Analytical treatments of micro-channel and micro-capillary flows

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Extensive work in the field of micro-channel and micro-capillary flows using the extended Navier-Stokes equations are carried out in this paper by taking the diffusive mass transport into account and provided the basis for analytical treatments of these flows. The results are compared with experimental results for micro-channels and showed good agreement. It is found that a characteristic pressure is useful to explain the comparisons. In addition, the work on micro-channel flows is extended to micro-capillary flows, to provide analytical treatments of this class of flows. The analytical results show similar behavior to that of micro-channel flows. Comparisons between the analytical results and experimental findings are also presented and discussed by introducing the characteristic pressure

Why Capillary Flows in Slender Triangular Grooves Are So Stable Against Disturbances

Ongoing development of fuel storage and delivery systems for space probes, interplanetary vehicles, satellites, and orbital platforms continues to drive interest in propellant management systems that utilize surface tension to retain, channel, and control flow in microgravity environments. Although it has been known for decades that capillary flows offer an ideal method of fuel management, there has been little research devoted to the general stability properties of such flows. In this work we demonstrate theoretically why capillary flows which channel wetting liquids in slender open triangular channels tend to be very stable against disturbances. By utilizing the gradient flow form of the governing fluid interface equation, we first prove that stationary interfaces in the presence of steady flow are asymptotically nonlinearly and exponentially stable in the Lyapunov sense. We then demonstrate that fluid interfaces exhibiting self-similar Washburn dynamics are transiently and asymptotically linearly stable to small perturbations. This second finding relies on a generalized nonmodal stability analysis due to the non-normality of the governing disturbance operator. Taken together, these findings reveal the robust nature of transient and steady capillary flows in open grooved channels and likely explain the prevalent use of capillary flow management systems in many emerging technologies ranging from CubeSats to point-of-care microfluidic diagnostic systems

Deposit Growth in the Wetting of an Angular Region with Uniform Evaporation

Solvent loss due to evaporation in a drying drop can drive capillary flows and solute migration. The flow is controlled by the evaporation profile and the geometry of the drop. We predict the flow and solute migration near a sharp corner of the perimeter under the conditions of uniform evaporation. This extends the study of Ref. 6, which considered a singular evaporation profile, characteristic of a dry surrounding surface. We find the rate of the deposit growth along contact lines in early and intermediate time regimes. Compared to the dry-surface evaporation profile of Ref. 6, uniform evaporation yields more singular deposition in the early time regime, and nearly uniform deposition profile is obtained for a wide range of opening angles in the intermediate time regime. Uniform evaporation also shows a more pronounced contrast between acute opening angles and obtuse opening angles.Comment: 12 figures, submitted to Physical Review

Fluid Vesicles in Flow

We review the dynamical behavior of giant fluid vesicles in various types of external hydrodynamic flow. The interplay between stresses arising from membrane elasticity, hydrodynamic flows, and the ever present thermal fluctuations leads to a rich phenomenology. In linear flows with both rotational and elongational components, the properties of the tank-treading and tumbling motions are now well described by theoretical and numerical models. At the transition between these two regimes, strong shape deformations and amplification of thermal fluctuations generate a new regime called trembling. In this regime, the vesicle orientation oscillates quasi-periodically around the flow direction while asymmetric deformations occur. For strong enough flows, small-wavelength deformations like wrinkles are observed, similar to what happens in a suddenly reversed elongational flow. In steady elongational flow, vesicles with large excess areas deform into dumbbells at large flow rates and pearling occurs for even stronger flows. In capillary flows with parabolic flow profile, single vesicles migrate towards the center of the channel, where they adopt symmetric shapes, for two reasons. First, walls exert a hydrodynamic lift force which pushes them away. Second, shear stresses are minimal at the tip of the flow. However, symmetry is broken for vesicles with large excess areas, which flow off-center and deform asymmetrically. In suspensions, hydrodynamic interactions between vesicles add up to these two effects, making it challenging to deduce rheological properties from the dynamics of individual vesicles. Further investigations of vesicles and similar objects and their suspensions in steady or time-dependent flow will shed light on phenomena such as blood flow.Comment: 13 pages, 13 figures. Adv. Colloid Interface Sci., 201

Capillary rise of a liquid between two vertical plates making a small angle.

The penetration of a wetting liquid in the narrow gap between two vertical plates making a small angle is analyzed in the framework of the lubrication approximation. At the beginning of the process, the liquid rises independently at different distances from the line of intersection of the plates except in a small region around this line where the effect of the gravity is negligible. The maximum height of the liquid initially increases as the cubic root of time and is attained at a point that reaches the line of intersection only after a certain time. At later times, the motion of the liquid is confined to a thin layer around the line of intersection whose height increases as the cubic root of time and whose thickness decreases as the inverse of the cubic root of time. The evolution of the liquid surface is computed numerically and compared with the results of a simple experiment

Vibration isolation technology: Sensitivity of selected classes of space experiments to residual accelerations

Progress performed on each task is described. Order of magnitude analyses related to liquid zone sensitivity and thermo-capillary flow sensitivity are covered. Progress with numerical models of the sensitivity of isothermal liquid zones is described. Progress towards a numerical model of coupled buoyancy-driven and thermo-capillary convection experiments is also described. Interaction with NASA personnel is covered. Results to date are summarized and they are discussed in terms of the predicted space station acceleration environment. Work planned for the second year is also discussed

Developing flow pattern maps for accelerated two-phase capillary flows

The prediction offlow pattern transitions is extremely important to understand the coupling of thermal andfluiddynamic phenomena in two phase systems and it contributes to the optimum design of heat exchangers. Twophaseflow regimes have been extensively studied under controlled massflow rate and velocity. On the otherhand, less effort has been spent in the literature on the cases where theflow motion is purely thermally inducedand consequently the massflow rate or the velocity of the phases are not known a priori. In the present work,flow pattern transitions and bubble break-up and coalescence events have been investigated in a passive twophase wickless capillary loop, where the massflow rate is intrinsically not controllable. Modified Froude, Weberand Bond numbers have been introduced, considering the actual acceleration of thefluid and the length of thebubble as merit parameters for the transitions. The proposed nondimensional investigation was developed byanalysing experimental data obtained with ethanol and FC-72, as workingfluids, different heat input levels(from 9 to 24 W) as well as three different gravity levels (through a parabolicflight campaign). A new empiricaldiabaticflow pattern map for accelerated two-phase capillaryflows is presented, together with quantitativecriteria for the calculation of theflow regime transitions, defining the physic limits for the bubble coalescenceand break-up. This kind of new regime maps will be useful to the further development of comprehensive de-signing tools for passive two-phase wickless heat transfer devices