Hydrodynamics of diatom chains and semiflexible fibres

Abstract

Diatoms are non-motile, unicellular phytoplankton that have the ability to form colonies in the form of chains. Depending upon the species of diatoms and the linking structures that hold the cells together, these chains can be quite stiff or very flexible. Recently, the bending rigidities of some species of diatom chains have been quantified. In an effort to understand the role of flexibility in nutrient uptake and aggregate formation, we begin by developing a three-dimensional model of the coupled elastic -hydrodynamic system of a diatom chain moving in an incompressible fluid. We find that simple beam theory does a good job of describing diatom chain deformation in a parabolic flow when its ends are tethered, but does not tell the whole story of chain deformations when they are subjected to compressive stresses in shear. While motivated by the fluid dynamics of diatom chains, our computational model of semiflexible fibres illustrates features that apply widely to other systems. The use of an adaptive immersed boundary framework allows us to capture complicated buckling and recovery dynamics of long, semiflexible fibres in shear.

Simulating flexible fiber suspensions using a scalable immersed boundary algorithm

“…The boundary between classes III and IV is not as sharply defined, but can still Tables 2 and 4. be assigned to a value of flexibility χ ≈ 65.0. These class boundaries are consistent with the simulations reported by Nguyen and Fauci [44]. Based on these observations, we conclude that the dimensionless flexibility χ provides a useful measure for characterizing orbit classes at the lower Reynolds numbers considered here.…”

The Dynamics of Microtubule/Motor-Protein Assemblies in Biology and Physics

“…The most basic and easy to use of these is local slender-body theory, which gives a local anisotropic relation between elastic and drag forces. Nonlocal hydrodynamic interactions can be captured through the use of higher-order, more complex, slender-body formulations (Tornberg & Shelley 2004) or through other approaches, such as immersed boundary methods (Peskin 2002, Nguyen & Fauci 2014, bead-rod models (Hämäläinen et al 2011), or regularized Stokeslet methods (Olson et al 2013). These methodologies and their applications to understanding fluid-structure interactions, such as buckling instabilities at low Reynolds numbers, have recently been reviewed (Lindner & Shelley 2015).…”

Numerical Analysis of the Immersed Boundary Method for Cell-Based Simulation

“…update the cell population to take account of cellular processes including cell death, division, growth, shrinkage, and procession through the cell cycle, discussed shortly; 2. calculate the internal and external forces acting on each node, using (13); 3. loop over each immersed boundary node and propagate the associated force to the fluid mesh domain, as described by (21); 4. loop ever each fluid source and propagate the associated strength to the fluid mesh domain, as described by (23); 5. solve the Navier-Stokes equations (6a) and (6b) using the fast Fourier transform algorithm detailed in subsection 4.8 to generate new fluid velocities; 6. use the new fluid velocities to update immersed boundary node and fluid source locations as described by (22) and (24). An example of a simple simulation performed using this implementation within Chaste is visualized in Figure 2, where an elliptical immersed boundary relaxes over time towards a circular shape.…”

“…Also in three dimensions is a comprehensive model of the cochlea by Givelberg and Bunn [10], in a very different Reynolds number regime, demonstrating the versatility and range of IB methods. More recently, IB methods in three dimensions have been applied to ever more complex geometries, and studies include an investigation of the hydrodynamics of diatom chains [24], a model of actively swimming jellyfish [17], and a study of aortic heart valve dynamics [11]. These studies utilize the IBAMR implementation.…”