University at Buffalo,
Department of Mechanical and Aerospace Engineering
Director of Graduate Studies,
Department of Mechanical and Aerospace Engineering,
University at Buffalo
University at Buffalo,
Department of Mechanical and Aerospace Engineering
University at Buffalo,
Department of Mechanical and Aerospace Engineering
Department of Engineering Sciences and Applied Mathematics
Ph.D. in Mechanical Engineering
University of Michigan
Master of Science in Mathematics
University of Michigan
Bachelor of Science in Mechanical Engineering
Michigan Technological University
Many engineering systems involve moving interfaces. Examples include the self-assembly of molecules on surfaces due to electric fields and the dynamics of lipid bilayer vesicles.
I am interested in using advanced computational techniques to provide insight into the physics of such systems. These computational techniques couple multiple physics, such as those seen in multiphase fluid flow, into a coherent scheme which allows for the determination of the important parameters needed to obtain the desired behavior.
In this project a three-dimensional numerical model of vesicle electrohydrodynamics in the presence of DC electric fields is developed. The vesicle membrane is modeled as a thin capacitive interface through the use of a new semi-implicit level set Jet scheme. The enclosed volume and surface area are conserved both locally and globally by a new Navier-Stokes projection method. The electric field calculations explicitly take into account the capacitive interface by an implicit Immersed Interface Method formulation, which calculates the electric potential field and the trans-membrane potential simultaneously. The results match well with previously published experimental, analytic and two-dimensional computational works.
This research will result in a new unified numerical and experimental framework to understand and predict the behavior of mono-dispersed colloidal particles and liquid droplets in an immiscible liquid/liquid system during exposure to electric fields. This work will: 1) model the electrohydrodynamics of general three-dimensional colloidal particle/droplet systems, 2) experimentally investigate the dynamics of the system to provide validation of the numerical work and give insight into the influence of materials, 3) provide information about colloidal particle motion both in the fluids and on the droplet surface, and 4) systematically investigate the electrohydrodynamics of this system to provide a complete picture of the dynamics. The combined set of models and algorithms will result in a significant advancement of droplet based technologies such as directed drug delivery, micro-reactors, and micro-fluidics.
Tracking a level set and it's derivatives lead to highly accurate descriptions of a moving interface. In this project the original advection schemes, which are only applicable to linear velocity fields, are extended to allow for the investigation of stiff, non-linear interface motion. This work will aid in the other modeling projects currently underway within the group.
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often, thermal fluctuations, modelled as stochastic noise, are present in the system and the phase segregation process occurs on a surface. In this work, the segregation process is modelled via the Cahn–Hilliard–Cook model, which is a fourth-order parabolic stochastic system. Coarsening is analysed on two sample surfaces: a unit sphere and a dumbbell. On both surfaces, a statistical analysis of the growth rate is performed, and the influence of noise level and mobility is also investigated. For the spherical interface, it is also shown that a lognormal distribution fits the growth rate well.
The Cahn–Hilliard system has been used to describe a wide number of phase separation processes, from co-polymer systems to lipid membranes. In this work the convergence properties of a closest-point based scheme are investigated. In place of solving the original fourth-order system directly, two coupled second-order systems are solved. The system is solved using an approximate Schur-decomposition as a preconditioner. The results indicate that with a sufficiently high-order time discretization the method only depends on the underlying spatial resolution.
Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. a semi-implicit method is combined with a level set jet scheme to handle stiff nonlinear advection problems. The new method offers an improvement over the semi-implicit gradient augmented level set method previously introduced by requiring only one smoothing step when updating the level set jet function while still preserving the underlying methods higher accuracy. Sample results demonstrate that accuracy is not sacrificed while strict time step restrictions can be avoided.
The conservation of mass is a common issue with multiphase fluid simulations. In this work a novel projection method is presented which conserves mass both locally and globally. he fluid pressure is augmented with a time-varying component which accounts for any global mass change. The resulting system of equations is solved using an efficient Schur-complement method. Using the proposed method four numerical examples are performed: the evolution of a static bubble, the rise of a bubble, the breakup of a thin fluid thread, and the extension of a droplet in shear flow. The method is capable of conserving the mass even in situations with morphological changes such as droplet breakup.
