We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a ... more We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a Hele-Shaw channel with a small elevation along its centreline via physical experiment and numerical simulation of a depth-averaged model. For a single-bubble system we establish that, in general, the bubble propagation speed monotonically increases with bubble volume so that two bubbles of different sizes, in the absence of any hydrodynamic interactions, will either coalesce or separate in a finite time. However, our experiments indicate that the bubbles interact and that an unstable two-bubble state is responsible for the eventual dynamical outcome: coalescence or separation. These results motivate us to develop an edge-tracking routine and to calculate these weakly unstable two-bubble steady states from the governing equations. The steady states consist of pairs of ‘aligned’ bubbles that appear on the same side of the centreline with the larger bubble leading. We also discover, through...
Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of ... more Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of a sessile drop of yield-stress fluid on a pre-existing layer of the same fluid under vertical sinusoidal oscillations. We compare the behaviours of molten chocolate and Carbopol which are both shear-thinning with a similar yield stress but exhibit very different elastic properties. We find that these materials spread when the forcing acceleration exceeds a threshold which is determined by the initial deposition process. However, they exhibit very different spreading behaviours: whereas chocolate exhibits slow long-term spreading, the Carbopol drop rapidly relaxes its stress by spreading to a new equilibrium shape with an enlarged footprint. This spreading is insensitive to the history of the forcing. In addition, the Carbopol drop performs large-amplitude oscillations with the forcing frequency, both above and below the threshold. We investigate these viscoelastic oscillations and provide evidence of complex nonlinear viscoelastic behaviour in the vicinity of the spreading threshold. In fact, for forcing accelerations greater than the spreading threshold, our drop automatically adjusts its shape to remain at the yield stress. We discuss how our vibrated-drop experiment offers a new and powerful approach to probing the yield transition in elastoviscoplastic fluids.
The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plate... more The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of non-axisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by [1]. We then employ direct numerical simulations to show that in the parameter regime where the axisymmetrically expanding air bubble is unstable to nonaxisymmetric perturbations, the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of non-unimodal perturbations (e.g. via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed in constant-width Hele-Shaw cells.
We characterise novel propagation modes that occur when semi-infinite air fingers and finite air ... more We characterise novel propagation modes that occur when semi-infinite air fingers and finite air bubbles displace viscous fluid from microchannels. The presence of an axially-uniform rectangular occlusion within a rectangular cross-section leads to a multiplicity of modes, in contrast to the single symmetric mode present in unoccluded channels. For air fingers, the asymmetric 1 , oscillatory 2 and localised modes 3 first identified in millimetric channels persist at the micron-scale, confirming that significant gravitational effects are not necessary to support these states. Sufficiently large finite bubbles exhibit analogous modes with quantitatively similar flow measures, indicating that the physical mechanisms supporting the propagation modes of finite bubbles are the same as those identified for the air fingers 4. In contrast to the air fingers, in which oscillations are always initiated near the finger tip and propagate backwards, oscillations in finite bubbles can arise from either end of the bubble.
Submitted for the DFD13 Meeting of The American Physical Society Can consecutive droplet depositi... more Submitted for the DFD13 Meeting of The American Physical Society Can consecutive droplet deposition yield uniform liquid films? 1 ANNE JUEL, ALICE THOMPSON, CARL TIPTON, ANDREW HAZEL, University of Manchester, MARK DOWLING, Cambridge Display Technology-Ink-jet printing is being used to manufacture highly customizable electronic components through the successional deposition of overlapping droplets of conductive ink onto a substrate. For vanishing contact angles, the fluid drops merge together on the substrate to form a wide, uniform thread. However, in practical operating regimes involving moderate contact angles, the fluid is redistributed to form non-uniform patterns, characterized by the development of an initial wide bulge (larger than any individual drop). This "head" is sometimes followed by a sequence of secondary bulges connected by narrow rivulets. We conduct new experiments with high-speed imaging to examine the morphological development of the thread resulting from the deposition of a moderate number of successive micro-scale drops (< 80) that may form up to two secondary bulges. We demonstrate that the spatial structure of the ink formation resulting from this complex deposition process can be predicted quantitatively with a simple physical model that incorporates contact angle hysteresis. The head formation occurs robustly due to an inviscid mechanism, while the secondary bulge formation arises from viscous effects.
