On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface

1990 ◽  
Vol 217 ◽  
pp. 547-573 ◽  
Author(s):  
Stergios G. Yiantsios ◽  
Robert H. Davis
Keyword(s):  
Solid Surface ◽  
Viscosity Ratio ◽  
Bond Number ◽  
Boundary Integral ◽  
Fractional Powers ◽  
Drop Shape ◽  
Wide Range ◽  
Deformable Interface ◽  
Long Time ◽  
Viscous Drop

The deformation of a viscous drop, driven by buoyancy towards a solid surface or a deformable interface, is analysed in the asymptotic limit of small Bond number, for which the deformation becomes important only when the drop is close to the solid surface or interface. Lubrication theory is used to describe the flow in the thin gap between the drop and the solid surface or interface, and boundary-integral theory is used in the fluid phases on either side of the gap. The evolution of the drop shape is traced from a relatively undeformed state until a dimple is formed and a long-time quasi-steady-state pattern is established. A wide range of drop to suspending phase viscosity ratios is examined. It is shown that a dimple is always formed, independently of the viscosity ratio, and that the long-time thinning rates take simple forms as inverse fractional powers of time.

scholarly journals Velocity measurements of individual droplets in liquid-liquid Taylor flows in circular capillaries

2021 ◽  
Vol 2116 (1) ◽  
pp. 012074
Author(s):  
Seyyed Saeed Shojaee Zadeh ◽  
Patrick Walsh ◽  
Vanessa Egan
Keyword(s):  
Strong Influence ◽  
Viscosity Ratio ◽  
Flow Regimes ◽  
Bond Number ◽  
Droplet Velocity ◽  
Velocity Measurements ◽  
Wide Range ◽  
Set Up ◽  
Varying Viscosity ◽  
Flow Velocities

Abstract This study is focused on the effect of droplet length on droplet velocity in liquid-liquid Taylor flows for microfluidic applications. An experimental set up was designed to measure droplet velocity over a wide range of droplet lengths and flow velocities while also varying viscosity ratio. Five different fluid combinations were examined by employing AR20, FC40, HFE7500 and water. Results indicate the complexity of predicting droplet velocity in such flow regimes and also show a strong influence of viscosity ratio and Bond number.

scholarly journals Methodology to calculate interfacial tension under electric field using pendent drop profile analysis

2019 ◽  
Vol 475 (2225) ◽  
pp. 20180852 ◽  
Author(s):  
Sameer Mhatre ◽  
Sébastien Simon ◽  
Johan Sjöblom
Keyword(s):  
Electric Field ◽  
Interfacial Tension ◽  
Laplace Equation ◽  
Profile Analysis ◽  
Normal Component ◽  
Bond Number ◽  
Interfacial Property ◽  
Adsorption Dynamics ◽  
Drop Shape ◽  
Long Time

In this paper, we present a methodology to calculate interfacial tension of a water–oil interface under an electric field. The Young–Laplace equation, conventionally used to estimate surface/interfacial tension in axisymmetric drop shape analysis (ADSA), is modified to include electrostatic effects. The solution needs normal component of the Maxwell stress at the interface which is calculated separately by solving the Laplace equation for electric potential. The optimized fitting between the resulting theoretical profile and the experimentally obtained profile results into Bond number which is used to calculate the apparent value of interfacial tension. The algorithm can process a large number of drop profiles in one go. The methodology can be applied in the ADSA studies for adsorption dynamics where a drop is held for a long time while surface active molecules are allowed to adsorb. The method discussed in this paper will help the future studies in adsorption dynamics at fluid interfaces under electric field and the resulting interfacial property evolution.

