5 results
Distribution and timing of Holocene and late Pleistocene glacier fluctuations in western Mongolia
- Frank Lehmkuhl, Michael Klinge, Henrik Rother, Daniela Hülle
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- Journal:
- Annals of Glaciology / Volume 57 / Issue 71 / March 2016
- Published online by Cambridge University Press:
- 03 March 2016, pp. 169-178
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Despite being a key location for paleoglaciological research in north-central Asia, with the largest number of modern and Pleistocene glaciers, and in the transition zone between the humid Russian Altai and dry Gobi Altai, little is known about the precise extent and timing of Holocene and late Pleistocene glaciations in western Mongolia. Here we present detailed information on the distribution of modern and late Holocene glaciers, and new results addressing the geomorphological differentiation and numerical dating (by optically stimulated luminescence, OSL) of Pleistocene glacial sequences in these areas. For the Mongolian Altai, geochronological results suggest large ice advances correlative to marine isotope stages (MIS) 4 and 2. This is in contrast to results from the Khangai mountains, central Mongolia, showing that significant ice advances additionally occurred during MIS3. During the Pleistocene, glacial equilibrium-line altitudes (ELAs) were ~500 to >1000m lower in the more humid portion of the Russian and western Mongolian Altai, compared to 300-600 m in the drier ranges of the eastern Mongolian Altai. Pleistocene ELAs in the Khangai mountains were depressed by 700-1000 m, suggesting more humid conditions at times of major glaciation than in the eastern Mongolian Altai. This paleo-ELA pattern reveals that the precipitation gradient from the drier to the more humid regions was more pronounced during glacial times than at present.
Gravity-induced collisions of spherical drops covered with compressible surfactant
- ALEXANDER Z. ZINCHENKO, MICHAEL A. ROTHER, ROBERT H. DAVIS
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- Journal:
- Journal of Fluid Mechanics / Volume 667 / 25 January 2011
- Published online by Cambridge University Press:
- 14 January 2011, pp. 369-402
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Gravity-induced collisions of two spherical drops covered with an insoluble surfactant at low Reynolds numbers are considered. Unlike in previous collision studies, the present work accounts for nonlinear coupling between the surfactant distribution and drop hydrodynamics by solving the full unsteady convective–diffusion equation for the surfactant transport. Our method includes high-order three-dimensional multipole expansions for hydrodynamics and a Galerkin-type approach for the surfactant transport with implicit marching. The efficiency of the algorithm allows for calculating thousands of trajectories to very close contact and determining the collision efficiency (related to the critical initial horizontal offset) by trial and error. The solution is valid for arbitrary surface Péclet (Pes) and Marangoni (Ma) numbers and sets limitations on approximations used in prior work for collision-efficiency calculations. Two limiting cases are observed: at small Pes or large Ma, the variation in surfactant coverage is small, and the results for the incompressible surfactant model are recovered, while for large Pes and small Ma, the collision efficiency approaches the clean-interface value. For moderate drop-size ratios (radius ratio k ≤ 0.5), the results generally fall between these limits. At larger size ratios, however, the collision efficiency may even exceed the geometrical Smoluchowski limit for both drops and bubbles. Moreover, with even moderate redistribution of the surfactant, equal-sized drops can move relative to one another and collide. These novel effects do not exist for clean drops or drops covered with an incompressible surfactant, and they are due to the nonlinear coupling between surfactant dynamics and flow. This surfactant-enhanced coalescence takes place, for example, in a physical system of air bubbles in water if the surfactant surface concentration is dilute (Γ ≈ 1×10−9 mol m−2, much smaller than the typical maximum-packing value of 10−5−10−6 mol m−2).
Buoyancy-driven interactions of viscous drops with deforming interfaces
- JOSEPH KUSHNER, MICHAEL A. ROTHER, ROBERT H. DAVIS
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- Journal:
- Journal of Fluid Mechanics / Volume 446 / 10 November 2001
- Published online by Cambridge University Press:
- 23 October 2001, pp. 253-269
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Experiments were conducted on the interactions of two different-sized deformable drops moving due to gravity in an immiscible viscous fluid at low Reynolds number. As the drops come close to each other, several interactions are possible: (i) separation of the drops, (ii) capture of the smaller drop behind the larger drop, (iii) breakup of the smaller drop into two or more drops, and (iv) pass-through of one drop through the other, with possible cycle interaction or leap-frogging. The interactions depend on several system parameters, including the drop-to-medium viscosity ratio, the radius ratio of the two drops, the initial horizontal offset of the two drops at large vertical separation, and the gravitational Bond number (which represents the ratio of buoyant forces to interfacial tension forces for the larger drop and describes how much the drops will deform). Experimental analysis was conducted by videotaping trajectories of glycerol–water drops of various compositions falling in castor oil. The results show good agreement with available theoretical results, both for interaction maps and individual trajectories. The results also provide data beyond the present limitations of theoretical algorithms and reveal the new pass-through phenomenon.
