Journal of Volcanology and Geothermal Research 86Ž. 1998 107±115 Orientation distribution of microlites in obsidian Michael Manga ) Department of Geological Sciences, UniÕersity of Oregon, Eugene, OR 97403, USA Revised 16 June 1998 Abstract The shape and three-dimensional orientation distribution of microlites are measured in obsidian from Little Glass Mountain, CA. Measurements are made from thin sections using an image series of high magnification digital micrographs taken serially through different focal depths. These measurements agree well with the theoretically predicted and experimentally measured distribution of long slender rods in a Newtonian fluid undergoing simple shear flow. In this type of flow, rods in a dilute suspension rotate periodically, spending most of the time aligned with the flow. Measurements of the detailed orientation distribution integrated with theoretical models provide a tool for inferring flow dynamics and the timing of magmatic processes. q 1998 Elsevier Science B.V. All rights reserved. Keywords: microlites; obsidian; flow dynamics; magmatic processes 1. Introduction Smith et al., 1994; Ventura et al., 1996. Here, I examine the three-dimensional orientation distribu- The nature of magmatic processes, such as solidi- tion of rod-shaped albite microlites in obsidian, and fication, degassing and flow behavior, are often in- consider the relationship between microlite orienta- ferred from the textures and structures preserved in tion and properties of the flow. volcanic rocks. Measured vesicle-size distributions, The goal here is to show how measured orienta- for example, can be used to infer eruption parame- tion distributions can be interpreted within a theoreti- ters, such as nucleation depth and ascent velocity cal framework. I begin by reviewing the dynamics of Ž.Toramaru, 1989 , and crystal-size distributions can long slender particles in shear flows, including re- be used to infer solidification ratesŽ. Cashman, 1993 . search results from the last few years. Next, a new Preferred orientations and imbricated crystals can method is presented for quantifying the three-dimen- also be used to infer strainsŽ e.g., Shelley, 1985; sional orientation of microlites; the technique is then applied to an obsidian sample from Little Glass Mountain, CA. Agreement between measured and theoretical distributions suggests that the technique may be useful in determining the emplacement his- ) Tel.: q1-541-346-5574; Fax: q1-541-346-4692; E-mail: tory and dynamics of obsidian flows, when applied [email protected] to a representative suite of oriented samples. 0377-0273r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S0377-0273Ž. 98 00084-5 108 M. MangarJournal of Volcanology and Geothermal Research 86() 1998 107±115 2. Orientation of microlites: theoretical considera- tions Consider a rod-shaped particle immersed in a flow, uext, in which inertial forces can be neglected. Specifically, the Reynolds number of the rod, GL2rn is <1, where G is the magnitude of the local strain rate, L is the rod's length, and n is the kinematic viscosity of the liquid. I consider two end-member flows, a pure shear flow: uext s Ž.Gx, yGy,0 , Ž. 1 and a simple shear flow: uext s Ž.Gy,0,0 . Ž. 2 ext s ext ext ext Here, u Žu xyz, u , u ., and x, y and z indi- cate distances in the coordinate system shown in Fig. 1a. For the pure shear flow, the x direction is the direction of extension; for the simple shear flow, the x direction is the flow direction and vorticity is in the z direction. Two angles are defined in order to characterize the orientation of the rod: f, measured from the y direction, and u, measured from the z direction. JefferyŽ. 1922 first solved the equations of motion for an axisymmetric ellipsoidal particle in a low-Re- ynolds-number simple shear flow and found that such a particle will rotate with period: s q r r Ž. u T 2p Ž.Rll1 R G,3 Ž.Fig. 1. a Definition of coordinate system, orientation angles and f, and the direction of the simple shear flow considered here, Eq.Ž.Ž. 2 . b Illustration of Jeffery orbits for different values of the where Rl is the aspect ratio of the ellipsoid. Brether- tonŽ. 1962 showed that the equations developed by orbit constant C. JefferyŽ. 1922 apply to any axisymmetric object and that the dynamics of rod-shaped particles is equiva- lent to the dynamics of ellipsoids with aspect ratio and R f1.35R , where R denotes the aspect ratio of 2 y lr r du Rl 1 the rod. Nonaxisymmetric particles may undergo sG sin u cos u sin f cos f,5Ž. dt R2 q1 either chaotic, periodic or quasi-periodic rotations l Ž.Yarin et al., 1997 . where t is time. Each of these closed trajectories The differential equations governing the motion Ž.sometimes called Jeffery orbits can be conveniently of particles in a simple shear flow areŽ e.g., Jeffery, characterized by an `orbit constant'Ž. Fig. 1b : 1922. : 1 f u 22fq 2f 2 d G tan Ž.Rl cos sin s R22cos fqsin 2f 4 Cs .6 2 q Ž.l Ž. Ž. dt Rl 1 Rl M. MangarJournal of Volcanology and Geothermal Research 86() 1998 107±115 109 The analogous expressions to Eqs.