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An immersed boundary method for Brownian dynamics simulation of polymers in complex geometries: Application to DNA flowing through a nanoslit with embedded nanopits
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View: Figures


Image of FIG. 1.
FIG. 1.

DNA flowing through a nanoslit with embedded nanopit arrays (reproduced with permission from Ref. 6.) (a) Scanning electron micrograph of typical 1 × 1 μm square pits embedded in a nanoslit at 1 μm intervals. (b) Epifluorescent images of stained λ-DNA molecules confined in a 107 nm deep slit embedded with 1 × 1 μm pits spaced 2 μm apart. (c) Fluorescent images of λ-DNA traveling across a nanopit array under an applied pressure of 40 mbar in the device shown in (b).

Image of FIG. 2.
FIG. 2.

Schematic of the domain and distribution of polymer beads and boundary nodes. The domain is a rectangular parallelepiped of dimensions L x × L y × L z in which the flow satisfies periodic boundary conditions. The beads of a polymer molecule are shown by the filled symbols, and their positions are contained in the vector R. The no-slip boundary ∂Ω b is represented by regularized point forces located at boundary nodes R b , which are separated with a characteristic spacing h. The computational grid for solution of the “global” flow problem is regular, with grid spacings determined by the screening parameter α in the GGEM splitting of the force density, Eqs. (24)–(26).

Image of FIG. 3.
FIG. 3.

Properties of M bb for the case where a rigid sphere with radius R = 3 is represented by uniformly distributed points on the surface and the parameters for the calculation are L x = L y = L z = 10, Δx = Δy = Δz = 0.25, ξ = 4.0. (a) Condition number as a function of number of points on the sphere shell. (b) Relative residual as a function of number of iterations.

Image of FIG. 4.
FIG. 4.

Screening function gr) (Eq. (27)) for the GGEM algorithm.

Image of FIG. 5.
FIG. 5.

Comparison of the x-component of the velocity field driven by a point force (lines) acting along + x -axis with that generated by a regularized point force (symbols) with modified Gaussian form (Eq. (27), α = 2.0). (Top) velocity along x-axis. (Bottom) velocity along y-axis.

Image of FIG. 6.
FIG. 6.

Comparison of Hasimoto's result37 (symbols) and numerical solution (lines) for the x component of velocity due to a point force acting along +x direction in a periodic domain.

Image of FIG. 7.
FIG. 7.

Error ||E||2 as a function of (a) screening parameter α and (b) mesh size Δx for a point force at the center of a cubic periodic domain.

Image of FIG. 8.
FIG. 8.

(a) Velocity profile of laminar flow through a slit. The line represents the analytic profile and the symbols represent the numerical result by IBM. (b) Error of IBM as a function of boundary grid size h and the slope is 1.22.

Image of FIG. 9.
FIG. 9.

Validation of GGEM/IBM algorithm. Open symbols are numerical results and lines are analytical calculations. (a) Velocity profile u x around a unit sphere with no-slip boundary condition. Open circles represent points along x-axis and open squares are for points along y-axis. (b) Stokeslet near a single wall. Velocity profile of u x along +z direction for various (x, y) pairs. Open squares are for (x, y) = (3, 3) and open circles are for (x, y) = (1, 1).

Image of FIG. 10.
FIG. 10.

Schematic (top) and discretized representation (bottom) of the nanopit problem. Gray spheres indicate points at which no-slip boundary conditions are satisfied and red spheres are beads of the polymer chain.

Image of FIG. 11.
FIG. 11.

(Top) Streamlines in the nanopit and (bottom) contour plot of the streamwise velocity on the xz plane.

Image of FIG. 12.
FIG. 12.

Snapshots of a hopping event (from (a) to (f)) (top-down view, Pe = 3.5).

Image of FIG. 13.
FIG. 13.

(a) Time series of the x-component of the center-of-mass of a λ-DNA molecule driven through a nanopit array for two low values of Pe. (b) Residence time distribution and best fit to an exponential distribution for the conditions shown in (a).

Image of FIG. 14.
FIG. 14.

Mean residence time τ vs. Péclet number Pe for simulations including and neglecting hydrodynamic interactions (labeled HI and FD, respectively).

Image of FIG. 15.
FIG. 15.

Mean residence time τ vs. chain length N and Péclet number Pe. For the case Wi = 24, results with and without HI are shown.

Image of FIG. 16.
FIG. 16.

(a) Residence time distribution at high Péclet number and best fit to a Gaussian distribution. (b) Parameters for the Gaussian residence time distribution as a function of Péclet number.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An immersed boundary method for Brownian dynamics simulation of polymers in complex geometries: Application to DNA flowing through a nanoslit with embedded nanopits