This is to certify that the work in this thesis entitled "Study of Capillary filling dynamics in a micro channel" by Manisha Swain, has been carried out under my guidance in partial fulfillment of the requirements for the degree of Bachelor of Technology in Mechanical Engineering under session in the Department of Mechanical Engineering, National Institute of Technology, Rourkela. Last but not the least, I thank other faculty members of Department of Mechanical Engineering, NIT Rourkela for their valuable advice at all stages for successful completion of this project report. In this study, an attempt has been made to investigate the influence of certain parameters on the equilibrium height achieved by the liquid in the microchannel.
The formulated governing equation was used to study the effect of parameters such as: phase change, aspect ratio and properties of the fluid numerically using MATLAB. Numerous applications of microfluidic devices in various fields such as biomedical science, MEMS devices, lab on a chip technology, microscale heat exchangers and microheat pipes have made the study of the subject both relevant and important. Deviations of the results obtained by theoretical simulations from the experimental observations have resulted in modification of existing theories.
Department of Mechanical Engineering, N.I.T., Rourkela Page 4 study the flow properties of two different fluids water and ether. The aim was to study the effect of the different flow parameters on the time course of liquid displacement and the equilibrium height achieved. The various parameters studied include consideration of phase changes, temperature differences across the interface, static and dynamic contact angle, different aspect ratios (w/H) of the rectangular microchannel.
An attempt was made to study the vibration damping in the two different fluids used.
LITERATURE SURVEY
Department of Mechanical Engineering, N.I.T., Rourkela Page 7 Stanley [29] conducted some experiments of the single-phase and two-phase fluid flow in microchannels machined on aluminum plate. Based on the experimental data, for water flow, it was stated that no transition occurred at any size of channels at any Reynolds numbers, from 2 to 10000. Guy Ramon and Alexander Oron extended the Lucas-Washburn equation to describe the phase change and interfacial mass transfer due to phase change – evaporation or condensation.
The augmented equation developed contained contributions related to mass loss/gain and also an additional effective force, the vapor drag that occurs as a result of the velocity jump at the interface. Department of Mechanical Engineering, N.I.T., Rourkela Page 8 vapor/air domain diffusion, buoyant convection and particle dynamics were brought together. Deryagin et al [1] and [2] demonstrated reduction of fluid pressure in the thin film region due to pressure detachment.
Potash and Wayner [3] concluded that the variation of decoupled pressure and capillary pressure along the meniscus provides the necessary pressure gradient for fluid supply to the thin-film region. Wayner et al [4] discussed the effects of decoupled pressure on the liquid supply and its role in suppressing evaporation. A comprehensive Young-Laplace equation was obtained for force balance on the thin film by introducing a disjunction pressure. Schonberg et al.
7] developed a fourth order ordinary differential equation for solving the extended Young-Laplace equation and obtained the thickness profile of the extended meniscus. It was concluded that the pressure gradient in the vapor region significantly influenced the thin-film profile. Wee [9] discussed the effects of liquid polarity, slip limit and thermocapillary effects on the thin film profile.
Recently, binary liquids [10] have been found to induce a distillation-driven capillary stress to counteract the thermocapillary stress, leading to an extension in the length of the thin film. Xu and Carey [13] performed a combined analytical and experimental investigation on fluid flow in V-grooves and highlighted the importance of pressure separation in overall heat transfer. Ma and Peterson [14] proposed a mathematical model for the evaporation heat transfer coefficient and temperature variation along the axial direction of a groove, which led to a better understanding of the axial heat transfer coefficient and temperature distribution in grooved surfaces.
THEORY
An important consequence of a non-zero surface tension is the presence of the so-called new Laplace pressure drop (∆psurf) at a curved interface in thermodynamic equilibrium. If we neglect any effect of gravity, there will be only two contributions to the change ∆G of the free energy of the system: an increase in the surface energy Gsurf due to an increased area and a decrease in the pressure-volume energy GpV due to the increased in volume. It is important to note the sign convention used here: the pressure is higher in the convex medium, i.e., the medium in which the center of curvature lies.
Another fundamental concept in the theory of surface effects in microfluidics is the contact angle that occurs at the contact line between three different phases, typically the solid wall of a channel and two immiscible fluids within that channel. The contact angle θ is defined as the angle between the solid-liquid and the liquid-gas interface at the contact line where three immiscible phases meet, as illustrated in Fig. The change of the interface areas is proportional to +δl, + δl cos θ, and –δl for the solid-liquid, liquid-gas, and solid-gas interfaces, respectively.].
