Braginsky (1963) has suggested that the geodynamo is gravitationally powered through the settling downwards of the heavy iron-rich component in the fluid outer core to form a growing solid inner core. Supposing for simplicity that the core is a binary alloy, we examine implications of Braginsky's idea and, in particular, discuss the importance of slurry layers in the fluid core. A thermodynamically acceptable theory for the motion of a slurry is developed, and approximations that make it tractable are discussed. The structure of a well-mixed slurry layer is elucidated. The theory is used to show how seismic waves traversing a slurry are damped and dispersed as a result of melting and re-freezing of the solid phase caused by the passage of the wave.