WE PROPOSE THEORETICAL AND NUMERICAL STUDIES OF CONSTRAINED VAPOR-LIQUID INTERFACES IN THE PRESENCE OF PHASE CHANGE I.E. EVAPORATION AND/OR CONDENSATION. THESE STUDIES WILL RESULT IN BETTER UNDERSTANDING OF HEAT AND MASS TRANSFER IN TWO-PHASE SYSTEMS IN WHICH THE EFFECTS OF CAPILLARY FORCES AND THERMOCAPILLARITY ARE IMPORTANT. THE MAIN FOCUS OF THE WORK IS ON A SPECIFIC GEOMETRIC CONFIGURATION USED IN A RECENT SPACE EXPERIMENT REFERRED TO AS A CONSTRAINED VAPOR BUBBLE (CVB). WE PROPOSE TO USE ASYMPTOTIC METHODS TO SIMPLIFY THE SYSTEM OF GOVERNING EQUATIONS FOR FLUID FLOW AND HEAT TRANSFER FOR THIS CONFIGURATION FOLLOWED BY NUMERICAL SOLUTIONS OF THE RESULTING EQUATIONS USING MODERN COMPUTATIONAL TECHNIQUES. THE PROPOSED WORK HAS A WIDE RANGE OF GROUND AND SPACE APPLICATIONS INCLUDING TWO-PHASE COOLING SYSTEMS FOR TRADITIONAL ELECTRONIC DEVICES SUCH AS LAPTOP COMPUTERS AS WELL AS NOVEL THERMAL MANAGEMENT SYSTEMS FOR EMERGING APPLICATIONS SUCH AS PROTON EXCHANGE MEMBRANE FUEL CELLS AND PHOTOVOLTAIC CELLS FOR SOLAR ENERGY HARVESTING. THE SMALL LENGTH SCALES IN MANY OF THESE SYSTEMS IMPLY THAT INTERFACIAL PHENOMENA ARE VERY IMPORTANT WHILE THE EFFECTS OF GRAVITY ARE SECONDARY. SOME ASPECTS OF THE PROPOSED WORK ARE ALSO RELEVANT FOR MODELING OF PHYSICAL PROCESSES SUCH AS SELF-ASSEMBLY OF COLLOIDAL PARTICLES FROM EVAPORATING DROPLETS CONDENSATION OF DROPLETS IN NOVEL DEVICES FOR ENERGY CONVERSION AND WATER DESALINATION. THE LIQUID TRANSPORT MECHANISMS BY CAPILLARY FORCES ARE ALSO IMPORTANT TO STUDY FOR SPACE APPLICATIONS SUCH AS ADVANCED COOLING SYSTEMS FOR SPACECRAFT SINCE CONVENTIONAL METHODS FOR LIQUID TRANSPORT CAN FAIL OR BECOME IMPRACTICAL IN SUCH APPLICATIONS. FOR EXAMPLE ANY SYSTEM THAT RELIES ON THE FORCE OF GRAVITY FOR FUNCTIONING IS LIKELY TO FAIL IN THE MICROGRAVITY ENVIRONMENT. TRANSPORTING LIQUIDS BY EXTERNAL PRESSURE GRADIENTS WHILE NOT IMPOSSIBLE IN SPACE TYPICALLY REQUIRES MECHANICAL PUMPS OFTEN MAKING SUCH SYSTEMS IMPRACTICAL BECAUSE OF THE PAYLOAD WEIGHT RESTRICTIONS.