# Viscosity of the Mantle: Constraints from Post-glacial Rebound

## Summary

In this lab, students determine the viscosity of a relatively viscous fluid by measuring the rate of rebound of a partially submerged object following a rapid decrease in its mass. This experiment is carried out in the context of an analysis of post-glacial rebound as a measurement of the viscosity of the mantle.

Used this activity? Share your experiences and modifications

## Learning Goals

Goals include
• exploring a process that decays exponentially with time,
• determining the relaxtion time for this process,
• relating the relaxation time to the viscosity of a fluid,
• and reinforcing key concepts developed in lecture.

## Context for Use

This laboratory experiment was developed as part of a course on "The Fluid Earth", which covers topics from flow of surficial fluids and magmas to convection in the mantle and core. Students in this class have completed calculus. Before students encounter this lab, the fluid dynamics problem of flow of a liquid through a channel is developed in lecture. This introduction to determining mantle viscosity from measurement of the rate of post-glacial rebound is then used as a starting point for discussing mantle convection and the importance of Rayleigh number.

## Description and Teaching Materials

Activity Description/Assignment (Acrobat (PDF) PRIVATE FILE 526kB Jul17 04)
Solution Set (Excel PRIVATE FILE 29kB Jul9 04)

## Teaching Notes and Tips

In this lab, students determine the viscosity of a relatively viscous fluid by measuring the rate of rebound of a partially submerged object following a rapid decrease in mass. This project, which involves both lecture and lab components, builds several quantitative skills. Participants will need to use their physical intuition, call upon their background in calculus, employ dimensional analysis, and plot experimentally determined data to extract a physical property (viscosity). For context, this lab builds on previous discussions of isostatic equilibrium and flow of fluids through a channel.

## Assessment

Students write a lab report that contains their analysis of the experimental results in tabular and graphical form. As part of this report, they must determine the viscosity of the fluid used in the experiment from the relaxation time for "post-glacial" rebound. Subsequently, a related homework problem is assigned and an exam question is used to determine the student's grasp of the concepts.

## References and Resources

The Bowels of the Earth, John Elder, Oxford University Press, pp. 21-22, 1976.
Geodynamics, D.L. Turcotte and G. Schubert, Cambridge University Press, 2nd ed., pp. xx-yy, 2002.
Mantle convection in the earth and planets, G. Schubert, D.L. Turcotte and P. Olsen, Cambridge University Press, pp. xx-yy, 2001.