Ž. 4 and Ž. 5 for c<1. that hydrodynamic interactions among the a pure shear flow areŽ. e.g., Gay, 1966 : particles can be neglected. Suspensions of rods are 3 2 y called `dilute' if nL <1, where n is the number df Rl 1 sG sin 2f 7 density, i.e., number of microlites per unit volume 2 q Ž. dt Rl 1 Ž.e.g., Batchelor, 1971 . In the so-called `semidilute' 3 2 - and limit, nL is no longer <1, but nL d 1, where d is the rod's diameterŽ e.g., Fredrickson and Shaqfeh, du 1df sy cot 2f sin 2u .8Ž. 1989. In the semidilute limit, particles are still dt 2dt separated by many particle diameters, but not by Whereas particles in a simple shear flow rotate con- many particle lengths. The effects of interactions tinuously, particles in a pure shear flow become, and between particles on their orientation is discussed in remain, aligned in the direction of extension. more detail below. In order to highlight the difference in orientation Finally, I note that the two flows considered here distributions between pure and simple shear flows, are only end members, and in general, flows will calculated distributions are shown in Fig. 2 for ellip- involve a combination of both pure and simple shear. s Due to the linearity of the equations of motion soids with aspect ratio Rl 10. I assume the parti- cles are initially randomly oriented and do not inter- governing flow at Reynolds numbers <1, Eqs.Ž. 4 , act hydrodynamically. I obtain these theoretical dis- Ž.Ž.5 , 7 and Ž. 8 can be added linearly to describe the tributions by integrating the equations of motion Eqs. evolution of particle orientation. Ž.4 , Ž. 5 , Ž. 7 and Ž. 8 for one million random initial orientations. The orientation distribution is character- ized by the standard deviations s and s of the u f 3. Orientation distribution: measurements angles u and f, respectively. In the pure shear flow, all particles become aligned with the direction of extension and both su and sf approach zero. In the Two thin sections were prepared from a single simple shear flow, however, su and sf approach sample of obsidian from the Little Glass Mountain, finite constants. The actual distributions of f and u CA, obsidian flow. The sample was collected from for the simple shear flow are shown later. the front of the flow. The sample is visually `flow' The equations presented above apply only if the banded, and contains alternating `dark' and `light' suspension is sufficiently diluteŽ volume fractions bands ranging in thickness from less than 1 mm to about 5 mm. The color differences result from varia- tions in microlite crystallinity. The thin sections were cut both parallel to the flow direction inferred from the orientation of stretched vesicles and perpendicu- lar to the layering represented by the flow bands. In this particular sample, microlites are oriented parallel to the flow bands Ž.x direction ; however, this is not always the caseŽ. Fink, 1983 . Because the particle orbits determined by Eqs. Ž.4 , Ž. 5 , Ž. 7 and Ž. 8 are fully three-dimensional, the three-dimensional orientation of microlites must also be measured. In addition, a justified interpretation of preferred orientations requires ``simultaneous mea- surements of both grain shapes and grain orienta- tions''Ž. Willis, 1977 due to the dependence of parti- cle dynamics on their aspect ratio. Fig. 2. Standard deviation su and sf of the angles u and f as a function of strain for a pure shearŽ. dashed curves and simple The measurement technique involves making a set shearŽ. solid curves . of high-magnificationŽ. 500= digital photomicro- 110 M. MangarJournal of Volcanology and Geothermal Research 86() 1998 107±115 Fig. 3. Example of a set of stacked set of digitized images taken from various focal depths within a thin section. Sample is from the Big Obsidian Flow at Newberry, Oregon. The bold lines represent the orientation of the microlites, the thin curves are traces of the microlites in each image. The disks show the position of the focussed part of each microlite in each image. graphs at 2-mm depth intervals from the bottom for measuring three-dimensional orientationsŽ e.g., focal plane to the upper focal plane of the thin Shelley, 1985; Wada, 1992. : all possible orientations section. For a given image, the outline of each can be measured, orientation and shape are simulta- microlite is digitized in a computer-assisted drafting neously determined for each crystal, and measure- Ž.CAD program.