A device has a first part with a valve seat and storage chamber, and a second part with a flexible valve cover and actuator. The storage chamber may be formed from a pre-form blow-molded into a flexible pouch defining a variable-volume storage chamber. The flexible valve cover and valve seat form a normally closed valve seam therebetween. The valve cover is movable in response to fluid at an inlet to the seam exceeding a valve opening pressure of the one-way valve between (i) a normally closed position with valve cover and valve seat in contact with each other and defining the normally closed seam, and (ii) a second position with at least a portion of the valve cover spaced away from the valve seat to allow the fluid to pass through the seam. The one-way valve may have anti-spritz features for using the device to dispense a substance, such as to the eye. The device may contain prostaglandins without the device material absorbing the prostaglandins material and/or without the material being adsorbed into the drug.