This work addresses novel means for controlled mixing and reaction initiation in biomimetic confined compartments having volume elements in the range of 10(-12) to 10(-15) L. The method is based on mixing fluids using a two-site injection scheme into growing surfactant vesicles. A solid-state injection needle is inserted into a micrometer-sized vesicle (radius 5-25 mum), and by pulling on the needle, we create a nanoscale surfactant channel connecting injection needle and the vesicle. Injection of a solvent A from the needle into the nanotube results in the formation of a growing daughter vesicle at the tip of the needle in which mixing takes place. The growth of the daughter vesicle requires a flow of surfactants in the nanotube that generates a flow of solvent B inside the nanotube which is counterdirectional to the pressure-injected solvent. The volume ratio psi between solvent A and B inside the mixing vesicle was analyzed and found to depend only on geometrical quantities. The majority of fluid injected to the growing daughter vesicle comes from the pressure-based injection, and for a micrometer-sized vesicle it dominates. For the formation of one daughter vesicle (conjugated with a 100-nm radius tube) expanded from 1 to 200 mum in radius, the mixing ratios cover almost 3 orders of magnitude. We show that the system can be expanded to linear strings of nanotube-conjugated vesicles that display exponential dilution. Mixing ratios spanning 6 orders of magnitude were obtained in strings of three nanotube-conjugated micrometer-sized daughter vesicles.