NOVELTY - Process for distilling a fluid mixture (I) (comprising more- and less volatile components) in a microchannel distillation unit comprising microchannel distillation sections (II) comprises flowing a vapor (I) in a first (II), to form a more volatile component rich vapor phase (a) and a less volatile component rich liquid phase (b); separating (a) from (b); flowing (b) to another (II) upstream; and flowing (a) to another (II) downstream.    USE - The process is useful for distilling a fluid mixture in a microchannel distillation unit, e.g. separation of ethane and ethylene; styrene and ethyl benzene; oxygen and nitrogen; cyclohexane and cyclohexanol or cyclohexanone; isobutane or naphtha.    ADVANTAGE - The process avoids the use of equipments with large internal volumes, which slows down the start up, and responds to changes in operating conditions. The process is cost-effective. The process consumes significantly less energy and provides the same level of product output as the conventional distillation systems. The process reduces one or more of thermal response times, control feedback times and start-up times needed for achieving steady-state operations for continuous distillation processes.    DETAILED DESCRIPTION - Process for distilling a fluid mixture (I) in a microchannel distillation unit having microchannel distillation sections (II) comprises flowing a vapor phase of (I) in a section (A) in contact with a liquid phase of (I), part of the more volatile component transferring from the liquid phase to the vapor phase, part of the less volatile component transferring from the vapor phase to the liquid phase; separating the more volatile component rich vapor phase from the less volatile component rich liquid phase; flowing the less volatile component rich liquid phase to another (II) upstream from the first (II); and flowing the more volatile rich vapor phase to another (II) downstream from the first (II).    INDEPENDENT CLAIMS are also included for:    (1) a process for distilling a fluid mixture in a microchannel distillation unit comprising a process microchannel and an adjacent liquid channel, comprising flowing a vapor phase of the fluid mixture through the process microchannel comprising a plurality of microchannel distillation sections, which comprises an internal space for permitting vapor flow, an interior wall, a capture structure, a liquid inlet and a liquid outlet, the capture structure and the liquid outlet being downstream from the liquid inlet, the interior wall extending from the liquid inlet to the outlet, the capture structure being suitable for capturing liquid and permitting vapor to flow through it; flowing the liquid phase through the liquid channel in opposite direction to the direction of flow of the vapor phase in the process microchannel, the liquid channel including a wicking region; the liquid phase flowing from the liquid channel through the liquid inlet in a first microchannel distillation section of the process microchannel and flowing as a thin film along the interior wall to the capture structure within the first microchannel distillation section, the vapor phase flowing through the first microchannel distillation section in contact with the liquid phase flowing along the interior wall, part of the more volatile component transferring from the liquid phase to the vapor phase, part of the less volatile component transferring from the vapor phase to the liquid phase, the less volatile component rich liquid phase contacting the capture structure and flowing from the capture structure through the outlet of the first microchannel distillation section into the liquid channel, the more volatile component rich vapor phase flowing through the capture structure of the first microchannel distillation section;    (2) a process for distilling a fluid mixture in a distillation apparatus comprising a plurality of microchannel distillation units, each microchannel distillation unit comprising a plurality of microchannel distillation sections, comprising flowing a vapor phase of the fluid mixture in a first microchannel distillation section of at least one microchannel distillation unit in contact with a liquid phase of the fluid mixture, part of the more volatile component transferring from the liquid phase to the vapor phase to form a more volatile component rich vapor phase, part of the less volatile component transferring from the vapor phase to the liquid phase to form a less volatile component rich liquid phase; separating the more volatile component rich vapor phase from the less volatile component rich liquid phase; flowing the less volatile component rich liquid phase to another microchannel distillation section in the microchannel distillation unit upstream from the first microchannel distillation section; and flowing the more volatile rich vapor phase to another microchannel distillation section in the microchannel distillation unit downstream from the first microchannel distillation section;    (3) a microchannel distillation unit, comprising a process microchannel and a liquid channel (comprising a wicking region); the liquid channel being adjacent to the process microchannel (comprising a plurality of microchannel distillation sections); each microchannel distillation section comprising an internal space for permitting vapor flow, an interior wall for permitting liquid to flow as a thin film along the interior wall, a capture structure for capturing liquid and permitting vapor to flow through it, a liquid outlet for permitting liquid to flow from the capture structure into the liquid channel, and a liquid inlet for permitting liquid to flow from the liquid channel into the process microchannel; and    (4) a microchannel distillation unit, comprising a liquid channel, a first process microchannel, a second process microchannel, a first vapor channel, a second vapor channel, a third vapor channel, a vapor inlet and a vapor outlet, the first process microchannel and the second process microchannel being adjacent to the liquid channel, where the liquid channel comprises a wicking region, part of the wicking region forming a wall of the first process microchannel and a wall of the second process microchannel, the first vapor channel being adjacent to the first process microchannel, the third vapor channel being adjacent to the second process microchannel, the second vapor channel being adjacent to the first and third vapor channels, the first and third vapor channels being positioned between the first and second process microchannels and the second vapor channel.