Nhan Phan-Thien

Simulating flow of DNA suspension using dissipative particle dynamics

We simulate DNA suspension microchannel flows using the dissipative particle dynamics (DPD) method. Two developments make this simulation more realistic. One is to improve the dynamic characteristics of a DPD system by modifying the weighting function of the dissipative force and increasing its cutoff radius, so that the Schmidt number can be increased to a practical level. Another is to set up a wormlike chain model in the DPD framework, according to the measured extension properties of a DNA molecule in uniform flows. This chain model is then used to study flows of a DNA suspension through microchannels. Interesting results on the conformation evolution of DNA molecules passing through the microchannels, including periodic contraction-diffusion microchannels, are reported.

Microchannel flow of a macromolecular suspension

In the delivery of DNA molecules by microfluidic devices, the channel width is very often in the same order as the size of the DNA molecules and the applicability of continuum mechanics at this level may be questioned. In this paper we use finitely extendable nonlinear elastic (FENE) chains to model the DNA molecules and employ the dissipative particle dynamics (DPD) method to simulate their behavior in the flow. Simple DPD fluids are found to behave just like a Newtonian fluid in Poiseuille flow. However, the velocity profiles of FENE chain suspensions can be fitted with power-law curves, especially for dilute suspensions. Some results on the conformation and migration of FENE chains are also reported.

Viscoelastic mobility problem of a system of particles

Abstract In this paper we present a new implementation of the distributed Lagrange multiplier/fictitious domain (DLM) method by making some modifications over the original algorithm for the Newtonian case developed by Glowinski et al. [Int. J. Multiphase Flow 25 (1999) 755], and its extended version for the viscoelastic case by Singh et al. [J. Non-Newtonian Fluid Mech. 91 (2000) 165]. The key modification is to replace a finite-element triangulation for the velocity and a “staggered” (twice coarser) triangulation for the pressure with a rectangular discretization for the velocity and the pressure. The sedimentation of a single circular particle in a Newtonian fluid at different Reynolds numbers, sedimentation of particles in the Oldroyd-B fluid, and lateral migration of a single particle in a Poiseuille flow of a Newtonian fluid are numerically simulated with our code. The results show that the new implementation can give a more accurate prediction of the motion of particles compared to the previous DLM codes and even the boundary-fitted methods in some cases. The centering of a particle and the well-organized Karman vortex street are observed at high Reynolds numbers in our simulation of a particle sedimenting in a Newtonian fluid. Both results obtained using the DLM method and the spectral element method reveal that the direct contribution of the viscoelastic normal stress to the force on a particle in the Oldroyd-B fluid is very important.

Flow around spheres by dissipative particle dynamics

The dissipative particle dynamics (DPD) method is used to study the flow behavior past a sphere. The sphere is represented by frozen DPD particles while the surrounding fluids are modeled by simple DPD particles (representing a Newtonian fluid). For the surface of the sphere, the conventional model without special treatment and the model with specular reflection boundary condition proposed by Revenga et al. [Comput. Phys. Commun. 121–122, 309 (1999)] are compared. Various computational domains, in which the sphere is held stationary at the center, are investigated to gage the effects of periodic conditions and walls for Reynolds number (Re)=0.5 and 50. Two types of flow conditions, uniform flow and shear flow are considered, respectively, to study the drag force and torque acting on the stationary sphere. It is found that the calculated drag force imposed on the sphere based on the model with specular reflection is slightly lower than the conventional model without special treatment. With the conventional...

Molecular dynamics simulation of a liquid in a complex nano channel flow

We report some molecular dynamics simulation results for a complex nano channel flow. In certain flow geometry, some of the flow features cannot be predicted by the Navier–Stokes equations with no-slip boundary conditions. The results show a loss of dynamic similarity for flows with similar geometry and global dimensionless flow parameters. Nano-sized vortex flow can be developed at low Reynolds numbers due to near-wall molecules having large enough momenta, resulting in qualitatively different flow field from that predicted by the Navier–Stokes equations.

