Lava Flow Physics

    Last weekend, I was able to travel to Syracuse with my Volcanology Class to conduct two experiments about lava flows using “man-made” lava. Lava is awesome, and is an excellent example of the relationship between chemical and physical qualities of materials and their physical behavior. 

    

    The velocity and style of a lava flow is primarily dictated by the lava’s viscosity, meaning resistance to flow. Viscosity is a function of multiple factors, specifically “the [lava] temperature T, the volume fraction of crystals [within the lava], and, to a lesser extent, the size and shape of the crystals” (Griffiths, 2000).  This is due to the nature of fluid flow, which is related to shear and strain. Shear stress is the force per unit area acting on a fluid, and strain rate is the rate of deformation experienced by a fluid when a load stress is applied (Harris, 2013). If the resistance to flow is high, more shear stress is required to achieve the same amount of change in strain rate than at low viscosity lavas (Harris, 2013). The relationship between stress and strain for lava (a Bingham fluid) is shown in the chart below (Harris, 2013).

    In our experiment, the beginning of the flow, when it was very hot, had a decreased viscosity and therefore a much higher velocity. As the lava flow traveled down the slope, its temperature cooled and it became more resistant to flow, eventually coming to a stop. 

    One goal of this experiment was to learn about lava tree formation. We didn’t quite succeed in creating lava trees (due to the scale of the experiment), but were able to make some interesting energy transfer observations. We set our lava to flow through two types of tree branches - a “wet” forest and a “dry” forest. We were curious to see if the hydration conditions of the wood had an effect on their ability to form lava trees. Something we didn’t even think about when designing the experiment was the effect the different trees may have on the flow itself. While watching the flow and when revisiting footage, we noticed that it seemed like the “wet” side of the flow took longer to catch fire than the “dry” side. Furthermore, the wet side had a decreased velocity compared to the dry side after exiting the “forest”. As a result, the wet side lava traveled less far than the dry lava. 

    This result can be explained by the conservation of energy. While fluid flow is more complex than linear kinematics, and this isn’t quite an inelastic or elastic collision, the law of conservation of energy can still be applied. When the lava passed through the wet forest, it required a greater amount of energy to ignite the trees than it did in the dry forest. So, more kinetic energy was lost and transformed to heat energy, and as a result the velocity decreased more. Then, kinematics can be used to explain resulting displacements. The lava with a greater initial velocity had a greater displacement before coming to rest, as explained by our kinematic equations (assuming they had equal accelerations). 

vf2 = vo2 + 2aΔx

0 = vo2 + 2aΔx

(-vo2) / 2a = Δx

Works Cited

Griffiths, R. W. (2000). The dynamics of lava flows. Annual review of fluid mechanics, 32(1), 477-518.

Harris, A. (2013). Lava flows. In S. Fagents, T. Gregg, & R. Lopes (Eds.), Modeling Volcanic Processes: The Physics and Mathematics of Volcanism (pp. 85-106). Cambridge: Cambridge University Press. doi:10.1017/CBO9781139021562.005