Metin Muradoglu

A front-tracking method for computation of interfacial flows with soluble surfactants

A finite-difference/front-tracking method is developed for computations of interfacial flows with soluble surfactants. The method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations together with the incompressible Navier-Stokes equations using a non-linear equation of state that relates interfacial surface tension to surfactant concentration at the interface. The method is validated for simple test cases and the computational results are found to be in a good agreement with the analytical solutions. The method is then applied to study the cleavage of drop by surfactant-a problem proposed as a model for cytokinesis [H.P. Greenspan, On the dynamics of cell cleavage, J. Theor. Biol. 65(1) (1977) 79; H.P. Greenspan, On fluid-mechanical simulations of cell division and movement, J. Theor. Biol., 70(1) (1978) 125]. Finally the method is used to model the effects of soluble surfactants on the motion of buoyancy-driven bubbles in a circular tube and the results are found to be in a good agreement with available experimental data.

Mixing in a drop moving through a serpentine channel: A computational study

The chaotic mixing in a drop moving through a winding channel is studied computationally in a two-dimensional setting. The molecular mixing is ignored and only the mixing due to the chaotic advection is considered. Passive tracer particles are used to visualize the mixing patterns and mixing is quantified by two distinct methods. It is found that both the quantification methods are consistent with visual observations as well as with each other. The effects of various non-dimensional parameters on the quality of mixing are studied and it is found that the capillary number, the ratio of the drop phase fluid viscosity to that of the ambient fluid and the relative size of the drop compared to the average channel width are the most critical parameters influencing the mixing. The mixing is found to be weakly dependent on Reynolds number.

PDF modeling of a bluff-body stabilized turbulent flame

The velocity-turbulent frequency-compositions PDF method combined with the consistent hybrid finite volume (FV)/particle solution algorithm is applied to a bluff-body stabilized turbulent flame. The statistical stationarity is shown and the performance of the PDF method is assessed by comparing the mean fields with the available experimental data. The effects of the model constants C1 in the turbulence frequency model and C in the mixing model on the numerical solutions are examined and it is found that all the mean fields are very sensitive to the changes in C1 while only the mixture fraction variance seems to be very sensitive to the changes in C but not the other mean fields. The spatial and bias errors are also examined and it is shown that the hybrid method is second order accurate in space and the bias error is vanishingly small in all the mean fields. The grid size and the number of particles per cell are determined for a 5% error tolerance. The chemistry is described by the simplest possible flamelet/PDF model. Hence the main focus of the paper is on the accurate calculations of the mean flow, turbulence and mixing, which lays the foundation for future work in which the chemistry is described in greater detail.

Impact of a compound droplet on a flat surface: A model for single cell epitaxy

The impact and spreading of a compound viscous droplet on a flat surface are studied computationally using a front-tracking method as a model for the single cell epitaxy. This is a technology developed to create two-dimensional and three-dimensional tissue constructs cell by cell by printing cell-encapsulating droplets precisely on a substrate using an existing ink-jet printing method. The success of cell printing mainly depends on the cell viability during the printing process, which requires a deeper understanding of the impact dynamics of encapsulated cells onto a solid surface. The present study is a first step in developing a model for deposition of cell-encapsulating droplets. The inner droplet representing the cell, the encapsulating droplet, and the ambient fluid are all assumed to be Newtonian. Simulations are performed for a range of dimensionless parameters to probe the deformation and rate of deformation of the encapsulated cell, which are both hypothesized to be related to cell damage. The deformation of the inner droplet consistently increases: as the Reynolds number increases; as the diameter ratio of the encapsulating droplet to the cell decreases; as the ratio of surface tensions of the air-solution interface to the solution-cell interface increases; as the viscosity ratio of the cell to encapsulating droplet decreases; or as the equilibrium contact angle decreases. It is observed that maximum deformation for a range of Weber numbers has (at least) one local minimum at We=2. Thereafter, the effects of cell deformation on viability are estimated by employing a correlation based on the experimental data of compression of cells between parallel plates. These results provide insight into achieving optimal parameter ranges for maximal cell viability during cell printing.

The effect of soluble surfactant on the transient motion of a buoyancy-driven bubble

The effect of soluble surfactants on the unsteady motion and deformation of a bubble rising in an otherwise quiescent liquid contained in an axisymmetric tube is computationally studied by using a finite-difference/front-tracking method. The unsteady incompressible flow equations are solved fully coupled with the evolution equations of bulk and interfacial surfactant concentrations. The surface tension is related to the interfacial surfactant concentration by a nonlinear equation of state. The nearly spherical, ellipsoidal, and dimpled ellipsoidal-cap regimes of bubble motion are examined. It is found that the surfactant generally reduces the terminal velocity of the bubble but this reduction is most pronounced in the nearly spherical regime in which the bubble behaves similar to a solid sphere and its terminal velocity approaches that of an equivalent solid sphere. Effects of the elasticity number and the bulk and interfacial Peclet numbers are examined in the spherical and ellipsoidal regimes. It is fou...