Fully developed viscous and viscoelastic flows in curved pipes

Some h-p finite element computations have been carried out to obtain solutions for fully developed laminar flows in curved pipes with curvature ratios from 0.001 to 0.5. An Oldroyd-3-constant model is used to represent the viscoelastic fluid, which includes the upper-convected Maxwell (UCM) model and the Oldroyd-B model as special cases, With this model we can examine separately the effects of the fluid inertia, and the first and second normal-stress differences. From analysis of the global torque and force balances, three criteria are proposed for this problem to estimate the errors in the computations

Dynamic simulation of sphere motion in a vertical tube

In this paper, the sedimentation of a sphere and its radial migration in a Poiseuille flow in a vertical tube filled with a Newtonian fluid are simulated with a finite-difference-based distributed Lagrange multiplier (DLM) method. The flow features, the settling velocities, the trajectories and the angular velocities of the spheres sedimenting in a tube at different Reynolds numbers are presented. The results show that at relatively low Reynolds numbers, the sphere approaches the tube axis monotonically, whereas in a high-Reynolds-number regime where shedding of vortices takes place, the sphere takes up a spiral trajectory that is closer to the tube wall than the tube axis. The rotation motion and the lateral motion of the sphere are highly correlated through the Magnus effect, which is verified to be an important (but not the only) driving force for the lateral migration of the sphere at relatively high Reynolds numbers. The standard vortex structures in the wake of a sphere, for Reynolds number higher than 400, are composed of a loop mainly located in a plane perpendicular to the streamwise direction and two streamwise vortex pairs. When moving downstream, the legs of the hairpin vortex retract and at the same time a streamwise vortex pair with rotation opposite to that of the legs forms between the loops. For Reynolds number around 400, the wake structures shed during the impact of the sphere on the wall typically form into streamwise vortex structures or else into hairpin vortices when the sphere spirals down. The radial, angular and axial velocities of both neutrally buoyant and non-neutrally buoyant spheres in a circular Poiseuille flow are reported. The results are in remarkably good agreement with the available experimental data. It is shown that suppresion of the sphere rotation produces significant large additional lift forces pointing towards the tube axis on the spheres in the neutrally buoyant and more-dense-downflow cases, whereas it has a negligible effect on the migration of the more dense sphere in upflow.

Numerical analysis of viscoelastic flow through a sinusoidally corrugated tube using a boundary element method

The flow of a viscoelastic fluid through a corrugated tube is important both for modeling the flow of polymeric fluids through porous media and for testing numerical methods in non‐Newtonian fluid mechanics. In this paper the boundary element method is used to solve this flow problem for various geometries. Newtonian, Maxwell, Oldroyd‐B, and modified Phan‐Thien–Tanner (MPTT) constitutive equations were used. The periodicity of the flow was guaranteed by treating the periodic conditions as parts of the system of equations. The effect of mesh refinement was considered and in some cases this was found to be negligible. The results are generally in good agreement with other investigators up to a Weissenberg number of about 6. After this point no convergence was reached with the present discretization. For the Maxwell and Oldroyd‐B fluids, the change in the flow resistance is small (∼5% decrease) as the Weissenberg number increases. An increase in the flow resistance with the Weissenberg number was observed in...

Particle-based simulations of red blood cells—A review

Particle-based methods have been increasingly attractive for solving biofluid flow problems, because of the ease and flexibility in modeling complex structure fluids afforded by the methods. In this review, we focus on popular particle-based methods widely used in red blood cell (RBC) simulations, including dissipative particle dynamics (DPD), smoothed particle hydrodynamics (SPH), and lattice Boltzmann method (LBM). We introduce their basic ideas and formulations, and present their applications in RBC simulations which are divided into three classes according to the number of RBCs in the simulation: a single RBC, two or multiple RBCs, and RBC suspension. Furthermore, we analyze their advantages and disadvantages. On weighing the pros and cons of the methods, a combination of the immersed boundary (IB) method and some forms of smoothed dissipative particle hydrodynamics (SDPD) methods may be required to deal effectively with RBC simulations.

A boundary element approach for parabolic differential equations using a class of particular solutions

Abstract Two boundary element methods are developed for solving a class of parabolic differential equations. The methods avoid performing time-consuming domain integrations by approximating a “generalized forcing function” in the interior of the domain with the use of radial basis functions. An approximate particular solution can be determined, and the original problem can be transformed into a homogeneous problem. Numerical examples demonstrate some advantages and disadvantages of the two methods.