A valve is provided that can selectively change the size of a flow channel in a valve in order to modulate the fluid flow through the valve. In one illustrative embodiment, the valve includes a housing that defines a cavity, with an inlet and an outlet extending into the cavity. A diaphragm is positioned in the cavity, where at least part of the diaphragm defines at least part of the fluid path. One or more electrodes are fixed relative to the diaphragm, and one or more electrodes are fixed relative to the housing such that the diaphragm can be electrostatically actuated to modulate the fluid flow through the valve.