Determining the wet-dry boundary and avoiding the related spurious thin-layer problem when solving the depth-averaged shallow-water (SW) equations (or similar granular flow models) remains an outstanding challenge, though it has been the focus of much research effort. In this paper, we introduce the use of level set and phase field based methods to address this issue and related problems. We also propose new heuristic methods to address this problem. We implemented all of these methods in TITAN2D, which is a parallel adaptive mesh refinement toolkit designed for numerical simulation of granular flows. Results of the methods for flow over a simple inclined plane and Colima volcano are used to illustrate the methods. For the inclined plane, we compared the results with experimental data and for Colima volcano they are compared to field data. Our approaches successfully captured the interface of the flow and solved the accuracy and stability problems related to the thin layer problem in SW numerical solution. The comparison of results shows that although all of the methods can be used to address this problem, each of them has its own advantages/disadvantages and methods have to be chosen carefully for each problem.
A three-dimensional numerical model of vesicle electrohydrodynamics in the presence of DC electric fields is presented. The vesicle membrane is modeled as a thin capacitive interface through the use of a semi-implicit, gradient-augmented level set Jet scheme. The enclosed volume and surface area are conserved both locally and globally by a new Navier-Stokes projection method. The electric field calculations explicitly take into account the capacitive interface by an implicit Immersed Interface Method formulation, which calculates the electric potential field and the trans-membrane potential simultaneously. The results match well with previously published experimental, analytic and two-dimensional computational works.
A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of different fluid and membrane properties. The dynamics of vesicles in the presence of DC electric fields is considered, both in the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full Prolate-Oblate-Prolate transition.In addition, there exists a critical electric field strength above which a vesicle will no longer tumble when exposed to linear shear flow.
The Immersed Interface Method is employed to solve the time-varying electric field equations around a three-dimensional vesicle. To achieve second-order accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The trans-membrane potential is determined implicitly as part of the algorithm. The method is compared to an analytic solution based on spherical harmonics and verifies the second-order accuracy of the underlying discretization even in the presence of solution discontinuities. A sample result for an elliptic interface is also presented.
Cryopreservation requires that stored materials be kept at extremely low temperatures and uses cryoprotectants that are toxic to cells at high concentrations. Lyopreservation is a potential alternative where stored materials can remain at room temperatures. That storage process involves desiccating cells filled with special glass-forming sugars. However, current desiccation techniques fail to produce viable cells, and researchers suspect that incomplete vitrification of the cells is to blame. To explore this hypothesis, a cell is modelled as a lipid vesicle to monitor the water content and membrane deformation during desiccation. The vesicle is represented as a moving, bending-resistant, inextensible interface and is tracked by a level set method. The vesicle is placed in a fluid containing a spatially varying sugar concentration field. The glass-forming nature is modelled through a concentration-dependent diffusivity and viscosity. It is found that there are optimal regimes for the values of the osmotic flow parameter and of the concentration dependence of the diffusivity to limit water trapping in the vesicle. Furthermore, it is found that the concentration dependencies of the diffusivity and viscosity can have profound effects on membrane deformations, which may have significant implications for vesicle damage during the desiccation process.
Here a semi-implicit formulation of the gradient augmented level set method is presented. The method is a hybrid Lagrangian--Eulerian method that may be easily applied in two or three dimensions. By tracking both the level set function and the gradient of the level set function, highly accurate descriptions of a moving interface can be formed. Stability is enhanced by the addition of a smoothing term to the gradient augmented level set equations. The new approach allows for the investigation of interfaces evolving by mean curvature and by the intrinsic Laplacian of the curvature. Sample results presented in both two and three dimensions demonstrate the applicability of the scheme. The influence of the smoothing term on stability and accuracy is also investigated.
The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise continuous in the domain while the embedded interface exerts singular forces on the surround fluids. This gives rise to discontinuous solutions in the pressure and velocity field. These jump conditions are required to develop accurate numerical methods, such as the Immersed Interface Method, for the solutions of the Stokes equations in such situations.
