Ebrahim M. Kolahdouz

Electrohydrodynamics of three-dimensional vesicles: A numerical approach

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 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.

Dynamics of three-dimensional vesicles in dc electric fields.

A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of varying electric field strength and different fluid and membrane properties. The dynamics of vesicles in the presence of dc electric fields is considered, in both 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.

A numerical model for the trans-membrane voltage of vesicles

Abstract 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.

Level set jet schemes for stiff advection equations: The semijet method

Abstract Many interfacial phenomena in physical and biological systems are dominated by high order geometric quantities such as curvature. Here 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.

A Semi-implicit Gradient Augmented Level Set Method

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.

A New Control Strategy to Improve the Ground Source Heat Pump’s Efficiency With a Recycled Product

Despite numerous efforts to impose control measures on the heat pump side of Ground Source Heat Pump (GSHP) systems, there has been little thought into the potential of control on the ground characteristics. This is perhaps because of a predisposition to believe that ground related works usually are associated with extra capital investment that makes any modification less favorable than making changes to the heat pump unit. An effective control strategy with a non-homogeneous soil profile for the ground side of horizontal GSHPs was investigated in this research. The model incorporates the effects of a variety of surface energy fluxes to provide an accurate estimate of the ground thermal regime. The developed model was utilized successfully in conjunction with the MATLAB Genetic Algorithm (GA) toolbox to obtain the optimized operational parameters for a GSHP in a cold climate condition (Buffalo, NY). A properly sized and engineered non-homogeneous soil profile demonstrated the potential to boost the capacity of GSHP systems to a significant level. The potential benefits of a recycled product of tire industry, Tire Derived Aggregate (TDA), as an insulation blanket was assessed via the optimization algorithm. TDA was demonstrated to be effective in heating mode in a cold climate environment by increasing the energy extraction rates from the ground by about 15% annual. The annual percentage increase in energy dissipation rate to the ground, in cooling season, with TDA blanket was 7.6%. The results are suggestive of the beneficial application of a layered system to increase the performance of GSHPs. A shift in design perspective toward consideration of more control strategies for the ground pipe side of GSHPs is suggested based on the model results.Copyright

Image-based immersed boundary model of the aortic root

Each year, approximately 300,000 heart valve repair or replacement procedures are performed worldwide, including approximately 70,000 aortic valve replacement surgeries in the United States alone. Computational platforms for simulating cardiovascular devices such as prosthetic heart valves promise to improve device design and assist in treatment planning, including patient-specific device selection. This paper describes progress in constructing anatomically and physiologically realistic immersed boundary (IB) models of the dynamics of the aortic root and ascending aorta. This work builds on earlier IB models of fluid-structure interaction (FSI) in the aortic root, which previously achieved realistic hemodynamics over multiple cardiac cycles, but which also were limited to simplified aortic geometries and idealized descriptions of the biomechanics of the aortic valve cusps. By contrast, the model described herein uses an anatomical geometry reconstructed from patient-specific computed tomography angiography (CTA) data, and employs a description of the elasticity of the aortic valve leaflets based on a fiber-reinforced constitutive model fit to experimental tensile test data. The resulting model generates physiological pressures in both systole and diastole, and yields realistic cardiac output and stroke volume at physiological Reynolds numbers. Contact between the valve leaflets during diastole is handled automatically by the IB method, yielding a fully competent valve model that supports a physiological diastolic pressure load without regurgitation. Numerical tests show that the model is able to resolve the leaflet biomechanics in diastole and early systole at practical grid spacings. The model is also used to examine differences in the mechanics and fluid dynamics yielded by fresh valve leaflets and glutaraldehyde-fixed leaflets similar to those used in bioprosthetic heart valves. Although there are large differences in the leaflet deformations during diastole, the differences in the open configurations of the valve models are relatively small, and nearly identical hemodynamics are obtained in all cases considered.