One-Dimensional Small Signal Waves in Electrofluidized Beds

An analysis is presented of one-dimensional small signal wave propagation and reflection in space charge free electrofluidized beds of polarizable particles. For an inviscid bed, the linearized governing partial differential equations are shown to be hyperbolic and are solved using the method of characteristics and a Fourier series method. With an applied electric field, small signal waves propagate at constant speed with and against the flow including reflections from boundaries. A semiinfinite bed is unstable with a small electric field but can be stabilized with a suitably strong electric field. A finite-length bed with zero perturbation voidage or spatial derivative of voidage at the top is always stable, as the steady state is bounded with time. However, with a mixed voidage-spatial derivative of voidage boundary condition at the top, the bed can be unstable. Surprisingly, a viscous bed has ranges of instability even though the inviscid bed is formally stable.