Austin Griffith
The Wobbly Ring
Dynamics of a ring as predicted by a geometrically exact elastic rod model. Top images show the time evolution of a ring with an initial velocity intended to excite two traveling waves. Balls on the ring indicate orientation of rod cross sections. Color indicates position along the rod. The two traveling waves move around the ring and distort it over time.
Bottom images are surface plots of the 3 translational variables (Shift, Slide, Rise) and 3 rotational variables (Tilt, Roll, Twist) that describe the spatial relationship between adjacent cross sections of the rod. Front edge of each surface plot represents position; left edge represents time. Ridges and valleys correspond to the traveling waves. Only Shift has an initial velocity but due to geometrical couplings all variables are eventually excited.
This is a project with Ricardo Cortez, Mac Hyman and Ricardo Ortiz.
Bree Cummins
Postdoctoral Researcher
A top-down view of the perturbation velocity field caused by a linear array of five thin sensory hairs in sinusoidal flow.
Research conducted at the Center for Computational Biology at Montana State University in collaboration with CCS.
Katharine Hamlington
Ph.D candidate, Biomedical Engineering
"Mixing Forks"
We are developing a portable antibody-based sensor to rapidly detect environmental contaminants. In order for the sensor to produce a signal, the contaminant (analyte) must be mixed with an antibody solution. However, mixing is difficult in channels with microscale dimensions because the flow is purely laminar - turbulence is nonexistent. We are computationally investigating the design of a passive micromixer to induce transverse flows that may improve mixing between the analyte and antibody.
The mixing and reaction between analyte (blue) and antibody (red) solutions that bind to form a complex (green) is simulated in a set of microfluidic sandwich mixers. Initially, the analyte enters the channel through the inlet "sandwiched" between two outer inlets carrying antibody (top of figure). The solutions flow downward through channels due to an applied pressure drop between the inlets and outlet. The velocity field is computed by solving the Stokes equations with the boundary element method. The grid-free particle strength exchange method is implemented to solve the convection-diffusion-reaction equation for the concentrations of analyte, antibody, and complex.
Of the three mixers shown here, the twisty design produced the highest concentration of analyte-antibody complex at the outlet region. The obstructed mixer is also effective, but the obstructions decrease the internal velocity such that the effluent requires a longer time to reach the end of the domain. This work is funded by NSF EPSCoR and is a collaboration with Louisiana Tech and Louisiana State University.
John Chrispell
Postdoctoral Researcher
Trace of the extra stress tensor and stream lines around an immersed fiber oscillating under surface tension in a periodic domain filled with viscoelastic fluid.
This is a CCS collaboration with UCLA, NYU and Washington State University.
Ricardo Cortez
Faculty
Dendritic tree created by a neuron morphology model in which leading branches can (1) extend, (2) bifurcate, or (3) stay where they are at every step. The outcome at each step is determined by a set of probabilities which change depending on the branch level and other variables.
Damir B. Khismatullin
Faculty, Department of Biomedical Engineering and Center for Computational Science
3-D Simulation of White Blood Cell Rolling on a Receptor-Coated Surface
Changes in the spatial distribution of PSGL-1 (ligand for surface-bound P-selectin) expressed on microvilli of a rolling human monocyte, according to numerical simulation. Rolling of the cell on the P-selectin-coated lower plate of the microchannel (height = 15 µm) is mediated by P-selectin/PSGL-1 binding kinetics and the hydrodynamic force exerted on the cell by shear flow (wall shear stress = 0.5 dyn/cm2). The cell has 729 quasi-uniformly distributed microvilli (not shown). Eight out of 25 PSGL-1 molecules present on the tip of each microvillus are marked by circles with different color fills. The computational algorithm used in the simulation is the viscoelastic Volume-of-Fluid algorithm for two-phase flow combined with a Monte Carlo algorithm for stochastic receptor-ligand binding.
This is a collaboration with George A. Truskey, Department of Biomedical Engineering, Duke University.
Hideki Fujioka
Computational Scientist
Distortion of Lung Alveoli around Surfactant-deficient Acinus
Pulmonary surfactant plays a vital role in reducing the surface tension of the liquid lining alveoli and airways. Alveolar type II cells produce the surfactant. When this ability is compromised, high surface tension makes the alveoli to be stiffer and the volume of the alveoli is smaller than the normal alveoli at a fixed air pressure. This causes the normal alveoli near the surfactant-deficient alveoli to be stretched, leading to their septal strain exceeding a normal range. A truncated-octahedron with six square and eight hexagonal faces is used as a representation of the geometry in the model of the alveolus. Each face consists of supporting beams that have a non-linear stress-strain relationship to simulate the physical properties of elastin and collagen fiber bundles. There are 25x25x25 alveoli with air-pressure of 10cmH2O. 15 alveoli with the surface tension of 65dyne/cm are placed in the middle. Displacement-based Finite Element Method is used.
