Cryomagmas are natural examples of complex multiphase fluids. Some preliminary statements are made about the rheology of densely packed suspensions that have important bearing on their flow rates and eruptive style.

Abstract no.104

Petford, Nick

English

Bournemouth University Research Online

RHEOLOGY AND MULTIPHASE FLOW IN CONGESTED AMMONIA-WATER-ICE SLURRIES.Nick Petford1, 1Centre for Earth and Environmental Science Research, Kingston University, Surrey, KT1 2EE, UK(n.petford@kingston.ac.uk)Introduction: Some aspects of the rheological be-haviour of ammonia-water-ice slurries have been inves-tigated by Kargel et al. [1] over a range of temperaturesand compositions relevant to the icy satellites. How-ever, a proper quantification of the rheology and flowbehaviour of fluid-particle suspensions remains a majortheoretical and experimental challenge. This complex,multiphysics problem is somewhat difficult to general-ize, as many mechanisms occur simultaneously andinterdependently. Suspension rheology is particularlyrelevant in this respect due to its strong influence onthe style of flow and emplacement of cryomagmas bothinternally and at the surface [2].This study is concerned with estimates of flow rhe-ology at high crystal loads ( > 50%), well above theexperimental range investigated in [1]. Such materialsare referred to in the micromechanics literature as con-gested [3], and magmas during their latter stages offlow, where cooling and crystallisation dominate, pro-vide excellent natural examples.Multiphase flow: Cryomagmas, along with theirsilicate counterparts, are prime examples of flows thatinvolve the transport of solids, gases (and other fluids)by a separate carrier phase. Such flows are called mul-tiphase, and have attracted much recent attention due totheir important range of engineering applications [4].Where the number density of the dispersed phase islarge, the influence of particles on the fluid motionbecomes significant and must be taken into account inany explanation of the bulk behaviour of the mixture.Numerical techniques for simulating multiphase flowrequire that computation of particle and fluid trajecto-ries are done simultaneously and iteratively, are still ina relatively unadvanced state [5]. Further complica-tions arise due to the interactions between particles andwalls, and when phase changes take place in the carrierfluid.Flow Rheology: Equations describing first and sec-ond-order order corrections to an infinite mixture witha Newtonian fluid viscosity (), and spherical particlesof equal size d comprising a solids volume fraction (),are well known, but valid strictly only for dilute sus-pensions where the grain packing is isotropic [6]. In-evitably a number of problems follow from this simpli-fication, one of the more serious being that in narrowchannels, particles are forced to come very close to-gether so that particle-particle interactions becomedominant. A measure of this is given by the Bagnoldnumber. This has led to the important observation thatfor all cases where a shear gradient exists in denselypacked suspensions (> 0.3), a migration effect takesplace [7].Lubrication limit. Rather than attempt third-order(and higher) corrections to the viscosity term as ex-trapolated from dilute suspensions, a more sensibleway to proceed might be to tackle the problem by de-riving formulations for the effective viscosity ofdensely packed suspensions directly. One approachthat holds promise is based on the lubrication limitconcept of particle interactions [8]. This limit domi-nates when the surface contact distance between twoparticles (h) is << d. An approximate expression link-ing the ratio d/h to the solidosity (> 0.2) is:3(1 )6 (2 )dh (1)with the derived estimate of the effective viscosity ()36 (2 )(1 ) . (2)Application to congested ammonia-water-iceslurries: Using eqn. 2 it is possible to make some pre-liminary statements about the rheology of an initiallydensely packed suspension that have bearing on theflow rates of cryomagmas. Fig. 1 is a plot showing thechanging effective viscosity of the mixture as a func-tion of melt viscosity and particle content (solidosity).The melt viscosity of the continuous phase, an ammo-nia-water liquid (NH3 c. 21-35%) over the temperatureinterval 40 < 104 K/T < 60, varies from ~ 10-3 to 10 Pas [1]. From eqn. 2, the order of magnitude increase ineffective viscosity with increasing solids content andmelt viscosity ranges from 0.02 Pa s (= 0.4) to 7 x103 Pa s (= 0.8). The estimated effective viscosity ofa congested slurry with a 20% porosity where the liq-uid phase is at the ammonia water-ice peritectic (T =176.2,~ 4 Pa s [1] is c. 103 Pa s.Flow velocities and segregation: The new esti-mates of effective viscosities can in principle be usedto place order of magnitude constraints on flow veloci-ties of congested ammonia-water-ice slurries in