Vesicles exposed to the human circulatory system experience a wide range of flows and Reynolds numbers. Previous investigations of vesicles in fluid flow have focused on the Stokes flow regime. In this work the influence of inertia on the dynamics of a vesicle in a shearing flow is investigated using a novel level-set computational method in two dimensions. A detailed analysis of the behavior of a single vesicle at finite Reynolds number is presented. At low Reynolds numbers the results recover vesicle behavior previously observed for Stokes flow. At moderate Reynolds numbers the classical tumbling behavior of highly viscous vesicles is no longer observed. Instead, the vesicle is observed to tank-tread, with an equilibrium angle dependent on the Reynolds number and the reduced area of the vesicle. It is shown that a vesicle with an inner/outer fluid viscosity ratio as high as 200 will not tumble if the Reynolds number is as low as 10. A new damped tank-treading behavior, where the vesicle will briefly oscillate about the equilibrium inclination angle, is also observed. This behavior is explained by an investigation on the torque acting on a vesicle in shear flow. Scaling laws for vesicles in inertial flows have also been determined. It is observed that quantities such as vesicle tumbling period follow square-root scaling with respect to the Reynolds number. Finally, the maximum tension as a function of the Reynolds number is also determined. It is observed that, as the Reynolds number increases, the maximum tension on the vesicle membrane also increases. This could play a role in the creation of stable pores in vesicle membranes or for the premature destruction of vesicles exposed to the human circulatory system.
A new numerical method to model the dynamic behavior of lipid vesicles under general flows is presented. A gradient-augmented level set method is used to model the membrane motion. To enforce the volume- and surface-incompressibility constraints a four-step projection method is developed to integrate the full Navier–Stokes equations. This scheme is implemented on an adaptive non-graded Cartesian grid. Convergence results are presented, along with sample two-dimensional results of vesicles under various flow conditions.
Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the second-order derivatives of the signed distance function for arbitrary interfaces. In addition to enforcing the condition |∇ϕ|2=1, where ϕ is the level set function, the method ensures that ∇(|∇ϕ|)2=0 and ∇∇(|∇ϕ|)2=0 are also satisfied. Results indicate that for both two- and three-dimensional interfaces the resulting level set and curvature field are smooth even for coarse grids. Convergence results show that using first-order upwind derivatives and the augmented fast marching method result in a second-order accurate level set and gradient field and a first-order accurate curvature field.
Sophomore level course covering introductory topics in thermodynamics such as the First and Second Laws of Thermodynamics, thermodynamics properties, and physical applications such as internal combustion engines. An online version of the course was developed in 2015 and will be offered yearly thereafter.
A graduate level course covering numerical methods to model moving interfaces. Methods covered include marker particle, level set, volume of fluid, and phase field methods. Advance topics related to recent research is also covered.
This is a course in Linear Algebra and a first course in programming using MATLAB. Upon completion of this course students should have a firm grasp of important topics in Linear Algebra and their application in engineering contexts as well as programming skills in MATLAB, including array manipulation, loop and branching structures, user-defined functions, and plotting.
Introduce freshman to linear algebra, including matrix inverse, solution sets, projections, and least squares. Also introduce students to programming using MATLAB. Most students have no previous programming experience.
Integration techniques covered included double, triple and surface integrals in polar, cylindrical and spherical coordinates. Vector calculus topics included line integrals, Green’s Theorem, Surface integrals, Divergence Theorem and Stokes’ Theorem.
Introduces methods to solve ordinary differential equations and first-order systems of ordinary differential equations. The methods are then used to solve engineering applications.
Introduces numerical methods to solve first-order ordinary differential equations and first-order systems of ordinary differential equations. The methods are then used to solve engineering applications.
Feel free to contact me regarding assistance in your research.
326 Jarvis, University at Buffalo, Buffalo, New York 14260-4400
You can find me at my office located at 326 Jarvis Hall, on the North Campus of University at Buffalo.
I am at my office most days from 8:00 am to 4:30 pm.