This is to certify that the work in this thesis entitled "Study of Capillary filling dynamics in a microtube" by Swati Sahoo, was carried out under my supervision in partial fulfillment of the requirements for the degree of Bachelor of Technology in Mechanical Engineering during session in the Department of Mechanical Engineering, National Institute of Technology, Rourkela. Last but not the least, I express my sincere thanks to other faculty members of the Department of Mechanical Engineering, NIT Rourkela, for their valuable advice at every stage for the successful completion of this project report. Capillary filling dynamics in a microtube and different aspects of this type of flow have remained a long-running problem in the last decade considering its numerous applications in various fields.
In this study, we tried to study the influence of certain parameters on the equilibrium height reached by the liquid in the microtube. Lucas Washburn's equation has been modified using the concept of phase change and vapor reflection and also takes into account input effects in terms of added mass. The formulated governing equation was used to study the effect of parameters such as: phase change, different interface temperature difference and fluid properties numerically using MATLAB.
Microfluidics deals with the behavior of fluids in the sub-millimeter range, and its study requires a different approach from the conventional ones used for macrofluidics, although the underlying physics for both remains the same. It is a multidisciplinary field including engineering, physics, chemistry, microtechnology and biotechnology. Numerous applications of microfluidic devices in various fields such as biomedical science, MEMS devices, lab-on-a-chip technology, micro-scale heat exchanger and micro heat pipes have been studied. of the subject both relevant and significant. Deviations of results obtained from theoretical simulations from experimental observation have resulted in the modification of existing theories.
It is used in the creation of microfluidic biochips that are used in clinical pathology and whose function is
LITERATURE SURVEY
Stanley conducted some experiments on single-phase and two-phase fluid flow. Based on experimental data for water flow, it was found that no transition occurred for any channel size at any Reynolds number, from 2 to 10000. Guy Ramon and Alexander Oron extended the Lucas-Washburn equation to account for phase change and interphase transfer mass due to phase change - evaporation or condensation.
The improved equation that was developed included contributions related to mass loss/gain and also an additional effective force, vapor recoil that occurs due to the velocity jump at the. Of the various geometries examined, circular, trapezoidal, and triangular cross-sections gained more importance than others. A comprehensive Young-Laplace equation was obtained for force balance on the thin film by introducing a disjunction pressure. Schonberg et al. [5] investigated the thin film by ignoring Pc.
Ma and Peterson [14] proposed a mathematical model for the evaporative heat transfer coefficient and temperature variation along the axial direction of a groove, leading to a better understanding of the axial heat transfer coefficient and temperature distribution on grooved. Morris [15] suggested a universal relationship between heat flow, contact angle, interfacial curvature, superheating and material properties, which can be extended to different geometries.
THEORY
A molecule in most liquids forms chemical bonds (arrows) with neighboring molecules that surround it. A molecule on the surface of a liquid misses chemical bonds in the direction of the surface (dashed lines). An important consequence of the non-zero surface tension is the presence of the so-called Young.
Neglecting any effect of gravity, there will be only two contributions to the change in °G of the system's free energy: the increase in surface energy Gsurf due to increased surface area and the decrease in pressure and volume energy GpV due to increase in volume. It is important to note the sign convention used here: the pressure is highest in a convex medium, i.e. the medium in which the center of curvature is. Another fundamental concept in the theory of surface effects in microfluidics is the contact angle.
The two concepts, contact angle and surface tension, allow to understand the capillary forces acting on flows with two fluids inside. The contact angle θ is defined as the angle between the solid-liquid interface and the liquid-gas interface. The change in interfacial 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. 3(b) that the interface area changes are proportional to +δl, +δl cos θ and -δl for solid-liquid, liquid-gas and solid-gas interfaces, respectively. The contact angle of the pipe-liquid-air system is denoted by θ, and the surface tension of the liquid-air interface is called.
THEORETICAL FORMULATION
The resulting mass flux[18] can be approximated using kinetic theory which in linearized form reads;. The radius of curvature is a function of the contact angle θ, which in turn depends on the accuracy. The capillary effect in the microtube results in the formation of a triple junction due to the interaction of the solid-liquid, liquid-gas and solid-gas interfaces. To model the contact lines in motion, the physical phenomena affecting the capillary must be evaluated. action.
The contact angle is not static but is in fact dynamic as it depends on velocity.
Results and discussion
Fig-6 Time course of displacement of fluid in the tube with and without phase change consideration. The effect of phase change is induced due to temperature difference between liquid and the vapor in the tube. This leads to vapor backlash as discussed in chapter 4. As seen in equation (7), vapor backlash always causes a pressure in the negative direction, thus opposing the flow. The effect of temperature difference causing phase change is obvious as it affects the frequency and amplitude of oscillations.
This indicates that due to an increase in the temperature difference, the evaporation increases, thus increasing the vapor recoil time (j>0), which opposes the capillary flow. Fig-8:-Time course of displacement of liquid into the pipe for water for different temperature differences across the interface. It is seen that ether oscillates faster than water due to the lower surface tension of ether and the oscillations in the case of water decay faster than ether, possibly due to the higher viscosity of water, which gives a higher damping effect.
Figure-9: Time course of liquid displacement into the ether channel for different capillary radii R of the microtube. This is also evident from the governing equation (9), which shows that the displacement is inversely proportional to the radius. As the radius increases, the driving force, which is surface tension, decreases, so its motion is slowed down.
Effect of contact angle: Figure 10 shows the effect of contact angle when a liquid flows in a microtube. Figure 11:- Time course of liquid displacement in microtube for dynamic contact angle and static contact angle. As the velocity decreases with increasing time, therefore, according to Tanner's law, the capillary number also decreases and, consequently, the apparent angle also decreases.
However, since the surface tension force depends on the cosine of the angle, the displacement increases with time compared to the static contact angle.
CONCLUSIONS
Som, Heat transfer in an evaporating thin liquid film moving slowly along the walls of an inclined microchannel, Int. Ko, An Analytical Study of the Effects of Surface Roughness on Boundary Layer Permeability, AF Office of Scien. Lide (eds.), CRC Handbook of Chemistry and Physics, 87th ed., Taylor and Francis, Boca Raton, 2007; Internet version: http://www.hbcpnetbase.com.
