An experimental study of drop deformation and breakup in extensional flow at high capillary number

2001 ◽  
Vol 13 (6) ◽  
pp. 1568-1576 ◽  
Author(s):  
Jong-Wook Ha ◽  
L. Gary Leal
Keyword(s):  
Experimental Study ◽  
Capillary Number ◽  
Extensional Flow ◽  
Drop Deformation

scholarly journals Comparison of Experimental and Numerical Transient Drop Deformation during Transition through Orifices in High-Pressure Homogenizers

2021 ◽  
Vol 5 (3) ◽  
pp. 32
Author(s):  
Benedikt Mutsch ◽  
Peter Walzel ◽  
Christian J. Kähler
Keyword(s):  
High Pressure ◽  
Visual Analysis ◽  
Imaging Technique ◽  
Extensional Flow ◽  
Droplet Breakup ◽  
Experimental Results ◽  
Drop Deformation ◽  
Droplet Deformation ◽  
Shadow Imaging ◽  
Good Agreement

The droplet deformation in dispersing units of high-pressure homogenizers (HPH) is examined experimentally and numerically. Due to the small size of common homogenizer nozzles, the visual analysis of the transient droplet generation is usually not possible. Therefore, a scaled setup was used. The droplet deformation was determined quantitatively by using a shadow imaging technique. It is shown that the influence of transient stresses on the droplets caused by laminar extensional flow upstream the orifice is highly relevant for the droplet breakup behind the nozzle. Classical approaches based on an equilibrium assumption on the other side are not adequate to explain the observed droplet distributions. Based on the experimental results, a relationship from the literature with numerical simulations adopting different models are used to determine the transient droplet deformation during transition through orifices. It is shown that numerical and experimental results are in fairly good agreement at limited settings. It can be concluded that a scaled apparatus is well suited to estimate the transient droplet formation up to the outlet of the orifice.

Rheological Aspects of Drops Deforming in Finite Reynolds Number Oscillatory Extensional Flows

2004 ◽  
Author(s):  
Xiaoyi Li ◽  
Kausik Sarkar
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Extensional Flow ◽  
Three Dimensional ◽  
Industrial Applications ◽  
Drop Deformation ◽  
Interface Morphology ◽  
Drop Dynamics ◽  
Variation Of Parameters ◽  
Broad Implication

The evolving morphology of droplets in a flowing emulsion determines its rheological properties. A two-way interaction between drops and the flow governs the rheological stresses arising from drop deformation. In this paper, the rheology of droplet emulsions under oscillatory extensional flow is investigated using direct numerical simulation (DNS). The deformation of a three dimensional drop is simulated. The rheological responses are related with the interface morphology using Bachelor’s stress formulation [6]. Detailed investigation of the variation of parameters such as interfacial tension, flow frequency and inertia displayed complex non-Newtonian response of the emulsion that will have broad implication in industrial applications. The results are explained and discussed with a simple model for the drop dynamics.

Evolution and stationarity of liquid toroidal drop in compressional Stokes flow

2017 ◽  
Vol 835 ◽  
pp. 1-23 ◽  
Author(s):  
B. K. Ee ◽  
O. M. Lavrenteva ◽  
I. Smagin ◽  
A. Nir
Keyword(s):  
Cross Sections ◽  
Capillary Number ◽  
Initial Conditions ◽  
Extensional Flow ◽  
Building Blocks ◽  
Physical Parameters ◽  
Ambient Fluid ◽  
Medicinal Substances ◽  
Expansion Dynamic ◽  
Axisymmetric Disturbances

Dynamics of fluid tori in slow viscous flow is studied. Such tori are of interest as future carriers of biological and medicinal substances and are also viewed as potential building blocks towards more complex particles. In this study the immiscible ambient fluid is subject to a compressional flow (i.e., bi-extensional flow), and it comprises a generalization of our earlier report on the particular case with viscosity ratio$\unicode[STIX]{x1D706}=1$(see Zabarankinet al.,J. Fluid Mech., vol. 785, 2015, pp. 372–400), where$\unicode[STIX]{x1D706}$is the ratio between the torus viscosity and that of the ambient fluid. It is found that, for all viscosity ratios, the torus either collapses towards the axis of symmetry or expands indefinitely, depending on the initial conditions and the capillary number,Ca. During these dynamic patterns the cross-sections exhibit various forms of deformation. The collapse and expansion dynamic modes are separated by a limited deformation into a deformed stationary state which appears to exist in a finite interval of the capillary number,$0<Ca<Ca_{cr}(\unicode[STIX]{x1D706})$, and is unstable to axisymmetric disturbances, which eventually cause the torus either to collapse or to expand indefinitely. The characteristic dimensions and shapes of these unstable stationary tori and their dependence on the physical parametersCaand$\unicode[STIX]{x1D706}$are reported.

