Generation of secondary droplets in coalescence of a drop at a liquid–liquid interface

2010 ◽  
Vol 655 ◽  
pp. 72-104 ◽  
Author(s):  
B. RAY ◽  
G. BISWAS ◽  
A. SHARMA
Keyword(s):  
Critical Value ◽  
Bond Number ◽  
Viscous Force ◽  
Time Range ◽  
Main Body ◽  
Ohnesorge Number ◽  
Partial Coalescence ◽  
Daughter Droplets ◽  
Secondary Droplets ◽  
Secondary Drop

When a droplet of liquid 1 falls through liquid 2 to eventually hit the liquid 2–liquid 1 interface, its initial impact on the interface can produce daughter droplets of liquid 1. In some cases, a partial coalescence cascade governed by self-similar capillary-inertial dynamics is observed, where the fall of the secondary droplets in turn continues to produce further daughter droplets. Results show that inertia and interfacial surface tension forces largely govern the process of partial coalescence. The partial coalescence is suppressed by the viscous force when Ohnesorge number is below a critical value and also by gravity force when Bond number exceeds a critical value. Generation of secondary drop is observed for systems of lower Ohnesorge number for liquid 1, lower and intermediate Ohnesorge number for liquid 2 and for low and intermediate values of Bond number. Whenever the horizontal momentum in the liquid column is more than the vertical momentum, secondary drop is formed. A transition regime from partial to complete coalescence is obtained when the neck radius oscillates twice. In this regime, the main body of the column can be fitted to power-law scaling model within a specific time range. We investigated the conditions and the outcome of these coalescence events based on numerical simulations using a coupled level set and volume of fluid method (CLSVOF).

Dynamics of drop coalescence at fluid interfaces

2009 ◽  
Vol 620 ◽  
pp. 333-352 ◽  
Author(s):  
FRANÇOIS BLANCHETTE ◽  
TERRY P. BIGIONI
Keyword(s):  
Bond Number ◽  
Capillary Waves ◽  
Fluid Interfaces ◽  
Ohnesorge Number ◽  
Liquid Drops ◽  
Drop Coalescence ◽  
Partial Coalescence ◽  
Flat Interface ◽  
Low Viscosity ◽  
Set Up

Drop coalescence was studied using numerical simulations. Liquid drops were made to coalesce with a body of the same liquid, either a reservoir or a drop of different size, each with negligible impact velocity. We considered either gas or liquid as a surrounding fluid, and experimental results are discussed for the gas–liquid set-up. Under certain conditions, a drop will not fully coalesce with the liquid reservoir, leaving behind a daughter drop. Partial coalescence is observed for systems of low viscosity, characterized by a small Ohnesorge number, where capillary waves remain sufficiently vigourous to distort the drop significantly. For drops coalescing with a flat interface, we determine the critical Ohnesorge number as a function of Bond number, as well as density and viscosity ratios of the fluids. Studying the coalescence of two drops of different sizes reveals that partial coalescence may occur in low-viscosity systems provided the size ratio of the drops exceeds a certain threshold. We also determine the extent to which the process of partial coalescence is self-similar and find that the viscosity of the drop has a large effect on the droplet's vertical velocity after pinch off. Finally, we report on the formation of satellite droplets generated after a first pinch off and on the ejection of a jet of tiny droplets during coalescence of a parent drop significantly deformed by gravity.

STUDY ON ELECTROHYDRODYNAMIC CAPILLARY INSTABILITY OF VISCOELASTIC FLUIDS IN PRESENCE OF AXIAL ELECTRIC FIELD

2012 ◽  
Vol 04 (03) ◽  
pp. 1250027 ◽  
Author(s):  
D. K. TIWARI ◽  
MUKESH KUMAR AWASTHI ◽  
G. S. AGRAWAL
Keyword(s):  
Electric Field ◽  
Flow Analysis ◽  
Critical Value ◽  
Deborah Number ◽  
Wave Number ◽  
Conductivity Ratio ◽  
Ohnesorge Number ◽  
Capillary Instability ◽  
Axial Electric Field ◽  
Linear Viscoelastic

Linear viscoelastic potential flow analysis of capillary instability in presence of axial electric field has been studied. A dispersion relation is derived for the case of axially imposed electric field and stability is discussed in terms of various parameters such as electric field, Deborah number, Ohnesorge number, permittivity ratio and conductivity ratio etc. Stability criterion is given in the terms of critical value of wave number as well as critical value of applied electric field. The system is unstable when electric field is less than the critical value of electric field, otherwise it is stable. It has been found that in presence of the electric field the growth rates for viscoelastic fluid are higher than viscous fluid. Various graphs have been plotted for growth rate and critical electric field.

