Instability of flow with temperature‐dependent viscosity: A model of magma dynamics

In material whose viscosity is very temperature dependent, flow from a chamber through a cooled slot can develop a fingering instability or time‐dependent behavior, depending on the elastic properties of the chamber, the viscosity‐temperature relationship, and the geometry of the slot. A laboratory experiment is described where syrup flows from a reservoir through a tube immersed in a chilled bath to an exit hole at constant pressure. Flow is either steady or periodic depending on the temperature of the bath and the flow rate into the reservoir. A theory indicates that the transition from steady to periodic flow depends on nonlinearities in the steady state relation between pressure and flow rate. A general stability criterion is advanced that states that the Peclet number must be within a certain range for instability to develop. Parameters governing the oscillation period are determined. Theory also indicates that flow through a slot would develop finger‐like instabilities under certain conditions. Qualitative laboratory experiments with paraffin spreading over a cold plate reveal the fingering.