In this fluid dynamics video, we study a two-phase flow in an elastic Hele-Shaw cell that involve... more In this fluid dynamics video, we study a two-phase flow in an elastic Hele-Shaw cell that involves two distinct fluid-and solid-based instabilities: viscous fingering and sheet buckling. We show that the relative importance of the two instabilities is controlled by a single non-dimensional parameter, which provides a measure of the elasticity of the flexible wall. We employ numerical simulations to show that for relatively stiff [soft] walls, the system's behaviour is dominated by viscous fingering [sheet buckling]. Strong interactions between the two instabilities arise in an intermediate regime and lead to the development of extremely complex fingering and buckling patterns.
The development of viscous fingers in circular Hele-Shaw cells is a classical and widely studied ... more The development of viscous fingers in circular Hele-Shaw cells is a classical and widely studied fluid mechanical problem. The introduction of wall elasticity (via the replacement of one of the bounding plates by an elastic membrane) can weaken or even suppress the fingering instability, but it also makes the system susceptible to additional solid-mechanical instabilities. We show that in elastic-walled Hele-Shaw cells that are bounded by sufficiently thin elastic sheets the (fluid-based) viscous fingering instability can arise concurrently with a (solid-based) wrinkling instability. We study the interaction between these distinct instabilities, using a theoretical model that couples the depth-averaged lubrication equations for the fluid flow to the Föppl-von Kármán equations, which describe the deformation of the thin elastic sheet. We employ a linear stability analysis to determine the growth rate of non-axisymmetric perturbations to the axisymmetrically expanding bubble, and perf...
Recent experiments by Pailha et al. [Phys. Fluids 24, 021702 (2012)10.1063/1.3682772] uncovered a... more Recent experiments by Pailha et al. [Phys. Fluids 24, 021702 (2012)10.1063/1.3682772] uncovered a rich array of propagation modes when air displaces oil from axially uniform tubes that have local variations in flow resistance within their cross-sections. The behaviour is particularly surprising because only a single, symmetric mode has been observed in tubes of regular cross-section, e.g., circular, elliptical, rectangular, and polygonal. In this paper, we present experimental results describing a new mode, an asymmetric localised air finger, that persists in the limit of zero propagation speed. We show that the experimental observations are consistent with a model based on capillary static calculations within the tube's cross-section, and the observed bistability is a consequence of the existence of multiple solutions to the Young–Laplace equations. The model also provides an upper bound for the previously reported symmetry-breaking bifurcation [A. de Lózar, A. Heap, F. Box, A....
We show that a simple change in pore geometry can radically alter the behavior of a fluid-displac... more We show that a simple change in pore geometry can radically alter the behavior of a fluid-displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross section can force a transition from a steadily propagating centered finger to a state that exhibits spatial oscillations formed by periodic sideways motion of the interface at a fixed distance behind the moving finger tip. We characterize the dynamics of the oscillations, which suggest that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution.
We study steep capillary-gravity waves that form at the interface between two stably stratified l... more We study steep capillary-gravity waves that form at the interface between two stably stratified layers of immiscible liquids in a horizontally oscillating vessel. The oscillatory nature of the external forcing prevents the waves from overturning, and thus enables the development of steep waves at large forcing. They arise through a supercritical pitchfork bifurcation, characterized by the square root dependence of the height of the wave on the excess vibrational Froude number (W, square root of the ratio of vibrational to gravitational forces). At a critical valueWc, a transition to a linear variation inWis observed. It is accompanied by sharp qualitative changes in the harmonic content of the wave shape, so that trochoidal waves characterize the weakly nonlinear regime, but ‘finger’-like waves form forW≥Wc. In this strongly nonlinear regime, the wavelength is a function of the product of amplitude and frequency of forcing, whereas forW
ester-We report the suppression of interfacial fingering instabilities resulting from the injecti... more ester-We report the suppression of interfacial fingering instabilities resulting from the injection of air into the narrow, fluid-filled gap between two parallel plates (a Hele-Shaw cell), when one of the boundaries is replaced by an elastic membrane. In a rigid cell, if the air is injected at a sufficiently fast flow rate, the interface is unstable, ultimately resulting in the development of a complex dendritic fingers. In the elastic-walled cell, interfacial instabilities develop at much larger air-injection rates because membrane deformations reduce destabilising pressure perturbations ahead of the propagating interface, and fundamentally alter the interfacial pattern that develops. We characterise the dependence of the instability on the parameters of the system, and present simple scaling arguments to explain the experimentally observed behaviour.
