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).
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).
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.
Screening function g(αr) (Eq. (27)) for the GGEM algorithm.
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.
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.
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.
(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.
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).
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.
(Top) Streamlines in the nanopit and (bottom) contour plot of the streamwise velocity on the x − z plane.
Snapshots of a hopping event (from (a) to (f)) (top-down view, Pe = 3.5).
(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).
Mean residence time τ vs. Péclet number Pe for simulations including and neglecting hydrodynamic interactions (labeled HI and FD, respectively).
Mean residence time τ vs. chain length N and Péclet number Pe. For the case Wi = 24, results with and without HI are shown.
(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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