White chunks, flakes, or eggshell-like particles that clog faucet aerators and showerheads are likely a build-up of calcium carbonate from water heater tanks. The problem can be caused by older tanks, water heater tanks that are set to a higher temperature, or tanks that are experiencing dip tube failure. The problem can likely be cleared by flushing the water heater tank, inspecting the dip tube (and replacing, if needed), lowering the temperature on your tank, and cleaning all strainers and aerators. Contact a qualified plumber for additional information.