We consider the propagation of an air finger into a wide fluid-filled channel with a spatially va... more We consider the propagation of an air finger into a wide fluid-filled channel with a spatially varying depth profile. Our aim is to understand the origin of the multiple coexisting families of both steady and oscillatory propagating fingers previously observed in experiments in axially uniform channels each containing a centred step-like occlusion. We find that a depth-averaged model can reproduce all the finger propagation modes observed experimentally. In addition, the model reveals new modes for symmetric finger propagation. The inclusion of a spatially variable channel depth in the depth-averaged equations leads to: (i) a variable mobility coefficient within the fluid domain due to variations in viscous resistance of the channel; and (ii) a variable transverse curvature term in the dynamic boundary condition that modifies the pressure jump over the air–liquid interface. We use our model to examine the roles of these two distinct effects and find that both contribute to the stead...
Bubble transitions in strongly collapsed elastic tubes
Journal of Fluid Mechanics, 2009
The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elast... more The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elastic tube is investigated experimentally in a benchtop model of airway reopening. Localized regions of strong collapse are likely in the lung, because collapsing fluid-elastic instabilities promote extensive deformation of the airway cross-section beyond the point of opposite wall contact. We find that radical changes in the reopening mechanics occur at this point. We build on the recent identification by Heap & Juel (Phys. Fluids, vol. 20, 2008, article no. 081702) of three different steadily propagating bubbles (asymmetric, double-tipped and pointed) that are selected successively for increasing values of the capillary number (Ca, ratio of viscous to surface tension forces) in tubes initially collapsed beyond the point of opposite wall contact. The asymmetric bubble is also observed in less collapsed tubes for small values of Ca, and we show that it bifurcates super-critically from the u...
Streamwise variation in vessel geometry is a feature of many multiphase flows of practical intere... more Streamwise variation in vessel geometry is a feature of many multiphase flows of practical interest, ranging from natural porous media flows to man-made lab-on-the-chip applications. The variable streamwise geometry typically exerts a dominant influence on bubble motion, and can lead to undesirable phenomena such as clogging of the vessel. Here, we study clogging in a fundamental configuration, where a tube of square cross-section is suddenly expanded over a short streamwise distance. The extent to which a bubble driven by constant flux flow broadens to partially fill the expansion depends on the balance between viscous and surface tension stresses, measured by the capillary number $\mathit{Ca}$. This broadening is accompanied by the slowing and momentary arrest of the bubble as $\mathit{Ca}$ is reduced towards its critical value for trapping. For $\mathit{Ca}\lt {\mathit{Ca}}_{c} $ the pressure drag forces on the quasi-arrested bubble are insufficient to force the bubble out of the...
Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap... more Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluidstructure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyze the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behavior.
We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a ... more We study the dynamics of two air bubbles driven by the motion of a suspending viscous fluid in a Hele-Shaw channel with a small elevation along its centreline via physical experiment and numerical simulation of a depth-averaged model. For a single-bubble system we establish that, in general, the bubble propagation speed monotonically increases with bubble volume so that two bubbles of different sizes, in the absence of any hydrodynamic interactions, will either coalesce or separate in a finite time. However, our experiments indicate that the bubbles interact and that an unstable two-bubble state is responsible for the eventual dynamical outcome: coalescence or separation. These results motivate us to develop an edge-tracking routine and to calculate these weakly unstable two-bubble steady states from the governing equations. The steady states consist of pairs of ‘aligned’ bubbles that appear on the same side of the centreline with the larger bubble leading. We also discover, through...
Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of ... more Motivated by the industrial processing of chocolate, we study experimentally the fluidisation of a sessile drop of yield-stress fluid on a pre-existing layer of the same fluid under vertical sinusoidal oscillations. We compare the behaviours of molten chocolate and Carbopol which are both shear-thinning with a similar yield stress but exhibit very different elastic properties. We find that these materials spread when the forcing acceleration exceeds a threshold which is determined by the initial deposition process. However, they exhibit very different spreading behaviours: whereas chocolate exhibits slow long-term spreading, the Carbopol drop rapidly relaxes its stress by spreading to a new equilibrium shape with an enlarged footprint. This spreading is insensitive to the history of the forcing. In addition, the Carbopol drop performs large-amplitude oscillations with the forcing frequency, both above and below the threshold. We investigate these viscoelastic oscillations and provide evidence of complex nonlinear viscoelastic behaviour in the vicinity of the spreading threshold. In fact, for forcing accelerations greater than the spreading threshold, our drop automatically adjusts its shape to remain at the yield stress. We discuss how our vibrated-drop experiment offers a new and powerful approach to probing the yield transition in elastoviscoplastic fluids.
The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plate... more The displacement of a viscous fluid by an air bubble in the narrow gap between two parallel plates can readily drive complex interfacial pattern formation known as viscous fingering. We focus on a modified system suggested recently by [1], in which the onset of the fingering instability is delayed by introducing a time-dependent (power-law) plate separation. We perform a complete linear stability analysis of a depth-averaged theoretical model to show that the plate separation delays the onset of non-axisymmetric instabilities, in qualitative agreement with the predictions obtained from a simplified analysis by [1]. We then employ direct numerical simulations to show that in the parameter regime where the axisymmetrically expanding air bubble is unstable to nonaxisymmetric perturbations, the interface can evolve in a self-similar fashion such that the interface shape at a given time is simply a rescaled version of the shape at an earlier time. These novel, self-similar solutions are linearly stable but they only develop if the initially circular interface is subjected to unimodal perturbations. Conversely, the application of non-unimodal perturbations (e.g. via the superposition of multiple linearly unstable modes) leads to the development of complex, constantly evolving finger patterns similar to those that are typically observed in constant-width Hele-Shaw cells.
We characterise novel propagation modes that occur when semi-infinite air fingers and finite air ... more We characterise novel propagation modes that occur when semi-infinite air fingers and finite air bubbles displace viscous fluid from microchannels. The presence of an axially-uniform rectangular occlusion within a rectangular cross-section leads to a multiplicity of modes, in contrast to the single symmetric mode present in unoccluded channels. For air fingers, the asymmetric 1 , oscillatory 2 and localised modes 3 first identified in millimetric channels persist at the micron-scale, confirming that significant gravitational effects are not necessary to support these states. Sufficiently large finite bubbles exhibit analogous modes with quantitatively similar flow measures, indicating that the physical mechanisms supporting the propagation modes of finite bubbles are the same as those identified for the air fingers 4. In contrast to the air fingers, in which oscillations are always initiated near the finger tip and propagate backwards, oscillations in finite bubbles can arise from either end of the bubble.
