Electrofluidic and electrowetting display pixels, electrofluidic and electrowetting displays, and methods of operating electrofluidic and electrowetting display pixels. The pixel includes a hydrophobic channel formed between first and second substrates and containing a polar fluid and a non-polar fluid, of which at least one is visible through at least one substrate. An electrode with a dielectric is electrically connected to a voltage source. A Laplace barrier defines a fluid pathway for fluid movement in the channel. The polar fluid moves a first position when the voltage source is biased at a first voltage of less than or equal to a threshold voltage to provide a first display state. The polar fluid moves to a second position when the voltage source is biased with a second voltage, greater than the first voltage, to provide a second display state.