009
Publisher: American Chemical Society (ACS)
Date: 04-05-2018
Publisher: Cambridge University Press (CUP)
Date: 04-10-2021
DOI: 10.1017/JFM.2021.690
Abstract: Surfactant transport from foam film to foam film is an essential (yet poorly understood) aspect of the viscoplastic yielding behaviour of flowing foam. Recent experimental and modelling work by Bussonnière & Cantat ( J. Fluid Mech. , vol. 922, 2021, A25) has, however, helped to advance understanding of the relevant surfactant transport processes: the significance of that work is described herein.
Publisher: Elsevier BV
Date: 06-2011
Publisher: Springer Science and Business Media LLC
Date: 15-06-2018
Publisher: Springer Science and Business Media LLC
Date: 07-2012
DOI: 10.1140/EPJE/I2012-12064-3
Abstract: The so-called topological T1 process, during which bubbles within a foam exchange neighbours is studied. The Durand and Stone model (Phys. Rev. Lett., 97, 226101 (2006)) describes the growth of a film that is newly created during the T1 process, and also the evolution of surfactant concentration on this newly created film. Here some characteristic features of the Durand and Stone model (not previously described by Durand and Stone) are elucidated. In particular it is shown that the surfactant concentration on the newly created film is predicted to undergo an extremely rapid initial evolution, which occurs long before the film itself approaches anywhere near its final equilibrium length. Associated with this, the predicted length of the newly created film tends to exhibit an extremely rapid acceleration early on in its growth. An intermediate asymptotic analysis is developed to explain the above model predictions, by focussing on the regime when the film is several times larger than its initial length, but still several times smaller than its final length. A physical explanation is offered for these predictions in terms of slippage between material points instantaneously at the end of the newly created film, and the evolving location of the film endpoint itself: this slippage implies surfactant being transferred onto the newly created film from neighbouring films, overwhelming the amount of surfactant initially present. The implications of these predictions for the likely observations in an experimental study of the T1 process are discussed.
Publisher: Elsevier BV
Date: 02-2006
Publisher: Elsevier BV
Date: 07-2021
Publisher: The Royal Society
Date: 02-2020
Abstract: The viscous froth model for two-dimensional (2D) dissipative foam rheology is combined with Marangoni-driven surfactant redistribution on a foam film. The model is used to study the flow of a 2D foam system consisting of one bubble partially filling a constricted channel and a single spanning film connecting it to the opposite channel wall. Gradients of surface tension arising from film deformation induce tangential flow that redistributes surfactant along the film. This redistribution, and the consequent changes in film tension, inhibit the structure from undergoing a foam-destroying topological change in which the spanning film leaves the bubble behind foam stability is thereby increased. The system’s behaviour is categorized by a Gibbs–Marangoni parameter, representing the ratio between the rate of motion in tangential and normal directions. Larger values of the Gibbs–Marangoni parameter induce greater variation in surface tension, increase the rate of surfactant redistribution and reduce the likelihood of topological changes. An intermediate regime is, however, identified in which the Gibbs–Marangoni parameter is large enough to create a significant gradient of surface tension but is not great enough to smooth out the flow-induced redistribution of surfactant entirely, resulting in non-monotonic variation in the bubble height, and hence in foam stability.
Publisher: Elsevier BV
Date: 2016
DOI: 10.1016/J.JCIS.2015.10.017
Abstract: The relative immobility of foam in porous media suppresses the formation of fingers during oil displacement leading to a more stable displacement which is desired in various processes such as Enhanced Oil Recovery (EOR) or soil remediation practices. Various parameters may influence the efficiency of foam-assisted oil displacement such as properties of oil, the permeability and heterogeneity of the porous medium and physical and chemical characteristics of foam. In the present work, we have conducted a comprehensive series of experiments using customised Hele-Shaw cells filled with either water or oil to describe the effects of foam quality, permeability of the cell as well as the injection rate on the apparent viscosity of foam which is required to investigate foam displacement. Our results reveal the significant impact of foam texture and bubble size on the foam apparent viscosity. Foams with smaller bubble sizes have a higher apparent viscosity. This statement only applies (strictly speaking) when the foam quality is constant. However, wet foams with smaller bubbles may have lower apparent viscosity compared to dry foams with larger bubbles. Furthermore, our results show the occurrence of more stable foam-water fronts as foam quality decreases. Besides, the complexity of oil displacement by foam as well as its destabilizing effects on foam displacement has been discussed. Our results extend the physical understanding of foam-assisted liquid displacement in Hele-Shaw cell which is a step towards understanding the foam flow behaviour in more complex systems such as porous media.
Publisher: Elsevier BV
Date: 09-2015
Publisher: Elsevier BV
Date: 03-2011
Publisher: Cambridge University Press (CUP)
Date: 24-07-2020
DOI: 10.1017/JFM.2020.458
Publisher: American Physical Society (APS)
Date: 13-11-2006
Publisher: The Royal Society
Date: 11-2022
Abstract: A two-dimensional foam system comprised of three bubbles is studied via simulations with the viscous froth model. Bubbles are arranged in a so-called staircase configuration and move along a channel due to imposed driving back pressure. This flowing three-bubble system has been studied previously on the basis that it interpolates between a simpler staircase structure (a simple lens, which breaks up via so-called topological transformations if driven at high pressure) and an infinite staircase (which sustains arbitrarily large driving pressure without breaking). Depending on bubble size relative to channel size, different solution branches for the three-bubble system were found: certain branches terminate (as for the simple lens) in topological transformations and others reach (as for an infinite staircase) a geometrically invariant migrating state. The methodology used previously was, however, a purely steady state one, and hence did not interrogate stability of the various branches, nor the role of imposing different driving pressures upon topological transformation type. To address this, unsteady state three-bubble simulations are realized here. Stable solution branches without topological transformation exist for comparatively low driving pressures. For sufficiently high imposed back pressures, however, topological transformations occur, albeit with imposed pressure now influencing the transformation type.
Publisher: Elsevier BV
Date: 10-2004
Publisher: American Physical Society (APS)
Date: 22-04-2009
Publisher: Elsevier BV
Date: 03-2020
DOI: 10.1016/J.JENVMAN.2019.109996
Abstract: An alternative method was proposed to optimize the treatment process of palm oil mill effluent (POME) in an effort to address the poor removal efficiencies in terms of the chemical and biological oxygen demand (COD and BOD), total suspended solids (TSS) as well as oil and grease (O&G) content in treated POME along with many environmental issues associated with the existing POME treatment process. The elimination of the cooling ponds and the insertion of a dewatering device in the treatment process were recommended. The dewatering device should enhance the anaerobic digestion process by conferring a means of control on the digesters' load. The objective of this study is to identify the optimum solid: liquid ratio (total solids (TS) content) that would generate the maximum amount of biogas with better methane purity consistently throughout the anaerobic digestion of POME, all while improving the treated effluent quality. It was established that a 40S:60L (4.02% TS) was the best performing solid loading in terms of biogas production and methane yield as well as COD, BOD, TSS, and O&G removal efficiencies. Meanwhile, at higher solid loadings, the biogas production is inhibited due to poor transport and mass transfer. It is also speculated that sulfate-reducing bacteria tended to inhibit the biogas production based on the significantly elevated H
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Paul Grassia.