The present disclosure relates to a pump mechanism driven by differential pressure conditions and method for delivery of materials. In one embodiment, the pump mechanism may be used to deliver treatment chemical to a plunger apparatus or directly to a wellbore by exploiting pressure conditions found at a well. In certain embodiments, the pump mechanism is able to balance high pressure conditions available within a petroleum formation against low pressure conditions present in a common flow line serving the well. In so balancing these pressures, the pump mechanism is able to automatically tune itself to the needs of the well, ensuring continued operation over a wider range of operating conditions. The pump mechanism has the further advantages of lower operation costs and less environmental impact as compared with existing pumps. The pump mechanism can be used in connection with a chemical applicator which can be used to apply chemical into, onto, or below, a plunger or plunger/dispenser apparatus used in plunger lift operations, or to apply chemical directly down the well. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.