6 results
The symmetric draining of capillary liquids from containers with interior corners
- Mark M. Weislogel, Joshua T. McCraney
-
- Journal:
- Journal of Fluid Mechanics / Volume 859 / 25 January 2019
- Published online by Cambridge University Press:
- 26 November 2018, pp. 902-920
-
- Article
- Export citation
-
A new lubrication model solution is found for the late-stage draining of a wetting capillary liquid from a linear interior corner. The solution exploits the symmetry of volumetric sink conditions at opposing ends of such a ‘double-drained’ interior corner flow with applications ranging from liquid recovery in microfluidic devices on Earth to liquid fuel scavenging in large fuel tanks aboard spacecraft. At long times $t$, the nominal liquid depth is $h\sim t^{-1}$, the liquid volume is $V\sim t^{-2}$ and the maximum volumetric liquid removal rate is $Q\sim t^{-3}$. The constraints under which the solution is valid are provided. To qualitatively assess the value of the solution, representative experiments are conducted at larger length scales aboard the International Space Station and at microfluidic length scales in a terrestrial laboratory. Both sets of experiments confirm the predicted power-law dependences. We show that the separation of variables solution offers a method to predict maximum drain rates from related geometries where a single drain location provides the required symmetry of the problem.
Compound capillary rise
- Mark M. Weislogel
-
- Journal:
- Journal of Fluid Mechanics / Volume 709 / 25 October 2012
- Published online by Cambridge University Press:
- 23 August 2012, pp. 622-647
-
- Article
- Export citation
-
Irregular conduits, complex surfaces, and porous media often manifest more than one geometric wetting condition for spontaneous capillary flows. As a result, different regions of the flow exhibit different rates of flow, all the while sharing common dynamical capillary pressure boundary conditions. The classic problem of sudden capillary rise in tubes with interior corners is revisited from this perspective and solved numerically in the self-similar visco-capillary limit à la Lucas–Washburn. Useful closed-form analytical solutions are obtained in asymptotic limits appropriate for many practical flows in conduits containing one or more interior corner. The critically wetted corners imbibe fluid away from the bulk capillary rise, shortening the viscous column length and slightly increasing the overall flow rate. The extent of the corner flow is small for many closed conduits, but becomes significant for flows along open channels and the method is extended to approximate hemiwicking flows across triangular grooved surfaces. It is shown that an accurate application of the method depends on an accurate a priori assessment of the competing viscous cross-section length scales, and the expedient Laplacian scaling method is applied herein toward this effect.
Quasi-steady capillarity-driven flows in slender containers with interior edges
- Mark M. Weislogel, J. Alex Baker, Ryan M. Jenson
-
- Journal:
- Journal of Fluid Mechanics / Volume 685 / 25 October 2011
- Published online by Cambridge University Press:
- 23 September 2011, pp. 271-305
-
- Article
- Export citation
-
In the absence of significant body forces the passive manipulation of fluid interfacial flows is naturally achieved by control of the specific geometry and wetting properties of the system. Numerous ‘microfluidic’ systems on Earth and ‘macrofluidic’ systems aboard spacecraft routinely exploit such methods and the term ‘capillary fluidics’ is used to describe both length-scale limits. In this work a collection of analytic solutions is offered for passive and weakly forced flows where a bulk capillary liquid is slowly drained or supplied by a faster capillary flow along at least one interior edge of the container. The solutions are enabled by an assumed known pressure (or known height) dynamical boundary condition. Following a series of assumptions this boundary condition can be in part determined a priori from the container dimensions and further quantitative experimental evidence, but not proof, is provided in support of its expanded use herein. In general, a small parameter arises in the scaling of the problems permitting a decoupling of the edge flow from the global bulk meniscus flow. The quasi-steady asymptotic system of equations that results may then be easily solved in closed form for a useful variety of geometries including uniform and tapered sections possessing at least one critically wetted interior edge. Draining, filling, bubble displacement and other imbibing flows are studied. Cursory terrestrial and drop tower experiments agree well with the solutions. The solutions are valued for the facility they provide in computing designs for selected capillary fluidics problems by way of passive transport rates and meniscus displacement. Because geometric permutations of any given design are myriad, such analytic tools are capable of efficiently identifying and comparing critical design criteria (i.e. shape and size) and the impact of various wetting conditions resulting from the fluid properties and surface conditions. Sample optimizations are performed to demonstrate the utility of the method.
