Proper treatment of drug addiction and abuse is critically important since it is estimated that the total overall costs of substance abuse in the United States exceed half a trillion dollars annually as reported by National Institute on Drug Abuse (NIDA). Conventional transdermal patches can provide a constant flux of drug in an easy and non invasive way. However many treatments, such as nicotine, fentanyl and clonidine, require variable rates of transdermal delivery. Membranes made of carbon nanotubes possess many advantageous attributes that include: 1) atomically flat graphite surface allows for ideal fluid slip boundary conditions 100,00 times faster than conventional pores 2) the cutting process to open CNTs inherently places functional chemistry at CNT core entrance to act as chemical gatekeepers and 3) CNT are electrically conductive allowing for electrochemical reactions and application of electric fields gradients at CNT tips. Thus CNT membranes are and ideal candidate to have a voltage controlled membrane as the active element in a transdermal drug delivery device. CNT membranes were functionalized with highly-charged anionic dye molecules to induce a highly efficient electroosmotic flow. The anionic charge density on CNTs was first enhanced through diazonium electrochemical modification followed by a quad-anionic dye amine functionalization. It was found that fluxes of both cationic and neutral molecules through the CNT membrane have been greatly increased under negative biases. High electro-osmotic flows of 0.05 cm/s at -300mV bias have been observed with 15% ion efficiency. Electro-osmosis within CNT membranes is strongly related to electric field strength, ionic strength and surface charge density. Employing this phenomenon, the delivery rate of clonidine was enhanced by more than 4 times under -300 mV bias compared to the rate at +300 mV bias. The rate was be increased from 2.8 to 13.8 nano-mole/hr-cm2, which matches the traditional five day opioid withdrawal symptom treatment that requires variable delivery rates ranging from 1.7 to 5.4 nano-mole/hr.cm2. Voltage controlled dosing across human skin samples is also demonstrated.