Graphical Representation of the Interplay of Viscosity and Rate of Shear Strain (Grades 9-12)
In a classic paper on the transition of pahoehoe to aa, a graphical approach was used to demonstrate how viscosity and rate of shear strain influenced the type of lava that formed. Prior to presenting this approach with your students, review this activity. The graphs can be drawn on the board or projected from an overhead.
Peterson and Tilling (1980) related the interplay of viscosity and rate of shear strain using a series of graphs. Viscosity is on the x-axis and increases to the right. Rate of shear strain is on the y-axis and increases upward. The shaded area is the transition zone threshold (TTZ), which separates conditions favorable for the development of pahoehoe (to the left) from aa (to the right). Point E represents the viscosity and rate of shear strain at the time of eruption. Point S is the end of the flow's history, when lava is solidified and characterized by very high viscosity. The following discussion of the graphs is from Peterson and Tilling (1980, p. 285-288).
Graph A: pahoehoe lobe on flat ground. After eruption (E), lava becomes part of a "typical" flow; as viscosity increases with cooling, the rate of shear strain decreases (E to 1). Lava becomes part of a slowly moving pahoehoe lobe on flat ground, and strain drops abruptly (2); as cooling continues, viscosity increases with concomitant decrease in strain rate (2-3). Shear strain ceases at 3; motion does not resume while lava continues to cool and solidify (3 to S). Because the lava does not cross the TTZ, it remains pahoehoe.
Graph B: flow over a steep slope; lava remains pahoehoe. Path follows "typical" flow conditions (E to 4). Flow encounters steep slope before viscosity increases (4); during rapid descent, lava experiences high rate of shear strain (5). Flow reaches flat ground at base of slope, strain rate drops to low value (6). Further cooling increases viscosity with small decrease in strain rate (6-7), motion ceases (7), and lava finally solidifies (S). Path does not cross TTZ; lava remains pahoehoe.
Graph C: flow over steep slope; lava changes to aa. Path follows "typical" flow conditions (E to 8). Flow encounters steep slope after appreciable cooling and increases in viscosity (8). During rapid descent, lava undergoes increased strain rate; path crosses TTZ (9) and reaches high rate of shear strain (10), transforming to aa. At end of descent, strain rate drops to low value at higher viscosity (11). Path crosses TTZ to reenter pahoehoe field, but lava continues to behave as aa because the pahoehoe-aa transition is irreversible. Shear strain ceases (12), but transient high stresses during continued cooling produces episodic, slow renewed movement (13) before lava finally solidifies (S).
Graph D: flow on constant slope; lava changes to aa. Lava is in a channel and under persistent relatively high rate of shear stain (E to 14). If the supply of lava is continuous, lava crosses TTZ and lava changes to aa (14). Lava continues to flow and follows path 14-15 until motion ceases (15), and lava cools and solidifies (S).
Graph E: chilled crust changes to aa. Flow begins under conditions similar to examples A, B, and C. Lava becomes part of a "plug" in the channel, and the shear strain drops to zero (16). The lava continues to cool but is a flexible crust floating in a stream of lava (17). The crust is disrupted and mixed into the underlying fluid lava. The sudden increase in shear strain causes the crust to change to aa as it crosses the TTZ (17-18). As the lava cools, it recrosses the TTZ into the pahoehoe field, but the lava remains aa and finally solidifies (S).
Graph F: stored lava is remobilized and changes to aa. Lava is transported to a pond (E to 20), where it cools, increases in viscosity, and remains motionless (20-21). The pond begins to drain into a lava tube and deforms slightly as the viscosity continues to increase (21-22). The tube ruptures and releases a flow with increased velocity, causing an increased rate of strain (23). The lava crosses the TTZ and changes to aa (23-24). Finally the flow solidifies (S).
Peterson, D.W., and Tilling, R.I., 1980, Transition of basaltic lava from pahoehoe to aa, Kilauea Volcano, Hawaii: field observations and key factors: Journal of Volcanology and Geothermal Research, v. 7, p. 271- 293.