Cusping, capture, and breakup of interacting drops by a curvatureless boundary-integral algorithm
- ALEXANDER Z. ZINCHENKO, MICHAEL A. ROTHER, ROBERT H. DAVIS
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- Journal:
- Journal of Fluid Mechanics / Volume 391 / 25 July 1999
- Published online by Cambridge University Press:
- 25 July 1999, pp. 249-292
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A three-dimensional boundary-integral algorithm for interacting deformable drops in Stokes flow is developed. The algorithm is applicable to very large deformations and extreme cases, including cusped interfaces and drops closely approaching breakup. A new, curvatureless boundary-integral formulation is used, containing only the normal vectors, which are usually much less sensitive than is the curvature to discretization errors. A proper regularization makes the method applicable to small surface separations and arbitrary λ, where λ is the ratio of the viscosities of the drop and medium. The curvatureless form eliminates the difficulty with the concentrated capillary force inherent in two-dimensional cusps and allows simulation of three-dimensional drop/bubble motions with point and line singularities, while the conventional form can only handle point singularities. A combination of the curvatureless form and a special, passive technique for adaptive mesh stabilization allows three-dimensional simulations for high aspect ratio drops closely approaching breakup, using highly stretched triangulations with fixed topology. The code is applied to study relative motion of two bubbles or drops under gravity for moderately high Bond numbers [Bscr ], when cusping and breakup are typical. The deformation-induced capture efficiency of bubbles and low-viscosity drops is calculated and found to be in reasonable agreement with available experiments of Manga & Stone (1993, 1995b). Three-dimensional breakup of the smaller drop due to the interaction with a larger one for λ=O(1) is also considered, and the algorithm is shown to accurately simulate both the primary breakup moment and the volume partition by extrapolation for moderately supercritical conditions. Calculations of the breakup efficiency suggest that breakup due to interactions is significant in a sedimenting emulsion with narrow size distribution at λ=O(1) and [Bscr ][ges ]5–10. A combined capture and breakup phenomenon, when the smaller drop starts breaking without being released from the dimple formed on the larger one, is also observed in the simulations. A general classification of possible modes of two-drop interactions for λ=O(1) is made.
Buoyancy-driven coalescence of slightly deformable drops
- MICHAEL A. ROTHER, ALEXANDER Z. ZINCHENKO, ROBERT H. DAVIS
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- Journal:
- Journal of Fluid Mechanics / Volume 346 / 10 September 1997
- Published online by Cambridge University Press:
- 10 September 1997, pp. 117-148
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The simultaneous effect of small deformation and short-range van der Waals attraction on the coalescence efficiency of two different-sized slowly sedimenting drops is considered. For spherical drops, it has been shown previously that the tangential mobility of drop surfaces makes collision possible even without van der Waals attraction; on the other hand, even a small amount of deformation precludes drops from coming into contact unless van der Waals attraction is accounted for. In the present work, the conditions are delineated when these two small-scale factors, acting in opposite directions, have a considerable combined effect on the coalescence efficiency. The problem is solved by matched asymptotic expansions valid for small capillary numbers (Ca). The outer solution, for two spherical drops moving in apparent contact without van der Waals attraction, determines the contact force as a function of time. This force is used as the driving force for the inner solution of the relevant integro-differential thin-film equations (coupling the flow in the small-gap region to that inside the drops) to determine whether coalescence occurs during the apparent contact motion. The initial gap profile for the inner solution is provided by matching with the outer trajectory for spherical drops approaching contact.
The analysis shows that, for Ca[Lt ]1, the near-contact deformation is mainly axisymmetric, greatly simplifying the inner solution; nevertheless, determination of the critical horizontal offsets leading to coalescence and the parametric analysis are computationally very intensive. To facilitate these tasks, a substantially new, highly efficient, and absolutely stable numerical method for solving stiff thin-film equations is developed. Unlike for spherical drops, when the upstream intersection area is a circle, the existence of a second coalescence zone for deformable drops is found over much of the parameter space. Results are mapped out for a range of four dimensionless parameters (capillary number, size and drop-to-medium viscosity ratios, dimensionless Hamaker parameter). As a physical application, predicted coalescence efficiencies are shown for a system of ethyl salicylate drops in diethylene glycol.
The present solution extends the range of drop sizes where the coalescence efficiencies are known theoretically and can be used in drop population dynamics. Comparison with full three-dimensional boundary-integral calculations for deformable drops without van der Waals attraction is also made to demonstrate that, when the drop-to-medium viscosity ratio is of the order of unity, the present asymptotic approach is valid in a wide range of small and moderately small capillary numbers.