The rheology of a bubbly liquid

Llewellin, Edward W.; Mader, Heidy M; Wilson, S. D. R.

doi:10.1098/rspa.2001.0924

Cited by 188 publications

(168 citation statements)

References 41 publications

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“…Adding bubbles to a liquid not only changes the magnitude of the viscosity but also modifies the behavior of the material giving it viscoelastic properties (Llewellin et al 2002). Both Rust and Manga (2002) and Stein and Spera (2002) identify two different regimes of such a material in flow.…”

Section: Introductionmentioning

confidence: 99%

“…When the applied strain rate is small, the bubbles act as rigid fillers increasing viscosity, while at large strain rates, where the flow line distortion is smaller due to bubble deformation, bubbles provide free slip surfaces and thus decreasing viscosity. Llewellin et al (2002) highlighted the importance of distinguishing between steady and unsteady flow. If shear conditions remain constant for a time much longer than the relaxation time of the bubble, the flow is assumed to be steady.…”

Section: Introductionmentioning

confidence: 99%

“…(2) Llewellin et al (2002) provided an extensive review of previous models developed so far together with their own model for suspensions of bubbles under steady and oscillatory shear conditions.…”

Section: Introductionmentioning

confidence: 99%

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Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

2017

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Bubble suspensions can be found in many different fields and studying their rheology is crucial in order to improve manufacturing processes. When bubbles are added to a liquid, the magnitude of the viscosity changes and the behavior of the material is modified, giving it viscoelastic properties. For the purpose of this work, the suspended bubbles are considered to be monodisperse. It is assumed that Brownian motion and inertia can be neglected and that the fluid of the matrix is Newtonian and incompressible. The suspension is subject to an oscillatory strain while remaining in the linear regime. The resulting equations are solved in 3D with direct numerical simulation using a finite element discretization. Results of an ordered and random distribution of bubbles of volume fractions up to 40% are presented. The presence of bubbles has an opposite effect on the rheology of the suspension depending on the applied frequency. When the frequency is low, bubbles act as rigid fillers giving a rise to viscosity. On the contrary, when the frequency is high, the strain rate is being accommodated by the gaseous phase. Hence, bubbles deform, leading to a decrease of the viscosity.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

2017

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“…The physical state of a magma controls a range of igneous processes, including crystal and bubble growth (e.g., Llewellin et al, 2002b;Hammer, 2008), the ability to exsolve gas (e.g., Gonnermann and Manga, 2007), or drive convection (e.g., Huppert and Sparks, 1981), and eventually whether the magma erupts or stalls (e.g., Caricchi et al, 2008). During magma as-5 cent, crystallisation and bubble expansion significantly alter the physical properties of a magma.…”

Section: Introductionmentioning

confidence: 99%

“…The capillary number (the ratio of viscous to restoring forces) therefore, is an important parameter when calculating 45 the viscosity of a bubble-melt mixture. Bubbles that are spherical increase the viscosity while elongated bubbles reduce the viscosity (e.g., Llewellin et al, 2002b;Rust and Manga, 2002).…”

Section: Introductionmentioning

confidence: 99%

Rheological controls on the eruption potential and style of an andesite volcano: A case study from Mt. Ruapehu, New Zealand

Kilgour

Mader

Blundy

et al. 2016

Journal of Volcanology and Geothermal Research

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. AbstractThe evolving magma rheology of three recent Ruapehu eruptions (1969, 1977, and 1995) is estimated using a combination of thermodynamic models and rheological calculations, supported by textural observations of the erupted scoria. We use a well-established thermodynamic model to determine the composition of these representative Ruapehu magmas from 300 MPa to ∼ 30MPa. The outputs of the model provide the changing crystal and bubble content in a closed system (assuming no gas loss), as well as the fractionating melt compositions. We calculate the melt viscosity, and the effect of bubbles and crystals, to quantify the rheology of the magma during ascent (under assumed equilibrium conditions). The moderately high phenocryst content of Ruapehu scoria (∼ 30 %) means that only a small amount of additional microlite crystallisation (∼ 5 %) would result in a yield strength, which may lead the magma to stall. However, if the strain rates are high enough, more crystallisation would be possible without developing a yield stress. This suggests that microlite-rich magmas are almost certain to stall unless they encounter significant fluid addition from a source such as a hydrothermal system, groundwater, or surface water (i.e., Ruapehu's Crater Lake).Ruapehu magmas are initially H 2 O-undersaturated and as a consequence, crystallisation and bubble growth were suppressed until the magma achieved saturation, at ∼ 100 to 50 MPa.From this analysis, we suggest that Ruapehu magmas are more likely to erupt compared to magmas of a similar composition that are H 2 O-saturated. This partly explains the regular, albeit small-volume eruptions at Ruapehu and the propensity for phreatomagmatic eruptions when the magma:water ratio is low.

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Rheological transitions in high‐temperature volcanic fault zones

et al. 2015

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Silicic magma experiences shear-induced brittle fracturing during its ascent, resulting in the formation of a magmatic fault at the conduit margin. Once the fault is formed, frictional behavior of the fault controls the magma ascent process. We observed torsional deformation of a magmatic fault gouge in situ at temperatures of 800 and 900°C using synchrotron radiation X-ray radiography. The torsional deformation rate was set at 0.1-10 rpm, corresponding to equivalent slip velocities of 2.27 × 10À3 m s À1 and shear strain rates of 0.014-1.16 s À1. The normal stresses used were 1, 5, and 10 MPa. The magmatic fault showed frictional sliding as well as viscous flow even above the glass transition temperature. The transition between frictional sliding and viscous flow depends on temperature, deformation rate, and normal stress on the fault. At 900°C, the fault showed viscous deformation at a normal stress of 10 MPa, while frictional sliding was predominant at 800°C. We propose the ratio of timescales of fault healing and deformation as a criterion for transition between frictional sliding and viscous flow. The experimentally calibrated criterion infers that frictional sliding is predominant from~500 m in depth during explosive eruption; this may explain rapid magma ascent without efficient outgassing. Frictional heating would in turn enhance fault healing, resulting in the reverse transition from frictional sliding to viscous flow, followed by deceleration of magma ascent. Therefore, cyclic transitions between frictional sliding and viscous flow are a possible explanation for the cyclic behavior of lava effusion.

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The rheology of a bubbly liquid

Cited by 188 publications

References 41 publications

Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

Direct numerical simulation of a bubble suspension in small amplitude oscillatory shear flow

Rheological controls on the eruption potential and style of an andesite volcano: A case study from Mt. Ruapehu, New Zealand

Rheological transitions in high‐temperature volcanic fault zones

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