The coalescence of water drops II. The coalescence problem and coalescence efficiency     

Nitza Arbel  Zev Levin 《Pure and Applied Geophysics》1977,115(4):895-914

By the use of the model of approaching drops (Arbel and Levin, 1977) the coalescence efficiencies of drops are computed. It is found that for interactions of drops at their terminal velocities the coalescence depends both on the size of the large drop and on the size ratio of the interacting drops in agreement with the experimental results of Whelpdale and List (1971) and Levin and Machnes (1977).The results were found to be sensitive to the assumption of the drops deformation and to the critical separation distance. This distance is defined as the distance at which the drops begin to merge. The variations of the coalescence efficiency with these parameters is discussed.Appendix: List of symbols D distance between the deformed surfaces of the drops - D _o initial value ofD - D _s stop distance, the distance at which the impact velocity vanishes - D _c critical coalescence distance - E collection efficiency - E ₁ collision efficiency - E ₂ coalescence efficiency - E _2R coalescence efficiency for collisions with stationary targets - F _c centrifugal force - p ratio of the radii of the interacting drops - r _o initial distance between drops' centers - R _L radius of larger drop - R _s radius of smaller drop - R _D radius of deformation - v approach velocity of two deformed surfaces - v _o initial value ofv - V _i impact velocity (given negative sign when drops approach each other) - V _c critical impact velocity - W _i velocity of the smaller drop at infinity for it to reachD _o with velocityv _o - x _i impact distance, the distance between the trajectories of the two drops - x _c critical impact distance for coalescence -  average critical impact distance for coalescence - X _c critical impact distance for collisions - coefficient of deformation given in equation 1 - _i impact angle defined byWhelpdale andList (1971) given also inArbel andLevin (1977) - coefficient of deformation given in equation 2 - viscosity of air - _i impact angle used inArbel andLevin (1977) and here - _c critical angle for coalescence - average critical angle for coalescence On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

The coalescence of water drops I. A theoretical model of approaching drops     

Nitza Arbel  Zev Levin 《Pure and Applied Geophysics》1977,115(4):869-893

The approach of two water drops in the absence of air flow around them is theoretically investigated. By assuming deformation criteria it is possible to solve the equation of motion of the drops under the influence of a variety of forces. These forces include the viscous force exerted by the air between the two deformed surfaces, the London-Van Der Waals forces and the force of gravity. It is found that the viscous forces dominate over the whole distance of the interaction. The equations have analytical solutions when a head-on approach is considered and when the deformation of the drops is assumed constant during the interaction. The equations were solved numerically for other deformation criteria and for non head-on approaches.The results of the present model are used in the following paper to compute the coalescence efficiencies of water drops. The model is primarily applicable to situations in which the large drop is stationary and the small one approaches it from below. However, it could also be used for interaction between freely falling drops as long as their relative velocities exceed about 13 cm/sec.Appendix: List of symbols C constant of the motion - D distance between the deformed surfaces of the drops - D _o initial value ofD - D _m the value at which the viscous force is maximum - D _N normalized distance - D _s the distance at which the velocity of approach vanishes - F _c centrifugal force - F _g force due to gravity - F _N normalized viscous force - F _LV force due to London-Van der Waals effect - F _R radial component of the force - F _V viscous force - F _t tangential component of the force - g acceleration due to gravity - M _L mass of large drop - m _s mass of small drop - p ratio of radii of interacting drops - R radius of an arbitrary drop - r distance between the centers of mass of the two drops - R _D radius of deformation - R _L radius of larger drop - R _s radius of smaller drop - t time - u defined in equation 20 — has the meaning of kinetic energy - v relative velocity of the deformed surfaces - v ₀ initial value ofv - V ₀ initial relative velocity of the centers of the drops - V _c critical impact velocity - V _i impact velocity - V _N ,v _n normalized velocity - V _t tangential component of the velocity - W _i velocity of the small drop at infinity for it to reach the pointD ₀ at velocityV ₀ - x instantaneous impact distance -  average critical impact distance for coalescence - x ₀ initial value of the impact distance - x _c critical impact distance for coalescence - coefficient of deformation - _i impact angle according toWhelpdale andList (1971) - coefficient of deformation - viscosity - surface tension - F _s sum of forces acting on the small drop - F _L sum of forces acting on the large drop - time constant - _R Rayleigh's oscillation period On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

Infiltration processes and flow rates in developed karst vadose zone using tracers in cave drips   总被引：1，自引：0，他引：1  

Youval Arbel  Noam Greenbaum  Jens Lange  Moshe Inbar 《地球表面变化过程与地形》2010,35(14):1682-1693

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Water percolation process studies in a Mediterranean karst area     

J. Lange  Y. Arbel  T. Grodek  N. Greenbaum 《水文研究》2010,24(13):1866-1879

To investigate processes of water percolation, the drip response of stalactites in a karstic cave below a 143 m² sprinkling plot was measured. The experiment was conducted in Mount Carmel, Israel, at the end of the dry season and intended to simulate a series of two high‐intensity storms on dry and wet soils. In addition to hydrometric measurements (soil moisture, surface runoff, stalactite dripping rates), two types of tracers (electrical conductivity and bromide) were used to study recharge processes, water origin and mixing inside a 28‐m vadose zone. Results suggested that slow, continuous percolation through the rock matrix is of minor importance and that percolating water follows a complicated pattern including vertical and horizontal flow directions. While bromide tracing allowed identification of quick direct flow paths at all drips with maximum flow velocities of 4·3 m/h, mixing analysis suggested that major water fractions were mobilized by piston flow, pushing out water stored in the unsaturated zone above the cave. Under dry preconditions, 80 mm of artificial rainfall applied in less than 7 h was not enough to initiate significant downward water percolation. Most water was required to fill uppermost soil and rock storages. Under wet preconditions during the second day sprinkling, higher water contents in soils and karst cavities facilitated piston flow effects and a more intense response of the cave drips. Results indicate that in Mediterranean karst regions, filling of the unsaturated zone, including soil and rock storages, is an important precondition for the onset of significant water percolation and recharge. This results in a higher seasonal threshold for water percolation than for the generation of surface runoff. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献