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Abstract
The work presented in this thesis concerns numerical and experimental studies of flow
induced deformation of drops suspended in a second and immiscible liquid.
In the numerical part a model is implemented which is based on a Finite Element (FE)
Stokes solver coupled with a Volume of Fluid (VOF) tracking procedure. The FE solver
is based on Q2PO elements while the VOF procedure is based on PLIC (Piecewise Linear
Interface Calculation) interface reconstruction and a split operator Lagrangian advection
procedure which CQILSerVes mass rigorously. The model is fully 3D and can be used for simulating
the transient behavior of two phase liquid systems with moving interface topologies.
In order to include interfacial tension in the flow calculations both the Continuous Surface
Stress (CSS) model of Lafaurie, Nardone, Scardovelli, Zaleski & Zanetti (1994) and the
Continuous Surface Force (CSF) model of Brackbill, Kothe & Zemach (1992) are implemented.
Due to the high interface curvatures associated with highly deformed drops it
is necessary to use a high resolution mesh for our calculations. This leads to extensive
computation times mainly due to factorization and back substitution of the discretized
flow field equations. In order to reduce the computational cost a 2level procedure is implemented
where the fluid tracking algorithms are associated with a fine VOF mesh while
the flow field variables are associated with a coarser FE mesh. In the 2level algorithm the
calculation of interfacial tension terms is carried out as a summation of contributions from
the VOF mesh. This corresponds to letting the curvature vary within elements of the FE
mesh.
The implemented model is tested in terms of spatial and temporal convergence by
simulating the deformation of a single drop in a simple shear flow field. Furthermore wall
effects are also investigated by varying the size of the computational domain which consists
of a box with variable mesh size. In the center of the domain, where the drop resides, the
mesh consists of a fine region whereas closer to the walls the elements gradually increase
in size. Tests show that wall effects are negligible when the distance from a drop with
initial radius ro to the domain boundaries is 24ro. In the spatial convergence tests the
resolution of the fine mesh region is varied and it is found that a VOF mesh with side
lengths hvof == ro/18 is adequate when the viscosity ratio, A, between the drop and the
continuous phase is one. More thorough tests are carried out both in simple shear and
planar elongation. These simulations include dependence of steadystate deformations on
the capillary number, dropbreak and drop merging. Generally the test results agree well
with results reported in the literature. However, simulations carried out for A different
from one indicate that the resolution of the FE mesh needs to be increased compared
to simulations carried out with A == 1. This is probably related to the method used for
calculating the viscosity in elements which include both liquid phases.
In the experimental part of the thesis the deformation of a single drop suspended
in liquid undergoing a complex dispersing flow is studied. The experimental setup is
based on a rotorstator device consisting of two concentric cylinders with teethed walls. In
order to monitor the drop deformation and drop position a twin camera system is applied.
In the subsequent data analysis the recorded movies are analysed using an automated
image analysis procedure which leads to the deformation history of the drop and the drop
trajectory in the device. However, due to the geometric complexity of the rotorstator
device numerical calculations are necessary in order to obtain the generated flow field.
The obtained experimental data is analysed by two different methods. In the first method
the recorded drop deformations are time averaged and compared to a defined apparent
shear rate which does not rely on numerical flow field calculations. The results from this
analysis indicate that there is a relationship between the average drop deformation and the
apparent shear rate.
In the second method the experimentally obtained particle track is used together with
numerical calculations in order to obtain the local flow experienced by the drop along its
track. The data from these calculations lead to timedependent shear and elongation rates
which are used for generating time dependent boundary conditions for the FEVOF simulations.
By using this procedure the flow field experienced by the drop in the rotorstator
device is emulated in the computational box used for carrying out drop shape simulations.
Comparison of simulated and experimentally obtained deformations show that in general
the agreement is acceptable on a qualitative level. However, the simulations predict deformations
which are up to 100% larger than experimentally observed. We have also compared
our FEVOF simulations with results from Boundary Integral (BI) simulations and find
good agreement between the two numerical methods.
A number of the conducted experiments resulted in drop breakup. The breakup
behavior in the rotorstator device is analyzed qualitatively by relating the configuration
of the cylinders with the initiation of the breakup sequence. Here we observe that drop
breakup is initiated when a drop travels from a region of minimum gap width into a region
with maximum gap width where there is a relaxation in the flow field. Furthermore we
observe that for small viscosity ratios (A ~ 0.1) tip streaming is predominant while for
larger viscosity ratios either binary or capillary breakup is predominant.
Original language  English 

Number of pages  189 

ISBN (Print)  9788791435730 
Publication status  Published  May 2008 
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Projects
 1 Finished

Design af Emulsioner
Egholm, R. D., Szabo, P., Rasmussen, H. K., Harlen, O. G. & Trägårdh, C.
01/07/2004 → 16/05/2008
Project: PhD