A Long Wavelength Model for Manufacturing of Continuous Metal Microwires by Thermal Fiber Drawing From a Preform

2017 ◽  
Vol 6 (1) ◽  
Author(s):  
Jingzhou Zhao ◽  
Xiaochun Li
Keyword(s):  
Interfacial Tension ◽  
Molten Metal ◽  
Capillary Number ◽  
Extensional Flow ◽  
Tension Stress ◽  
Core Diameter ◽  
Manufacturing Method ◽  
Long Wavelength ◽  
Thermal Drawing ◽  
Continuous Metal

Thermal drawing from a preform recently emerges as a scalable manufacturing method for the high volume production of continuous metal microwires for numerous applications. However, no model can yet satisfactorily provide effective understanding of core diameter and continuity from process parameters and material properties during thermal drawing. In this paper, a long wavelength model is derived to describe the dynamics of a molten metal micro-jet entrained within an immiscible, viscous, nonlinear free surface extensional flow. The model requires numerical data (e.g., drawing force and cladding profile) be measured in real time. Examination of the boundary conditions reveals that the diameter control mechanism is essentially volume conservation. The flow rate of molten metal is controlled upstream while the flow velocity is controlled downstream realized by solidification of the molten metal. The dynamics of the molten metal jet are found to be dominated by interfacial tension, stress in the cladding, and pressure in the molten metal. Taylor's conical fluid interface solution (Taylor, 1966, “Conical Free Surfaces and Fluid Interfaces,” Applied Mechanics, Springer, Berlin, pp. 790–796.) is found to be a special case of this model. A dimensionless capillary number Ca=2Fa/γA(0) is suggested to be used as the indicator for the transition from continuous mode (i.e., viscous stress dominating) to dripping mode (i.e., interfacial tension dominating). Experimental results showed the existence of a critical capillary number Cacr, above which continuous metal microwires can be produced, providing the first ever quantitative predictor of the core continuity during preform drawing of metal microwires.

Experimental Study of the Extrusion Characteristic of a Vane Extruder Based on Extensional Flow

2015 ◽  
Vol 35 (2) ◽  
pp. 215-220 ◽  
Author(s):  
Yin Xiaochun ◽  
Li Sai ◽  
He Guangjian ◽  
Zhang Guizhen ◽  
Qu Jinping
Keyword(s):  
Experimental Study ◽  
Extensional Flow

The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow

1997 ◽  
Vol 341 ◽  
pp. 165-194 ◽  
Author(s):  
XIAOFAN LI ◽  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Stokes Flow ◽  
Capillary Number ◽  
Surfactant Concentration ◽  
Drop Deformation ◽  
Main Body ◽  
Incident Flow ◽  
Spherical Drop ◽  
Convection Diffusion ◽  
Elasticity Number

The effect of an insoluble surfactant on the transient deformation and asymptotic shape of a spherical drop that is subjected to a linear shear or extensional flow at vanishing Reynolds number is studied using a numerical method. The viscosity of the drop is equal to that of the ambient fluid, and the interfacial tension is assumed to depend linearly on the local surfactant concentration. The drop deformation is affected by non-uniformities in the surface tension due to the surfactant molecules convection–diffusion. The numerical procedure combines the boundary-integral method for solving the equations of Stokes flow, and a finite-difference method for solving the unsteady convection–diffusion equation for the surfactant concentration over the evolving interface. The parametric investigations address the effect of the ratio of the vorticity to the rate of strain of the incident flow, the Péclet number expressing the ability of the surfactant to diffuse, the elasticity number expressing the sensitivity of the surface tension to variations in surfactant concentration, and the capillary number expressing the strength of the incident flow. At small and moderate capillary numbers, the effect of a surfactant in a non-axisymmetric flow is found to be similar to that in axisymmetric straining flow studied by previous authors. The accumulation of surfactant molecules at the tips of an elongated drop decreases the surface tension locally and promotes the deformation, whereas the dilution of the surfactant over the main body of the drop increases the surface tension and restrains the deformation. At large capillary numbers, the dilution of the surfactant and the rotational motion associated with the vorticity of the incident flow work synergistically to increase the critical capillary number beyond which the drop exhibits continuous elongation. The numerical results establish the regions of validity of the small-deformation theory developed by previous authors, and illustrate the influence of the surfactant on the flow kinematics and on the rheological properties of a dilute suspension. Surfactants have a stronger effect on the rheology of a suspension than on the deformation of the individual drops.

A slender drop in a nonlinear extensional flow

2016 ◽  
Vol 808 ◽  
pp. 337-361 ◽  
Author(s):  
Moshe Favelukis
Keyword(s):  
Stability Analysis ◽  
Capillary Number ◽  
Viscosity Ratio ◽  
Extensional Flow ◽  
Local Maximum ◽  
Creeping Flow ◽  
Time Dependent ◽  
Dimensionless Parameters ◽  
Breakup Mechanism ◽  
The One

The deformation of a slender drop in a nonlinear axisymmetric extensional and creeping flow has been theoretically studied. This problem, which was first suggested by Sherwood (J. Fluid Mech., vol. 144, 1984, pp. 281–295), is being revisited, and new results are presented. The problem is governed by three dimensionless parameters: the capillary number ($\mathit{Ca}\gg 1$), the viscosity ratio ($\unicode[STIX]{x1D706}\ll 1$), and the nonlinear intensity of the flow ($E\ll 1$). Contrary to linear extensional flow ($E=0$), where the local radius of the drop decreases monotonically (in the positive $z$ direction), in a nonlinear extensional flow ($E\neq 0$), two possible steady shapes exist: steady shapes (stable or unstable) with the local radius decreasing monotonically, and steady shapes (unstable) where the local radius of the drop has a local maximum, besides the one at the centre of the drop. Similar to linear extensional flow, the addition of nonlinear extensional effects does not change the end shape of the steady drop, which has pointed ends. A stability analysis has been done to distinguish between stable and unstable steady shapes and to determine the breakup point. Time-dependent studies reveal three types of breakup mechanism: a centre pinching mode, indefinite elongation, and a mechanism that remind us of tip-streaming, where a cusp is developed at the end of the drop.

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