Rivulet Instability with Effect of Coriolis Force

2006 ◽  
Vol 22 (3) ◽  
pp. 221-227 ◽  
Author(s):  
H.-C. Cho ◽  
F.-C. Chou
Keyword(s):  
Coriolis Force ◽  
Critical Radius ◽  
Deflection Angle ◽  
Characteristic Length ◽  
Bond Number ◽  
Viscous Force ◽  
Fingering Instability ◽  
High Bond ◽  
The Deflection Angle ◽  
Visualization Experiments

AbstractThe effect of Coriolis force on the rivulet (fingering) instability, the onset of rivulet phenomena during spin coating, is investigated by flow visualization experiments incorporating with dimensional analysis. This study demonstrates that the Coriolis force will affect significantly the critical radius of rivulet instability and the deflection angle of instability rivulet. For the cases of low Bond number, the effect of Coriolis force is a stabilizing factor, and the dimensionless critical radius increases slightly with increasing rotational Reynolds number Reω. In the case of high Bond number, the effect of Coriolis force becomes a destabilizing factor while Reω < 1, and a characteristic length is found by balancing the viscous force with the surface tension. For Reω > 1, the radial Corilois force, which is always pointing inward, plays a stabilizing role with magnitude Reω2.

scholarly journals Whipping Behavior of Rice Flour Dough

2021 ◽  
Vol 333 ◽  
pp. 02008
Author(s):  
Chiaki Ichikawa ◽  
Takahiro Fukunaga ◽  
Daitaro Ishikawa ◽  
Tomoyuki Fujii
Keyword(s):  
Bubble Diameter ◽  
Inertial Force ◽  
Rice Flour ◽  
Bond Number ◽  
Milling Process ◽  
Viscous Force ◽  
Movement Speed ◽  
Effective Diameter ◽  
Gravitational Acceleration ◽  
Flour Dough

In this study, the bubbles in rice flour dough were investigated under a constant temperature. The bubble size distribution is important for the control of food texture. If bubble sizes depend mainly on the inertial force, viscous force, and surface tension, then the normalized mean bubble diameter should be a function of the Reynolds number and Weber number. We obtained experimental data using a hand mixer, and compared the properties of doughs prepared using six rice flours; each flour was prepared through a different milling process. We also added the size effect of the rice flour particles as the Bond number. Furthermore, we performed a dynamic wettability test to estimate the wettability of the rice flour surface. The results of this test were described well by the Washburn equation, and dccosθ was calculated as a wettability parameter (where, dc: effective diameter of a capillary in a powder bed, cosθ: the contact angle). The mean bubble diameter (dbm) generated by whipping was expected to be affected by the thickness (d) of the rod of the mixer, its movement speed, physical properties of the material, and gravitational acceleration. Therefore, dimensionless mean diameter (dbm/d) was expressed by a dimensionless equation. The empirical equation obtained was generally applicable to the variety of materials selected for this study.

scholarly journals Numerical simulations and experiments on droplet coalescence dynamics over a liquid–air interface: mechanism and effect of droplet-size/surface-tension

2021 ◽  
Vol 3 (3) ◽  
Author(s):  
Javed Shaikh ◽  
Nagesh D. Patil ◽  
Atul Sharma ◽  
Rajneesh Bhardwaj
Keyword(s):  
Surface Tension ◽  
Excellent Agreement ◽  
Numerical Study ◽  
Droplet Diameter ◽  
Bond Number ◽  
Liquid System ◽  
Critical Values ◽  
Surface Tension Coefficient ◽  
Droplet Coalescence ◽  
Partial Coalescence

