The viscosity of magmatic silicate liquids; a model calculation

Abstract

INTRODUCTIONThere are very few aspects of igneous petrology which are not in some way closely related to the viscosity of magma. Rate of crystal growth, gravitative settling or rise of solids and bubbles, mode of volcanic eruption, flow differentiation mechanisms, flow characteristics of lavas, mass transfer in magmas under externally imposed pressure gradients or natural convection, rate of cooling of magmatic intrusions and lavas; all of these phenomena are critically dependent upon the viscosity of magmatic liquid or the effective viscosity of a magmatic suspension.Quantitative evaluation of any of the above igneous processes must begin with a knowledge of the viscosity of silicate liquids within the rather wide range of temperature and composition displayed by natural me^ts. The need for such viscosity data has long been recognized by petrologists, and many attempts have been made to determine effective viscosities from field observations of lava flow rates (Becker, 1897; Palmer, 1927; Nichols, 1939;Krauskopf, 1948; Hinakami, 1951; Walker, 1967, among others). Uncertainties related to temperature measurements; size, shape, and roughness of the flow channel; and gas and solid particle content make evaluation of such viscosity determinations very difficult. .Laboratory viscosity measurements on geologically significant liquids date back to the turn of the century. The first determinations were probably made by Doelter (1902), who was able to classify on a qualitative scale the viscosities of various rocks and minerals melted in the laboratory. Much of the early work is summarized by Kittl (1913).The measurements of Kani (1934aKani ( , 1934bKani ( , 1935, Kozu and Kani (1935), Kani and Hosakawa (1936), Volarovich (1936), and Volarovich and Tolstoi (1936) were valuable contributions towards an understanding of the temperature and composition dependence of silicate viscosity. Bowen (1934) measured the viscosities of molten orthoclase and albite, and included an interesting discussion of the significance of viscosity in petrology and liquid silicate experimental work. More recently, viscosity measurements on molten rocks have been reported by Euler and Winkler (1957), Shaw (1969), Carron (1969), and Murase and McBirney (1970).Newton's law of viscosity states that the shear stress in liquids undergoing laminar flow is proportional to the local velocity gradient perpendicular to the stress. The proportionality constant in this relation is known as the viscosity coefficient, n. In Newtonian fluids it is independent of the magnitude of the shear stress. The silicate liquids discussed in this paper closely approximate the Newtonian model. Fluid suspensions of solids or bubbles are best described by non-Newtonian models. For a discussion of this problem in geological context the reader is referred to Shaw et al. (1968) and Shaw (1969). 3.The viscosities of silicate liquids are strongly dependent upon chemical composition. . For example, at 1300 C where most igneous rocks are completely melted, the composition range ...

The equation of state of a molten komatiite: 2. Application to komatiite petrogenesis and the Hadean Mantle

“…The convective velocity (from the mixing length formula (equation (10)) with a heat flux of 150 W/m 2 ) of the magma ocean will be approximately 10 cm/s. We estimate that the viscosity of crystal-free magma will be =1 P [Bottinga and Weill, 1972]. With these assumptions, a crystal radius of 2:3.5 em (equation (12b)) is required for crystal flotation/settling to occur in the absence of a boundary layer.…”

“…We estimate the crystal size by evaluating each of these equations, determining the Reynolds number for each case, and selecting the result that is consistent with the Re conditions. For perovskite in the lower mantle, the maximum crystal-liquid density contrast will be ::0.25 g/cm 3 • If the viscosity of molten Cl obeys an Arrhenius relationship, independent of pressure, then we would estimate a lower limit for the viscosity to be :: 0.01 P [Bottinga and Weill, 1972]. The combined pressure and temperature dependence of viscosity is unknown for silicate liquids under these conditions so this value for viscosity must be suspect.…”

The role of viscosity in the emplacement of high-temperature acidic flows of Serra Geral Formation in Torres Syncline (Rio Grande do Sul State, Brazil)

“…Hence, the evolution of viscometers for silicate liquids has been traced by changing from Arrhenian temperature dependence (e.g. Shaw 1972;Bottinga & Weill 1972) to non-Arrhenian models, considering magma composition and volatile effects (e.g. Baker 1996;Hess & Dingwell 1996;Russell et al 2002;Giordano & Dingwell 2003;Russell & Giordano 2005;Giordano et al 2006;Vetere et al 2006;Hui & Zhang 2007;Giordano et al 2008).…”

Non‐Newtonian rheology of igneous melts at high stresses and strain rates: Experimental results for rhyolite, andesite, basalt, and nephelinite

“…A complete understanding of magma rheology requires a comprehensive description of the rheology of the melt phase [Shaw, 1965], Most studies of shear viscosities of Silicate melts have been conducted at conditions of relatively high temperatures and low viscosities (see compilations by Bottinga and Weill [1972], Bansal and Doremus [1986], and Ryan and Blevins [1987]). In cases where the stress-strain rate relationship has been investigated over a significant ränge of strain rate, both Newtonian behavior (i.e., linear stress-strain rate relationship) [e.g., Scarfe et al, 1983] and non-Newtonian behavior [e.g., Li and Vhlmann, 1970;Simmons et al, 1982;Spera et al, 1982] have been observed.…”