Submitted for the DFD13 Meeting of The American Physical Society Can consecutive droplet depositi... more Submitted for the DFD13 Meeting of The American Physical Society Can consecutive droplet deposition yield uniform liquid films? 1 ANNE JUEL, ALICE THOMPSON, CARL TIPTON, ANDREW HAZEL, University of Manchester, MARK DOWLING, Cambridge Display Technology-Ink-jet printing is being used to manufacture highly customizable electronic components through the successional deposition of overlapping droplets of conductive ink onto a substrate. For vanishing contact angles, the fluid drops merge together on the substrate to form a wide, uniform thread. However, in practical operating regimes involving moderate contact angles, the fluid is redistributed to form non-uniform patterns, characterized by the development of an initial wide bulge (larger than any individual drop). This "head" is sometimes followed by a sequence of secondary bulges connected by narrow rivulets. We conduct new experiments with high-speed imaging to examine the morphological development of the thread resulting from the deposition of a moderate number of successive micro-scale drops (< 80) that may form up to two secondary bulges. We demonstrate that the spatial structure of the ink formation resulting from this complex deposition process can be predicted quantitatively with a simple physical model that incorporates contact angle hysteresis. The head formation occurs robustly due to an inviscid mechanism, while the secondary bulge formation arises from viscous effects.
In this fluid dynamics video, we study a two-phase flow in an elastic Hele-Shaw cell that involve... more In this fluid dynamics video, we study a two-phase flow in an elastic Hele-Shaw cell that involves two distinct fluid-and solid-based instabilities: viscous fingering and sheet buckling. We show that the relative importance of the two instabilities is controlled by a single non-dimensional parameter, which provides a measure of the elasticity of the flexible wall. We employ numerical simulations to show that for relatively stiff [soft] walls, the system's behaviour is dominated by viscous fingering [sheet buckling]. Strong interactions between the two instabilities arise in an intermediate regime and lead to the development of extremely complex fingering and buckling patterns.
The development of viscous fingers in circular Hele-Shaw cells is a classical and widely studied ... more The development of viscous fingers in circular Hele-Shaw cells is a classical and widely studied fluid mechanical problem. The introduction of wall elasticity (via the replacement of one of the bounding plates by an elastic membrane) can weaken or even suppress the fingering instability, but it also makes the system susceptible to additional solid-mechanical instabilities. We show that in elastic-walled Hele-Shaw cells that are bounded by sufficiently thin elastic sheets the (fluid-based) viscous fingering instability can arise concurrently with a (solid-based) wrinkling instability. We study the interaction between these distinct instabilities, using a theoretical model that couples the depth-averaged lubrication equations for the fluid flow to the Föppl-von Kármán equations, which describe the deformation of the thin elastic sheet. We employ a linear stability analysis to determine the growth rate of non-axisymmetric perturbations to the axisymmetrically expanding bubble, and perf...
Recent experiments by Pailha et al. [Phys. Fluids 24, 021702 (2012)10.1063/1.3682772] uncovered a... more Recent experiments by Pailha et al. [Phys. Fluids 24, 021702 (2012)10.1063/1.3682772] uncovered a rich array of propagation modes when air displaces oil from axially uniform tubes that have local variations in flow resistance within their cross-sections. The behaviour is particularly surprising because only a single, symmetric mode has been observed in tubes of regular cross-section, e.g., circular, elliptical, rectangular, and polygonal. In this paper, we present experimental results describing a new mode, an asymmetric localised air finger, that persists in the limit of zero propagation speed. We show that the experimental observations are consistent with a model based on capillary static calculations within the tube's cross-section, and the observed bistability is a consequence of the existence of multiple solutions to the Young–Laplace equations. The model also provides an upper bound for the previously reported symmetry-breaking bifurcation [A. de Lózar, A. Heap, F. Box, A....
We show that a simple change in pore geometry can radically alter the behavior of a fluid-displac... more We show that a simple change in pore geometry can radically alter the behavior of a fluid-displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross section can force a transition from a steadily propagating centered finger to a state that exhibits spatial oscillations formed by periodic sideways motion of the interface at a fixed distance behind the moving finger tip. We characterize the dynamics of the oscillations, which suggest that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution.