AbstractPresent study is on partial/complete coalescence dynamics of a droplet (surrounded by air) over a horizontal pool of the same liquid. Experimental and numerical studies are presented for both isopropanol and glycerol droplet of a constant diameter. Numerical study is presented in more detail for the isopropanol droplet to study the effect of diameter ($$D=0.035-6.7 mm$$ D = 0.035 - 6.7 m m ) and surface tension coefficient ($$\gamma =2-200 mN/m$$ γ = 2 - 200 m N / m ) on the coalescence dynamics. For partial coalescence of an isopropanol droplet and complete coalescence of a glycerol droplet, excellent agreement is demonstrated between our numerically and experimentally obtained interface dynamics; and a qualitative discussion on the mechanism of the partial and complete coalescence is presented. Three regimes of partial coalescence − viscous, inertio-capillary and gravity − proposed in the literature for a liquid-liquid system are presented here for the present liquid-air system while studying the effect of diameter of the isopropanol droplet. Probably for the first time in the literature, our numerical study presents a flow and vorticity dynamics based quantitativeevidence of the coalescence-mechanism, analogy with a freely vibrating Spring-Mass-Damper System, the gravity regime for a liquid-gas system, and the effect of surface tension coefficient $$\gamma$$ γ based coalescence dynamics study. The associated novel $$\gamma$$ γ based droplet coalescence regime map presents a critical Ohnesorge number $$Oh_{c}$$ O h c and critical Bond number $$Bo_{c}$$ B o c for a transition from partial to full coalescence; and such critical values are also presented for the transition under effect of the droplet diameter. The critical values based transition boundaries, obtained separately for the varying D and varying $$\gamma$$ γ , are demonstrated to be in excellent agreement with a correlation reported in the literature.

The buoyancy-driven motion of a train of viscous drops within a cylindrical tube

1992 ◽  
Vol 237 ◽  
pp. 627-648 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Cylindrical Tube ◽  
Terminal Velocity ◽  
Bond Number ◽  
Boundary Integral ◽  
Effective Radius ◽  
Creeping Flow ◽  
Boundary Integral Method ◽  
Main Body ◽  
Viscous Drops ◽  
Asymptotic Analyses

The buoyancy-driven motion of a train of viscous drops settling or rising along the axis of a vertical cylindrical tube is investigated. Under the assumption of creeping flow, the evolution of the drops is computed numerically using a boundary integral method that employs the axisymmetric periodic Green's function for flow in a cylindrical tube. Given the drop volume and assuming that the viscosity of the drops is equal to that of the suspending fluid, the motion is studied as a function of the radius of the tube, the separation between the drops, and the Bond number. Two classes of drops are considered: compact drops whose effective radius is smaller than the radius of the tube, and elongated drops whose effective radius is larger than the radius of the tube. It is found that compact drops may have a variety of steady shapes including prolate and oblate, dimpled tops, and shapes containing pockets of entrained ambient fluid. When the surface tension is sufficiently small, compact drops become unstable, evolving to prolate rings with elongated tails. The terminal velocity of compact drops is discussed and compared with that predicted by previous asymptotic analyses for spherical drops. Steady elongated drops assume the shape of long axisymmetric fingers consisting of a nearly cylindrical main body and two curved ends. Relationships between the terminal velocity of elongated drops, the gap between the drops and the wall of the tube, and the Bond number are established. The results are discussed with reference to previous analyses and laboratory measurements for inviscid bubbles.

Important Parameters in Drop Coalescence at Planar Surfaces

2005 ◽  
Author(s):  
H. Aryafar ◽  
H. P. Kavehpour
Keyword(s):  
Time Scales ◽  
High Speed ◽  
Digital Camera ◽  
Ohnesorge Number ◽  
Coalescence Process ◽  
Drop Coalescence ◽  
Drop Radius ◽  
Planar Surfaces ◽  
Secondary Drop ◽  
Principal Elements

An experimental study has been performed to establish the principal elements that govern drop coalescence. The study consisted of placing drops of various sizes and physical properties on a planar interface. The coalescence process was recorded with the aid of a high speed digital camera. The experimental portion of the project was aimed at capturing the time of coalescence and the size of the secondary drop that formed after coalescence had finished. Results of the experiments, when scaled properly, showed clear patterns with respect to inertial and viscous terms. Dimensional analysis indicated that Ohnesorge number, Oh, had a strong influence on the behavior of drop coalescence. The ratio of secondary drop radius to primary drop radius, ri, was calculated to be approximately constant when Oh was much smaller than unity. However, as Oh approached unity from the lower bound, the value of ri decayed. No secondary drop was observed when Oh was greater than unity. Normalized coalescence times confirmed this trend by being properly scaled with inertial time scales for small Ohnesorge number and preferring viscous time scales when Ohnesorge number was greater than unity.