The instability of a moving viscous drop

1990 ◽  
Vol 210 ◽  
pp. 1-21 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Surface Tension ◽  
Thin Filament ◽  
Viscosity Ratio ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Fredholm Integral Equations ◽  
Spherical Drop ◽  
Viscous Drop ◽  
Secondary Mechanism ◽  
Axisymmetric Perturbations

The deformation of a moving spherical viscous drop subject to axisymmetric perturbations is considered. The problem is formulated using two different variations of the boundary integral method for Stokes flow, one due to Rallison & Acrivos, and the other based on an interfacial distribution of Stokeslets. An iterative method for solving the resulting Fredholm integral equations of the second kind is developed, and is implemented for the case of axisymmetric motion. It is shown that in the absence of surface tension, a moving spherical drop is unstable. Prolate perturbations cause the ejection of a tail from the rear of the drop, and the entrainment of a thin filament of ambient fluid into the drop. Oblate perturbations cause the drop to develop into a nearly steady ring. The viscosity ratio plays an important role in determining the timescale and the detailed pattern of deformation. Filamentation of the drop emerges as a persistent but secondary mechanism of evolution for both prolate and oblate perturbations. Surface tension is not capable of suppressing the growth of perturbations of sufficiently large amplitude, but is capable of preventing filamentation.

Inertial effects on the dynamics, streamline topology and interfacial stresses due to a drop in shear

2011 ◽  
Vol 683 ◽  
pp. 149-171 ◽  
Author(s):  
Rajesh Kumar Singh ◽  
Kausik Sarkar
Keyword(s):  
Reynolds Number ◽  
Viscosity Ratio ◽  
Shear Plane ◽  
Interfacial Stress ◽  
Rigid Sphere ◽  
Interfacial Stresses ◽  
Drop Shape ◽  
Flow Axis ◽  
Viscous Drop ◽  
Varying Viscosity

AbstractDeformation of a viscous drop in shear at finite inertia and the streamlines around it are numerically investigated. Inertia destroys the closed streamlines found in Stokes flow. It creates reversed streamlines and streamlines spiralling around the vorticity axis. Spiralling streamlines spiral either towards the central shear plane or away from it depending on the viscosity ratio and the inertia. The zones of open or reversed streamlines as well as streamlines spiralling towards or away from the central shear plane are delineated for varying viscosity ratio and Reynolds number. In contrast to the infinite extent of the closed Stokes streamlines around a rigid sphere in shear, the region of the spiralling streamlines in the vorticity direction both for a rigid sphere and a drop shrinks with inertia. Inertia increases deformation, and introduces oscillations in drop shape. An approximate analysis explains the scaling of oscillation frequency and damping with Reynolds and capillary numbers. The steady-state drop inclination angle with the flow axis increases with increasing Reynolds number for small Reynolds number. But it decreases at higher Reynolds number, especially for larger capillary numbers. For smaller capillary numbers, drop inclination reaches higher than $4{5}^{\ensuremath{\circ} } $ (the direction of maximum extension), critically affecting the interfacial stresses due to the drop. It changes the sign of first and second normal interfacial stress differences (and thereby these components of the effective stresses of an emulsion of such drops). Increasing viscosity ratio orients the drop towards the flow axis, which increases the critical Reynolds number above which the drop inclination reaches more than $4{5}^{\ensuremath{\circ} } $.

The Problem of Identifying and Modeling the Relationship between Monetary Factor and Inflation in the Russian Economy

2008 ◽  
pp. 61-76
Author(s):  
A. Porshakov ◽  
A. Ponomarenko
Keyword(s):  
Money Supply ◽  
Money Demand ◽  
Russian Economy ◽  
Long Run ◽  
Complex Approach ◽  
Wide Range ◽  
Long Time ◽  
The Relationship ◽  
Supply Side Factors

The role of monetary factor in generating inflationary processes in Russia has stimulated various debates in social and scientific circles for a relatively long time. The authors show that identification of the specificity of relationship between money and inflation requires a complex approach based on statistical modeling and involving a wide range of indicators relevant for the price changes in the economy. As a result a model of inflation for Russia implying the decomposition of inflation dynamics into demand-side and supply-side factors is suggested. The main conclusion drawn is that during the recent years the volume of inflationary pressures in the Russian economy has been determined by the deviation of money supply from money demand, rather than by money supply alone. At the same time, monetary factor has a long-run spread over time impact on inflation.