We study steep capillary-gravity waves that form at the interface between two stably stratified l... more We study steep capillary-gravity waves that form at the interface between two stably stratified layers of immiscible liquids in a horizontally oscillating vessel. The oscillatory nature of the external forcing prevents the waves from overturning, and thus enables the development of steep waves at large forcing. They arise through a supercritical pitchfork bifurcation, characterized by the square root dependence of the height of the wave on the excess vibrational Froude number (W, square root of the ratio of vibrational to gravitational forces). At a critical valueWc, a transition to a linear variation inWis observed. It is accompanied by sharp qualitative changes in the harmonic content of the wave shape, so that trochoidal waves characterize the weakly nonlinear regime, but ‘finger’-like waves form forW≥Wc. In this strongly nonlinear regime, the wavelength is a function of the product of amplitude and frequency of forcing, whereas forW
ester-We report the suppression of interfacial fingering instabilities resulting from the injecti... more ester-We report the suppression of interfacial fingering instabilities resulting from the injection of air into the narrow, fluid-filled gap between two parallel plates (a Hele-Shaw cell), when one of the boundaries is replaced by an elastic membrane. In a rigid cell, if the air is injected at a sufficiently fast flow rate, the interface is unstable, ultimately resulting in the development of a complex dendritic fingers. In the elastic-walled cell, interfacial instabilities develop at much larger air-injection rates because membrane deformations reduce destabilising pressure perturbations ahead of the propagating interface, and fundamentally alter the interfacial pattern that develops. We characterise the dependence of the instability on the parameters of the system, and present simple scaling arguments to explain the experimentally observed behaviour.
We consider the propagation of an air finger into a wide fluid-filled channel with a spatially va... more We consider the propagation of an air finger into a wide fluid-filled channel with a spatially varying depth profile. Our aim is to understand the origin of the multiple coexisting families of both steady and oscillatory propagating fingers previously observed in experiments in axially uniform channels each containing a centred step-like occlusion. We find that a depth-averaged model can reproduce all the finger propagation modes observed experimentally. In addition, the model reveals new modes for symmetric finger propagation. The inclusion of a spatially variable channel depth in the depth-averaged equations leads to: (i) a variable mobility coefficient within the fluid domain due to variations in viscous resistance of the channel; and (ii) a variable transverse curvature term in the dynamic boundary condition that modifies the pressure jump over the air–liquid interface. We use our model to examine the roles of these two distinct effects and find that both contribute to the stead...
Bubble transitions in strongly collapsed elastic tubes
Journal of Fluid Mechanics, 2009
The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elast... more The selection of long air bubbles propagating steadily in a strongly collapsed fluid-filled elastic tube is investigated experimentally in a benchtop model of airway reopening. Localized regions of strong collapse are likely in the lung, because collapsing fluid-elastic instabilities promote extensive deformation of the airway cross-section beyond the point of opposite wall contact. We find that radical changes in the reopening mechanics occur at this point. We build on the recent identification by Heap & Juel (Phys. Fluids, vol. 20, 2008, article no. 081702) of three different steadily propagating bubbles (asymmetric, double-tipped and pointed) that are selected successively for increasing values of the capillary number (Ca, ratio of viscous to surface tension forces) in tubes initially collapsed beyond the point of opposite wall contact. The asymmetric bubble is also observed in less collapsed tubes for small values of Ca, and we show that it bifurcates super-critically from the u...
Streamwise variation in vessel geometry is a feature of many multiphase flows of practical intere... more Streamwise variation in vessel geometry is a feature of many multiphase flows of practical interest, ranging from natural porous media flows to man-made lab-on-the-chip applications. The variable streamwise geometry typically exerts a dominant influence on bubble motion, and can lead to undesirable phenomena such as clogging of the vessel. Here, we study clogging in a fundamental configuration, where a tube of square cross-section is suddenly expanded over a short streamwise distance. The extent to which a bubble driven by constant flux flow broadens to partially fill the expansion depends on the balance between viscous and surface tension stresses, measured by the capillary number $\mathit{Ca}$. This broadening is accompanied by the slowing and momentary arrest of the bubble as $\mathit{Ca}$ is reduced towards its critical value for trapping. For $\mathit{Ca}\lt {\mathit{Ca}}_{c} $ the pressure drag forces on the quasi-arrested bubble are insufficient to force the bubble out of the...
Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap... more Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluidstructure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyze the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behavior.
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Papers by Anne Juel