A computational study of axial dispersion in segmented gas-liquid flow

Axial dispersion of a tracer in a two-dimensional gas-liquid flow is studied computationally using a finite-volume/front-tracking method. The effects of Peclet number, capillary number, and segment size are examined. At low Peclet numbers, the axial dispersion is mainly controlled by the convection through the liquid films between the bubbles and channel walls. In this regime, the computational results are found to be in a very good agreement with the existing model due to Pedersen and Horvath [Ind. Eng. Chem. Fundam. 20, 181 (1981)]. At high Peclet numbers, the axial dispersion is mainly controlled by the molecular diffusion, with some convective enhancement. In this regime, a new model is proposed and found to agree well with the computational results. These Peclet number regimes are shown to persist for different slug lengths. The axial dispersion is found to depend weakly on the capillary number in the diffusion-controlled regime. Finally, computational simulations are performed for the cases of six b...

An auxiliary grid method for computations of multiphase flows in complex geometries

A method is developed for computations of interfacial flows in complex geometries. The method combines a front-tracking method with a newly developed finite volume (FV) scheme and utilizes an auxiliary grid for computationally efficient tracking of interfaces in body-fitted curvilinear grids. The tracking algorithm reduces particle tracking in a curvilinear grid to tracking on a uniform Cartesian grid with a look up table. The algorithm is general and can be used for other applications where Lagrangian particles have to be tracked in curvilinear or unstructured grids. The spatial and temporal errors are examined and it is shown that the method is globally second order accurate both in time and space. The method is implemented to solve two-dimensional (planar or axisymmetric) interfacial flows and is validated for a buoyancy-driven drops in a straight tube and the motion of buoyancy-driven drops in a periodically constricted channel.

Motion of large bubbles in curved channels

We study the motion of large bubbles in curved channels both semi-analytically using the lubrication approximation and computationally using a finite-volume/fronttracking method. The steady film thickness is governed by the classical Landau– Levich–Derjaguin–Bretherton (LLDB) equation in the low-capillary-number limit but with the boundary conditions modified to account for the channel curvature. The lubrication results show that the film is thinner on the inside of a bend than on the outside of a bend. They also indicate that the bubble velocity relative to the average liquid velocity is always larger in a curved channel than that in a corresponding straight channel and increases monotonically with increasing channel curvature. Numerical computations are performed for two-dimensional cases and the computational results are found to be in a good agreement with the lubrication theory for small capillary numbers and small or moderate channel curvatures. For moderate capillary numbers the numerical results for the film thickness, when rescaled to account for channel curvature as suggested in the lubrication calculation, essentially collapse onto the corresponding results for a bubble in a straight tube. The lubrication theory is also extended to the motion of large bubbles in a curved channel of circular cross-section.

Simulations of soluble surfactants in 3D multiphase flow

A finite-difference/front-tracking method is developed for simulations of soluble surfactants in 3D multiphase flows. The interfacial and bulk surfactant concentration evolution equations are solved fully coupled with the incompressible Navier-Stokes equations. A non-linear equation of state is used to relate interfacial surface tension to surfactant concentration at the interface. Simple test cases are designed to validate different parts of the numerical algorithm and the computational results are found to be in a good agreement with the analytical solutions. The numerical algorithm is parallelized using a domain-decomposition method. It is then applied to study the effects of soluble surfactants on the motion of buoyancy-driven bubbles in a straight square channel in nearly undeformable (spherical) and deformable (ellipsoidal) regimes. Finally the method is used to examine the effects of soluble surfactants on the lateral migration of bubbles in a pressure-driven channel flow. It is found that surfactant-induced Marangoni stresses counteract the shear-induced lift force and can reverse the lateral bubble migration completely, i.e., the contaminated bubble drifts away from the channel wall and stabilizes at the center of the channel when the surfactant-induced Marangoni stresses are sufficiently large.

Implicit Multigrid Computations of Buoyant Drops Through Sinusoidal Constrictions

Two-dimensional computations of dispersed multiphase flows involving complex geometries are presented. The numerical algorithm is based on the front-tracking method in which one set of governing equations is written for the whole computational domain and different phases are treated as a single fluid with variable material properties. The front-tracking methodology is combined with a newly developed finite volume solver based on dual time-stepping, diagonalized alternating direction implicit multigrid method. The method is first validated for a freely rising drop in a straight channel, and it is then used to compute a freely rising drop in various constricted channels. Interaction of two buoyancy-driven drops in a continuously constricted channel is also presented.