While the contact angle in equilibrium is well defined, it turns out to depend in a complex way on the dynamic state of the moving contact line. For example, it can be observed that the contact angle at the advancing edge of a moving liquid droplet on a substrate is different from the contact angle at the receding edge. To derive the expression for the equilibrium contact angle, we again use the minimum free energy condition.
Now imagine that the liquid-gas interface is tilted by an infinitesimal angle about an axis parallel to the contact line and placed far away from the substrate interface. If you want to edit δl, the only change in free energy comes from changes in the interstitial regions near the contact line. 3.1(b) shows that the changes in interface areas are proportional to +δl, +δl cos θ and -δl for solid-liquid, liquid-gas and solid-gas interfaces respectively.
The equilibrium shape of any fluid will be determined by minimizing the free energy G, which consists of the surface energy and the gravitational potential energy of the mass, with a constant volume constraint. Department of Mechanical Engineering, N.I.T., Rourkela Page 16 is called the surface tension of the liquid-air interface. In physical terms, this deviation of the contact angle from its static value is due to the viscous bending of the interface at the contact lines.
THEORITICAL FORMULATION
Normally, the phase change at the interface creates large vapor accelerations due to a large disparity in liquid and vapor density, and the backlash is known as vapor backflow. The pressure exerted by vapor repulsion at the interface is directed to the liquid phase for both evaporation and condensation, and Hickman found that vapor repulsion can be very important in terms of the behavior of the gas-liquid interface where the phase change occurs, especially under reduced pressure conditions. This pressure is the result of the velocity jump that the steam undergoes during evaporation/condensation.
The resulting mass flux can be approximated using kinetic theory which in linearized form reads.
RESULTS AND DISCUSSION
Department of Mechanical Engineering, N.I.T., Rourkela Page 26 (Fig 5.1: Time course of displacement of liquid into the channel with phase change (evaporation) and without phase change consideration). The effect of the temperature difference, which induces the phase change, is evident and decreases the displacement of the meniscus. In the presence of evaporation, j>0 and therefore the movement of the interface will be slower than without phase change.
Department of Mechanical Engineering, N.I.T., Rourkela Page 27 Fig 5.2: Time course of displacement of liquid in the channel for ether for different temperature differences across the interface.(delt =Tl-Tv; where Tl is the temperature of the interface and Tv is the temperature of the vapor.). The effect of the temperature difference causing the phase change is clear and changes both the amplitude and frequency of the interfacial oscillations, when present. Fig-5.2 depicts that as the temperature difference across the interface increases, there is a decrease in the displacement of the meniscus.
Department of Mechanical Engineering, N.I.T., Rourkela Page 28 (Fig-5.3:-Time course of displacement of liquid into the channel of water for different temperature differences across the interface). It is also seen that for a certain aspect ratio (w/H) ether oscillates faster than water possibly due to the lower surface tension. It is also seen that water oscillations decay faster than ether due to the stronger damping effect of the higher viscosity of water. Department of Mechanical Engineering, N.I.T., Rourkela Page 29 (Fig-5.4: Time course of displacement of liquid into the channel of ether for different aspect ratios (w/H) of the rectangular microchannel.).
It is observed in fig-5.4 that as the aspect ratio increases, the amplitude of oscillations decreases and the oscillations also decay faster. This is due to the fact that the limiting effect due to the transverse side (side with smaller dimension) of the channel becomes less significant with increasing aspect ratio. Department of Mechanical Engineering, N.I.T., Rourkela Page 30 Fig-5.5: Effect of contact angle in the time course of fluid front flowing in a microchannel.
Department of Mechanical Engineering, N.I.T., Rourkela Page 31 Fig-5.6: Time course of displacement of fluid into the microchannel for dynamic contact angle and static contact angle. As the velocity decreases with time, the Capillary number also decreases in accordance with the same and consequently the apparent contact angle also decreases. Since the surface tension force is proportional to the cosine of this contact angle, it increases progressively as the contact angle decreases during the liquid inflow process.
CONCLUSIONS
Carey, Film evaporation from a microgrooved surface - an approximate heat transfer model and its comparison with experimental data, J. Som, Heat transfer in an evaporating liquid thin film moving slowly along the walls of an inclined microchannel, Int.