scholarly journals Investigation of CO2 Enhanced Oil Recovery Using Dimensionless Groups in Wettability Modified Chalk and Sandstone Rocks

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Vahid Alipour Tabrizy
Keyword(s):  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Bond Number ◽  
Injection Rate ◽  
Viscous Force ◽  
Gravity Forces ◽  
Dimensionless Groups ◽  
Porosity And Permeability ◽  
Reported Data ◽  
Positive Effect

The paper addresses enhanced oil recovery in chalk and sandstone rocks by CO2 injection, with different wettability, porosity, and permeability as well as injection rate and flooding conditions. Results indicate that an increase in Bond number has a positive effect on oil recovery whereas for capillary number, there is a limit in which recovery is improving. This limit is estimated when the pressure drop by viscous force is approximately equal to the threshold balance between capillary and gravity forces. A dimensionless group is proposed that combines the effect of capillarity, injection rate, permeability, and CO2 diffusion on the oil recovery. Recovery from all experiments in this study and reported data in the literature shows a satisfactory relationship with the proposed group.

scholarly journals Capillary waves control the ejection of bubble bursting jets

2019 ◽  
Vol 867 ◽  
pp. 556-571 ◽  
Author(s):  
J. M. Gordillo ◽  
J. Rodríguez-Rodríguez
Keyword(s):  
Capillary Wave ◽  
Bubble Radius ◽  
Bond Number ◽  
Capillary Waves ◽  
Liquid Density ◽  
Ohnesorge Number ◽  
Capillary Suction ◽  
Lower Base ◽  
Capillary Pressures ◽  
The Moment

Here we provide a theoretical framework describing the generation of the fast jet ejected vertically out of a liquid when a bubble, resting on a liquid–gas interface, bursts. The self-consistent physical mechanism presented here explains the emergence of the liquid jet as a consequence of the collapse of the gas cavity driven by the low capillary pressures that appear suddenly around its base when the cap, the thin film separating the bubble from the ambient gas, pinches. The resulting pressure gradient deforms the bubble which, at the moment of jet ejection, adopts the shape of a truncated cone. The dynamics near the lower base of the cone, and thus the jet ejection process, is determined by the wavelength $\unicode[STIX]{x1D706}^{\ast }$ of the smallest capillary wave created during the coalescence of the bubble with the atmosphere which is not attenuated by viscosity. The minimum radius at the lower base of the cone decreases, and hence the capillary suction and the associated radial velocities increase, with the wavelength $\unicode[STIX]{x1D706}^{\ast }$. We show that $\unicode[STIX]{x1D706}^{\ast }$ increases with viscosity as $\unicode[STIX]{x1D706}^{\ast }\propto Oh^{1/2}$ for $Oh\lesssim O(0.01)$, with $Oh=\unicode[STIX]{x1D707}/\sqrt{\unicode[STIX]{x1D70C}R\unicode[STIX]{x1D70E}}$ the Ohnesorge number, $R$ the bubble radius and $\unicode[STIX]{x1D70C}$, $\unicode[STIX]{x1D707}$ and $\unicode[STIX]{x1D70E}$ indicating respectively the liquid density, viscosity and interfacial tension coefficient. The velocity of the extremely fast and thin jet can be calculated as the flow generated by a continuous line of sinks extending along the axis of symmetry a distance proportional to $\unicode[STIX]{x1D706}^{\ast }$. We find that the jet velocity increases with the Ohnesorge number and reaches a maximum for $Oh=Oh_{c}$, the value for which the crest of the capillary wave reaches the vertex of the cone, and which depends on the Bond number $Bo=\unicode[STIX]{x1D70C}gR^{2}/\unicode[STIX]{x1D70E}$. For $Oh>Oh_{c}$, the jet is ejected after a bubble is pinched off; in this regime, viscosity delays the formation of the jet, which is thereafter emitted at a velocity which is inversely proportional to the liquid viscosity.

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