Capillary-driven flows along rounded interior corners
- YONGKANG CHEN, MARK M. WEISLOGEL, CORY L. NARDIN
-
- Journal:
- Journal of Fluid Mechanics / Volume 566 / 10 November 2006
- Published online by Cambridge University Press:
- 05 October 2006, pp. 235-271
-
- Article
- Export citation
-
The problem of low-gravity isothermal capillary flow along interior corners that are rounded is revisited analytically in this work. By careful selection of geometric length scales and through the introduction of a new geometric scaling parameter $\overline T_c$, the Navier–Stokes equation is reduced to a convenient$\,{\sim}\, O(1)$ form for both analytic and numeric solutions for all values of corner half-angle $\alpha$ and corner roundedness ratio $\lambda$ for perfectly wetting fluids. The scaling and analysis of the problem captures much of the intricate geometric dependence of the viscous resistance and significantly reduces the reliance on numerical data compared with several previous solution methods and the numerous subsequent studies that cite them. In general, three asymptotic regimes may be identified from the large second-order nonlinear evolution equation: (I) the ‘sharp-corner’ regime, (II) the narrow-corner ‘rectangular section’ regime, and (III) the ‘thin film’ regime. Flows are observed to undergo transition between regimes, or they may exist essentially in a single regime depending on the system. Perhaps surprisingly, for the case of imbibition in tubes or pores with rounded interior corners similarity solutions are possible to the full equation, which is readily solved numerically. Approximate analytical solutions are also possible under the constraints of the three regimes, which are clearly identified. The general analysis enables analytic solutions to many rounded-corner flows, and example solutions for steady flows, perturbed infinite columns, and imbibing flows over initially dry and prewetted surfaces are provided.
4 - Drops and bubbles
-
- By S. Chandra, C. T. Avedisian, M. P. Brenner, X. D. Shi, J. Eggers, S. R. Nagel, M. Tjahjadi, J. M. Ottino, PH. Marmottant, E. Villermaux, B. Vukasinovic, A. Glezer, M. K. Smith, A. Lozano, C. J. Call, C. Dopazo, D. E. Nikitopoulos, A. J. Kelly, D. Frost, B. Sturtevant, M. M. Weislogel, S. Lichter, M. Manga, H. A. Stone, J. Buchholz, L. Sigurdson, B. Peck
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
-
- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 42-53
-
- Chapter
- Export citation
-
Summary
The collision of a droplet with a solid surface
The photographs displayed above show the impact, spreading, and boiling history of n-heptane droplets on a stainless steel surface. The impact velocity, Weber number, and initial droplet diameter are constant (values of 1 m/s, 43 and 1.5 mm respectively), and the view is looking down on the surface at an angle of about 30°. The photographs were taken using a spark flash method and the flash duration was 0.5 μs. The dynamic behavior illustrated in the photographs is a consequence of varying the initial surface temperature.
The effect of surface temperature on droplet shape may be seen by reading across any row; the evolution of droplet shape at various temperatures may be seen by reading down any column. An entrapped air bubble can be seen in the drop when the surface temperature is 24°C. At higher temperatures vigorous bubbling, rather like that of a droplet sizzling on a frying pan, is seen (the boiling point of n-heptane is 98°C) but the bubbles disappear as the Leidenfrost temperature of n-heptane (about 200°C) is exceeded because the droplet become levitated above a cushion of its own vapor and does not make direct contact with the surface. The droplet shape is unaffected by surface temperature in the early stage of the impact process (t≤0.8 ms) but is affected by temperature at later time (cf. t≥ 1.6 ms) because of the progressive influence of intermittent solid-liquid contact as temperature is increased.
Capillary flow in an interior corner
- MARK M. WEISLOGEL, SETH LICHTER
-
- Journal:
- Journal of Fluid Mechanics / Volume 373 / 25 October 1998
- Published online by Cambridge University Press:
- 25 October 1998, pp. 349-378
-
- Article
- Export citation
-
The design of fluids management processes in the low-gravity environment of space requires an accurate description of capillarity-controlled flow in containers. Here we consider the spontaneous redistribution of fluid along an interior corner of a container due to capillary forces. The analytical portion of the work presents an asymptotic formulation in the limit of a slender fluid column, slight surface curvature along the flow direction z, small inertia, and low gravity. The scaling introduced explicitly accounts for much of the variation of flow resistance due to geometry and so the effects of corner geometry can be distinguished from those of surface curvature. For the special cases of a constant height boundary condition and a constant flow condition, the similarity solutions yield that the length of the fluid column increases as t1/2 and t3/5, respectively. In the experimental portion of the work, measurements from a 2.2 s drop tower are reported. An extensive data set, collected over a previously unexplored range of flow parameters, includes estimates of repeatability and accuracy, the role of inertia and column slenderness, and the effects of corner angle, container geometry, and fluid properties. At short times, the fluid is governed by inertia (t[lsim ]tLc). Afterwards, an intermediate regime (tLc[lsim ]t[lsim ] tH) can be shown to be modelled by a constant-flow-like similarity solution. For t[ges ]tH it is found that there exists a location zH at which the interface height remains constant at a value h(zH, t)=H which can be shown to be well predicted. Comprehensive comparison is made between the analysis and measurements using the constant height boundary condition. As time increases, it is found that the constant height similarity solution describes the flow over a lengthening interval which extends from the origin to the invariant tip solution. For t[Gt ]tH, the constant height solution describes the entire flow domain. A formulation applicable throughout the container (not just in corners) is presented in the limit of long times.