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Biomembranes

When lipid molecules are immersed in aqueous environment they aggregate spontaneously into a bilayers or membrane that forms an encapsulating bag called vesicle. This happens because lipids consist of a hydrophilic head group and a hydrophobic tail, which isolate themselves in the interior of the membrane. This phenomenon is of interest in biophysics because lipid membranes are ubiquitous in biological systems, and an understanding of vesicles provides an important element to understand real cells.
An ellipsoid is deformed to a shape that resembles a red blood cell. The second row shows the same frame with a middle cut.
The elastic behavior under large deformations and the dynamics of such deformations are poorly understood. Helfrich in 1973 was one of the first to introduce a model for the equilibrium shape of vesicles where the bending or curvature energy had to be minimized. Jenkins in 1976 arrived to the same model starting from continuum mechanical principles.

Collaborators

Prof. Ricardo H. Nochetto (UMD)
Dr M. Sebastian Pauletti

Some Numerical Simulations:

3D Boomerang, Inertia Effect, 3D Boomerang with Fluid, Red Blood Cell and Dumbbells Shapes.

3D Boomerang

A 3D simulation with a bended initial shape is considered. As expected, the flow decreases the bending and smoothes the sharp tails. Click on picture to animate (might take some time to load).
Two different time scales are observed (left) rapid initial time scale and (right) slow time scale. Click on pictures to animate (might take some time to load).

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Inertial Effect

Simulations without (left) or with (right) bulk fluids are compared. The effect of the inherent inertia of the fluid is emphasized here. The colors indicate the magnitude of the pression. Click on picture to animate (might take some time to load).

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3D Boomerang with Fluid

A 3D simulation with a bended initial shape and taking into account the bulk fluid is presented. Click on picture to animate (might take some time to load).

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Red Blood Cell and Dumbbell Shapes

An ellipsoidal initial shape is chosen. Depending on the aspect ratio, the equilibrium shape found has a (left) bi-concave or (right) dumbbells type shape. Click on pictures to animate (might take some time to load).
  
Finally, the fluid inside an 5x1x1 ellipsoid is taken into account. Click on picture to animate (might take some time to load).

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