dykes.However, the problem requires some knowledge of thepressure gradients available to drive the flow. Esti-mates of cryomagma properties on Europa suggest thatthe slurries can be either positively or negatively buoy-ant, depending upon factors such as initial melt compo-sition and bulk differentiation of the crust [9]. Theseparameters are not currently well known for any icyLunar and Planetary Science XXXVI (2005) 1043.pdfplanet in the solar system. However, for illustrativepurposes, Fig. 2. shows a plot of the predicted cryo-magma flow velocities for a pure liquid and cryo-magma slurry in a 1 metre-wide dyke for a density con-trast of 50-150 kg/m3 [9]. The gravity field (1.3 m/s2) istypical of the icy moons. The maximum average flowvelocity (u) for crystal-free pertiectic NH3-H2O melt isc. 4 m/s. Mean cryomagma flow velocities range froma maximum of 0.23 m/s to 2 x 10-3 m/s for highly con-gested magma (= 0.8, = 50 kg/m3 ). Slurry flowin a confined channel at high crystal loads is problem-atic. However, a migration effect is expected duringshear arising from fluctuations in particle velocity. Thistends to keep the margins of the flow relatively free ofparticles, thus lubricating the congested central plug.For relevant theory that captures both the solidosityand granular temperature fields due to velocity fluctua-tions in sheared suspensions see [e.g. 7,10].10-410-21001020.40.50.60.70.802000400060008000NH3-H2O melt viscosity (Pa s)solidosityeffectivevisocisty(Pas)1000200030004000500060007000effective viscosity(Pa s)Fig. 1. Plot showing estimated range in effective viscos-ity for ammonia-water-ice slurries (melt viscosities from [1]).100102104 5010015000.050.10.150.20.25density contrast (kg/m3)log effective viscosity (Pa s)flowvelocity(m/s)0.020.040.060.080.10.120.140.160.180.20.22Flow velocity(m/s)Fig: 2. Plot showing estimated range in flow velocitiesfor congested cryomagmas (40-80% solids).Shear-enhanced melt extraction: Should theeutectic melt phase mass density equal or exceed thatof the solid residue, upwards transport of cryomagmasdue to buoyancy forces is not possible. Stress corrosionand the generation of fluid-filed cracks during tidalflexing are potential alternative transport mechanisms[9]. Another is shear-induced dilatancy in the ice ma-trix. Arguably the low temperatures in the outer solarsystem make the viscous behaviour unlikely on shorttimescales, so ice might behave as a granular materialover the timescale of tidal loading (hours to days). Thiswould open up a way of extracting melt from its solidmatrix by a sucking action caused by fluctuating pres-sure gradients. The driving force is the externally im-posed shear strain rate. Detailed equations setting outthe theory of shear-enhanced melt extraction due todilatancy are given in [11]. While the application wasfocused on silicate magmas, this purely mechanicalmodel is equally suited to multiphase flow in low tem-perature systems. More information on the rheologicalproperties of ice would help in this respect [e.g. 12].Implications: Curious structural features andchanges in albedo on Ganymede (also Titan) may re-flect successive emplacement of darker (particle-rich)and lighter (melt dominated) cryomagmas [13], imply-ing segregation mechanisms at work. Flow segregationduring cryomagma ascent to form an axial slurry, fol-lowed by extraction of lower viscosity melt from thecongested mush by shear might be one way of achiev-ing some of the observed surface texturing. This hybridmodel of density-driven flow followed by shearing of adensely packed suspension may be tidally driven, re-sulting in episodic transitions between slurry flow(gravity-driven) and strain rate assisted flow of an effi-ciently segregated pure melt phase. This and other mul-tiphase flow behaviour including impact fluidization ofcryomagma slurries, is the subject of ongoing theoreti-cal investigations.References: [1] Kargel et al (1991) Icarus, 89, 93-112. [2] Croft et al. (1988) Icarus, 73, 279-293. [3]Koenders M.A. (1997) Acta Mechanica 122, 1-19 [4]Gidaspow D. (1994) Academic Press, San Diego. [5]Crowe et al. (1998) CRC Press, Boca Raton, Florida.[6] Bird et al. (1960) Transport Phenomena Wiley,NYC. [7] McTigue D.F and Jenkins, D.T. (1992) El-sevier Science Publishers, Amsterdam, 381-390 [8]Torquato et al. (1990) Phys Rev A, 41, 2059-2047. [9]Wilson, L and Head, J.W. (1997) LPS 29 Abs. 1138.[10] Petford N. and Koenders M.A. (1998) J. Geol.Soc. London, 155 873-881. [11] Petford. N andKoenders M.A. (2003) GJI 155, 857-869. [12] Steven-son D.J. (2003) Geophys. Res. Abstracts 5, 03289. [13]Croft et al. (1994) USGS Misc. Investigation SeriesMap I-2328.Lunar and Planetary Science XXXVI (2005) 1043.pdf

Rheology and Multiphase Flow in Congested Ammonia-Water-Ice Slurries

Abstract

Similar works

Full text

Available Versions

Bournemouth University Research Online