Comperehencive review of Tankana

2018 ◽  
Vol 3 (4) ◽  
Author(s):  
Dr. Jyotsna Sankpal ◽  
Dr. Jyotsna Takalikar
Keyword(s):  
Heart Disease ◽  
Medical Science ◽  
Menstrual Disorders ◽  
Therapeutic Applications ◽  
Indian Medical ◽  
Wide Range ◽  
Long Time

Rasa Shastra and Bhaishajya Kalpana is branch of the ancient Indian medical science based on herbs and herbo-mineral preparation. Tankana has been described under Uparasa Tankana, which is one among the Kshara Trayas has been used since very long time in Ayurveda. It has a wide range of therapeutic applications, including diseases like Varna (ulcers), Shvasa (asthma), Kasa (cough), Hrudya (beneficial to heart disease), Streepushpajanana (menstrual disorders) etc. It is used in the form of compound formulations like Parpati, Kupipakwa, Khalvee Rasayana, Churna, Vati, Lepa etc. In this paper Tankana Shodhana procedure, different synonyms, dose, Anupana, indications and different formulations containing Tankana Bhasma has been discussed.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

Reorientation of a single red blood cell during sedimentation

2016 ◽  
Vol 806 ◽  
pp. 102-128 ◽  
Author(s):  
D. Matsunaga ◽  
Y. Imai ◽  
C. Wagner ◽  
T. Ishikawa
Keyword(s):  
Angular Velocity ◽  
Blood Cell ◽  
Red Blood Cell ◽  
Blood Cells ◽  
Driving Force ◽  
Viscosity Ratio ◽  
Orientation Angle ◽  
Bond Number ◽  
Vertical Orientation ◽  
Main Factors

The reorientation phenomenon of a single red blood cell during sedimentation is simulated using the boundary element method. The cell settles downwards due to a density difference between the internal and external fluids, and it changes orientation toward a vertical orientation regardless of Bond number or viscosity ratio. The reorientation phenomenon is explained by a shape asymmetry caused by the gravitational driving force, and the shape asymmetry increases almost linearly with the Bond number. When velocities are normalised by the driving force, settling/drifting velocities are weak functions of the Bond number and the viscosity ratio, while the angular velocity of the reorientation drastically changes with these parameters: the angular velocity is smaller for lower Bond number or higher viscosity ratio. As a consequence, trajectories of the sedimentation are also affected by the angular velocity, and blood cells with slower reorientation travel longer distances in the drifting direction. We also explain the mechanism of the reorientation using an asymmetric dumbbell. From the analysis, we show that the magnitude of the angular velocity is explained by two main factors: the shape asymmetry and the instantaneous orientation angle.

Dynamics of Liquid Sheet Breakup in Splash Plate Atomization

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
G. Thunivumani ◽  
Hrishikesh Gadgil
Keyword(s):  
Solid Surface ◽  
Weber Number ◽  
Jet Impingement ◽  
Liquid Sheet ◽  
Force Balance ◽  
Impingement Angle ◽  
Wide Range ◽  
Perforated Sheet ◽  
Sheet Breakup ◽  
Regime Map

An experimental study was conducted to investigate the breakup of a liquid sheet produced by oblique impingement of a liquid jet on a plane solid surface. Experiments are carried out over a wide range of jet Weber number (80–6300) and various jet impingement angles (30 deg, 45 deg, and 60 deg) are employed to study the sheet dynamics. The breakup of a liquid sheet takes place in three modes, closed rim, open rim, and perforated sheet, depending upon the Weber number. The transitions across the modes are also influenced by the impingement angle with the transition Weber number reducing with increase in impingement angle. A modified regime map is proposed to illustrate the role of impingement angle in breakup transitions. A theoretical model based on force balance at the sheet edge is developed to predict the sheet parameters by taking the shear interaction between the sheet and the solid surface into account. The sheet shape predicted by the model fairly matches with the experimentally measured sheet shape. The breakup length and width of the sheet are measured and comparisons with the model predictions show good agreement in closed rim mode of breakup.

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