Micro-engineered devices (MED) are seeing a significant growth in performing separation processes1. Such devices have been implemented in a range of applications from chemical catalytic reactors to product purification systems like microdistillation. One of the biggest advantages of these devices is the dominance of capillarity and interfacial tension forces. A field where MEDs have been used is in gas-liquid separations. These are encountered, for example, after a chemical reactor, where a gaseous component being produced needs immediate removal from the reactor, because it can affect subsequent reactions. The gaseous phase can be effectively removed using an MED with an array of microcapillaries. Phase-separation can then be brought about in a controlled manner along these capillary structures. For a device made from a hydrophilic material (e.g. Si or glass), the wetted phase (e.g. water) flows through the capillaries, while the non-wetted dispersed phase (e.g. gas) is prevented from entering the capillaries, due to capillary pressure. Separation of liquid-liquid flows can also be achieved via this approach. However, the underlying mechanism of phase separation is far from being fully understood. The pressure at which the gas phase enters the capillaries (gas-to-liquid breakthrough) can be estimated from the Young-Laplace equation, governed by the surface tension (γ) of the wetted phase, capillary width (d) and height (h), and the interface equilibrium contact angle (θeq). Similarly, the liquid-to-gas breakthrough pressure (i.e. the point at which complete liquid separation ceases and liquid exits through the gas outlet) can be estimated from the pressure drop across the capillaries via the Hagen-Poiseuille (HP) equation. Several groups reported deviations from these estimates and therefore, included various parameters to account for the deviations. These parameters usually account for (i) flow of wetted phase through ‘n’ capillaries in parallel, (ii) modification of geometric correction factor of Mortensen et al., 2005 2 and (iii) liquid slug length (LS) and number of capillaries (n) during separation. LS has either been measured upstream of the capillary zone or estimated from a scaling law proposed by Garstecki et al., 2006 3. However, this approach does not address the balance between the superficial inlet velocity and net outflow of liquid through each capillary (qc). Another shortcoming of these models has been the estimation of the apparent contact angle (θapp), which plays a critical role in predicting liquid-to-gas breakthrough. θapp is either assumed to be equal to θeq or measured with various techniques, e.g. through capillary rise or a static droplet on a flat substrate, which is significantly different from actual dynamic contact angles during separation. In other cases, the Cox-Voinov model has been used to calculate θapp from θeq and capillary number. Hence, the empirical models available in the literature do not predict realistic breakthrough pressures with sufficient accuracy. Therefore, a more detailed in situ investigation of the critical liquid slug properties during separation is necessary. Here we report advancements in the fundamental understanding of two-phase separation in a gas-liquid separation (GLS) device through a theoretical model developed based on critical events occurring at the gas-liquid interfaces during separation.
Distribution of growth probabilities in fluid flow and diffusion-limited aggregation
