Direct contact between uremic blood and a fluid capable of receiving uremic toxins is possible. Such contact by itself is, however, not beneficial because the selection of molecules that are removed is dependent on diffusion coefficients in blood. This selection is inadequate and would result in the exhaustion of a patient's albumin pool before useful reduction in the urea pool was achieved. Direct contact that is accomplished by sandwiching blood between two layers of a sheathing fluid, followed by diafiltration of the sheathing fluid through conventional membranes and recirculation of the sheathing fluid, is possible. This adaptation of membraneless transport of molecules from blood eliminates almost all contact of blood with solid artificial surfaces and the subsequent diafiltration and recirculation of the sheathing fluid allows precise control of what is removed from the system. Slightly hyperosmotic protein is carried back by the recirculating sheathing fluid. Only solutes and water that pass the diafilter, which operates on a cell-free fluid, are able to leave the system. The system depends strongly on the ability to keep cells out of the sheathing fluid. Preliminary results and earlier reports indicate that this separation is possible and more precise measurements are underway. A quantitative design of a wearable dialyzer based on a circulating sheathing fluid is presented.