My current research involves the development of single particle dissipative particle dynamics (DPD) model and the application of the model in simulating complex fluid systems and biological systems at mesoscopic level. The complex fluid system can be colloidal suspensions, or polymer suspensions, and I am interested in their rheology and hydrodynamics. For biological system, I am now interested in modeling healthy red blood cells, malaria red blood cells, sickle cells and their effects on blood flow. The aim of this research is to understand the biological behavior in a quantitative way and provide some insight in medical therapy for certain blood diseases.

Research projects

Hydrodynamic interactions for single dissipative-particle-dynamics particles

The objective of this project is to verify whether Dissipative Particle Dynamics (DPD) particles immersed in a sea of DPD particles behave like Langevin particles suspended in a continuous Newtonian fluid solvent. Our principal test is to compare two effective DPD radii calculated by independent means. From the calculated coefficients of self-diffusion and viscosity the Stokes-Einstein equation yields an intrinsic radius, and from simulations of flow past a single fixed DPD particle a second radius is calculated from Stokes law. In the limit of small Reynolds number the two radii were found to approach each other. Hydrodynamic interactions were studied with Stokes flow past single DPD particles in unbounded/bounded domain, their closely spaced multi-particle clusters (straight-chains and hexagonal-packed aggregates) and their elastic filaments with bending resistance. For all cases of rigid bodies the simulation results are in good agreement with predictions derived analytically from the continuum Stokes system.

Related publications:

1. W. Pan, D. A. Fedosov, B. Caswell and G. E. Karniadakis, "Hydrodynamic Interactions for Single DPD Particles, and their Clusters and Filaments", Physical Review E, 78(4), 046706, 2008.

A new formulation for single-particle DPD model

We present a new formulation of dissipative particle dynamics (DPD) that leads to correct hydrodynamics in flows around bluff bodies represented by a single particle. In particular, we introduce a shear drag coefficient and a corresponding term in the dissipative force, which along with the angular momentum incorporate non-central shear forces between particles and preserve angular momentum. We consider several prototype flows to verify the performance of the proposed formulation with comparisons against theoretical and continuum-based simulation results. Our method is similar to the Fluid Particle Method (FPM) of Espanol (1998) and it has the computational and implementation simplicity of the standard DPD approach.

Related publications:

1. W. Pan, I. V. Pivkin, and G. E. Karniadakis, "Single-particle hydrodynamics in DPD: A new formulation", Europhysics Letters, 84, 10012, 2008.

Colloidal suspensions: rheology, microstructure and migration

We demonstrate that suspended spherical colloidal particles can be effectively modeled as single dissipative particle dynamics (DPD) particles provided that the conservative repulsive force is appropriately chosen. The suspension model is further improved with a new formulation, which augments standard DPD with non-central dissipative shear forces between particles while preserving angular momentum. Using the new DPD formulation we investigate the rheology (dependence of viscosity on volume fraction and shear rate), microstructure at high concentration and shear-induced migration, of a monodisperse suspension of colloidal particles in plane shear flows (Couette and Poiseuille). Specifically, to achieve a well-dispersed suspension we employ exponential conservative forces for the colloid-colloid and colloid-solvent interactions but keep the conventional linear force for the solvent-solvent interactions. Overall, the new method agrees very well with the Stokesian Dynamics method but it seems to have lower computational complexity and is applicable to general complex fluids systems.

Related publications:

1. W. Pan, B. Caswell and G. E. Karniadakis, "Rheology, Microstructure and Migration in Brownian Colloidal Suspensions", Langmuir, 26(1), 133-142, 2010.

Modeling red blood cells and blood flow

We propose a low-dimensional model to address RBC mechanics, the rheology and dynamics of blood flow. The low-dimensional RBC model is constructed as a closed-torus-like ring of colloidal particles. Each colloidal particle is represented by a single DPD particle. The proposed low-dimensional model is able to reproduce the elastic deformations of RBC and the correct hydrodynamics of blood flow with much less computational cost. Particularly, we find RBC linear and non-linear elastic deformations for healthy and different stages of the malaria parasite development match those obtained in optical-tweezers experiments. For some key features of blood flow, i.e., Fahraeus effect, Fahraeus-Lindqvist effect, and the cell-free layer (CFL), with the low-dimensional RBC model our simulations also reach a good accuracy in comparison with experimental data and empirical predictions. Furthermore, we investigate the influence of a geometrical constriction in the flow on the enhancement of the downstream cell free layer.

Related publications:

1. W. Pan, D. A. Fedosov, B. Caswell and G. E. Karniadakis, "A comparison of multiscale and low-dimensional models of red blood cells", submitted to Microvascular Research.
2. W. Pan, B. Caswell and G. E. Karniadakis, "A low-dimensional model for the red blood cell", Soft Matter, DOI:10.1039/C0SM00183J.