Graham Cummins
Propagation of the electrical response to synaptic input through a compartmental model of an invertebrate interneuron. Greater changes in the membrane potential are represented with warmer colors.
Research conducted at the Center for Computational Biology, Montana State University.
Hoa Nguyen
Post-doctoral Researcher
The diatoms are a group of photosynthetic, single-celled algae. They are a type of plankton with intricately patterned, glass-like cell walls. It is fascinating to watch live diatoms under the microscope. They have beautiful forms and different colors as seen in the background photo (credit: Manfred Kage/Science Photo Library).
We model Thalassiosira nordenskioeldii, a diatom with spines emanating from its top and bottom surfaces at different angles (top picture, copyright of the Biodiversity Institute of Ontario). In our simplified representation with eight spines (middle picture), the angles are 30 degrees. Immersing this structure in shear flow, we are able to observe a cross-section of the flow field (bottom pictures).
This is a CCS collaboration with the University of Maine and George Washington University.
Ricardo Ortiz
Postdoctoral Researcher
Stream arrows of flow field produced by a circular helical flagellum.
Simulations of Dinoflagellate Organisms in collaboration with Hoa Nguyen, Ricardo Cortez and Lisa Fauci.
Richard Stolz
Graduate student, Mathematics and Public Health
Antibody Warhol
All 20 possible point mutations to the antibody 5B2.
Sarah Lukens
Ph.D candidate, Mathematics
Chaotic systems are characterized by a rapid divergence of initial conditions, which may be quantified by averaging maximum linear growth rates over a finite time interval. These stretch rates form a scalar field with respect to a grid of initial conditions called a finite-time Lyapunov exponent (FTLE) field. For an integrative computational model of motile, internally actuated cilia along with a mucus layer modeled by linear elastic elements coupled with a viscous, incompressible fluid using the immersed boundary method, we show a surface plot of the FTLE field over a time period of 4.5 ciliary beats for three cilia. Maximum ridges in the FTLE field are defined as Lagrangian coherent structures which act as fluid-fluid boundaries which separate regions of qualitatively different flow.
This is a collaboration between CCS and Mississippi State University.
Priya Shilpa Boindala
Ph.D candidate, Mathematics
Collective dynamics of microorganisms in viscous flow has been the focus of our study. Though suspended in a fluid where the viscous forces are dominant and the inertial forces are negligible, the collective hydrodynamic interaction between these organisms and any surfaces present in the fluid domain result in turbulent fluid structures.
We have come up with two ways to represent an organism by eliminating its complex structure for application to studies of collective dynamics where the principal contribution comes from hydrodynamic interactions.
Shown here is a snapshot in time of a dynamic simulation due to 900 organisms in free space from our Two-point model in Regularized Stokes flow.
Shown here as red dots are the position of heads of each organism. The distance between a head and tail of a single organism is 0.1. The black lines are the fluid streamlines, which help visualize the regions of recirculation.
To the right is a zoomed in preview of a region in the whole plane. The magenta circles are plotted to bring attention to fluid recirculation regions that arise due to interactions between neighbors. The size of these regions is of the order of the size of an organism (diameter 0.1), which has been observed experimentally.
This is part of ongoing work towards my dissertation, under the guidance of Dr. Ricardo Cortez. It has been supported by NSF grant DMS-0094179.
Yuen-Yick Kwan
Post-doctoral researcher
Simulation of a chemical reaction in a microchannel mixer in which two fluids are inserted at the upper-left and lower-left regions, respectively. The figure on top shows the steady-state velocity field and the figure on bottom shows the concentration of the chemical reaction product at a certain time. This project is part of a science driver to develop miniaturized antibody-sensors, involving research groups at Tulane University, LATech, UNO and Xavier University. Funding for this project comes from NSF grant EPS-0701491 and Tulane University’s Center for Computational Science.
Weixiong Wang
Postdoctoral Researcher
3D Simulation of Non-Newtonian Fluid Flow in Double Concentric Cylinder Geometry with Slotted Rotor
(a) The geometry of the problem: two concentric cylinder walls (light region; outer cylinder is removed from the view) and a slotted rotor (dark region) inserted in the gap. Due to the circumferential periodicity, only one slot is simulated. The middle section (small white piece) is sliced from the domain to show numerical results. Shown are the distributions of (b) velocity, (c) strain rate, (d) apparent viscosity, and (e) shear stress (the second invariant of the stress tensor). The simulation is performed with commercial CFD software ANSYS Fluent 12.0. Rheological properties of a yield-stress fluid are described by a new constitutive model proposed by H. Zhu & D. De Kee (2005), which is implemented in the simulation code as a Fluent User Defined Function. This research is supported by a grant from ACS Petroleum Research Fund.
This project is in collaboration with Damir Khismatullin, Department of Biomedical Engineering, and Daniel De Kee, Department of Chemical and Biomolecular Engineering, and Tulane Institute of Macromolecular Engineering and Science.
