Current drug delivery devices (DDD) are mainly based on the use of diffusion as the main transport process. Diffusion-driven processes can only achieve low release rate because diffusion is a slow process. This represents a serious obstacle in the realization of recent successes in the suppression of lymphatic metastasis and in the prevention of limb and organ transplant rejection. Surprisingly, it was overlooked that there is a more favorable drug release mode which can be achieved when a special DDD is implanted near lymphatics. This opportunity can be realized when the interstitial fluid flow penetrates a drug delivery device of proper design and allows such fluid to flow out of it. This design is based on hollow fibers loaded with drug and whose hydrodynamic permeability is much higher than that of the surrounding tissue. The latter is referred to as hollow fiber of high hydrodynamic permeability (HFHP). The interstitial flow easily penetrates the hollow fiber membrane as well as its lumen with a higher velocity than that in the adjacent tissue. The interstitial liquid stream entering the lumen becomes almost saturated with drug as it flows out of the HFHP. This is due to the drug powder dissolution in the lumens of HFHP which forms a strip of drug solution that crosses the interstitium and finally enters the lymphatics. This hydrodynamically-driven release (HDR) may exceed the concomitant diffusion-driven release (DDR) by one or even two orders of magnitude. The hydrodynamics of the two-compartment media is sufficient for developing the HDR theory which is detailed in this paper. Convective diffusion theory for two compartments (membrane of hollow fiber and adjacent tissue) is required for exact quantification when a small contribution of DDR to predominating HDR is present. Hence, modeling is important for HDR which would lead to establishing a new branch in physico-chemical hydrodynamics. The release rate achieved with the use of HFHP increases proportional to the number of hollow fibers in the fabric employed in drug delivery. Based on this contribution, it is now possible to simultaneously provide high release rates and long release durations, thus overcoming a fundamental limitation in drug delivery. Perhaps this breakthrough in long-term drug delivery has potential applications in targeting lymphatics and in treating cancer and cancer metastasis without causing the serious side effects of systemic drugs.