Wenxiao Pan

Predicting human blood viscosity in silico

The viscosity of blood has long been used as an indicator in the understanding and treatment of disease, and the advent of modern viscometers allows its measurement with ever-improving clinical convenience. However, these advances have not been matched by theoretical developments that can yield a quantitative understanding of blood’s microrheology and its possible connection to relevant biomolecules (e.g., fibrinogen). Using coarse-grained molecular dynamics and two different red blood cell models, we accurately predict the dependence of blood viscosity on shear rate and hematocrit. We explicitly represent cell–cell interactions and identify the types and sizes of reversible rouleaux structures that yield a tremendous increase of blood viscosity at low shear rates. We also present the first quantitative estimates of the magnitude of adhesive forces between red cells. In addition, our simulations support the hypothesis, previously deduced from experiments, of yield stress as an indicator of cell aggregation. This non-Newtonian behavior is analyzed and related to the suspension’s microstructure, deformation, and dynamics of single red blood cells. The most complex cell dynamics occurs in the intermediate shear rate regime, where individual cells experience severe deformation and transient folded conformations. The generality of these cell models together with single-cell measurements points to the future prediction of blood-viscosity anomalies and the corresponding microstructures associated with various diseases (e.g., malaria, AIDS, and diabetes mellitus). The models can easily be adapted to tune the properties of a much wider class of complex fluids including capsule and vesicle suspensions.

Rheology, microstructure and migration in brownian colloidal suspensions.

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 noncentral dissipative shear forces between particles while preserving angular momentum. Using the new DPD formulation we investigate the rheology, microstructure 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. Our simulations yield relative viscosity versus volume fraction predictions in good agreement with both experimental data and empirical correlations. We also compute the shear-dependent viscosity and the first and second normal-stress differences and coefficients in both Couette and Poiseuille flow. Simulations near the close packingvolume-fraction (64%) at low shear rates demonstrate a transition to flow-induced string-like structures of colloidal particles simultaneously with a transition to a nonlinear Couette velocity profile in agreement with experimental observations. After a sufficient increase ofthe shear rate the ordered structure melts into disorder with restoration of the linear velocity profile. Migration effects simulated in Poiseuille flow compare well with experiments and model predictions. The important role of angular momentum and torque in nondilute suspensions is also demonstrated when compared with simulations by the standard DPD, which omits the angular degrees of freedom. 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.

Many-body dissipative particle dynamics simulation of liquid/vapor and liquid/solid interactions.

The combination of short-range repulsive and long-range attractive forces in many-body dissipative particle dynamics (MDPD) is examined at a vapor/liquid and liquid/solid interface. Based on the radial distribution of the virial pressure in a drop at equilibrium, a systematic study is carried out to characterize the sensitivity of the surface tension coefficient with respect to the inter-particle interaction parameters. For the first time, the approximately cubic dependence of the surface tension coefficient on the bulk density of the fluid is evidenced. In capillary flow, MDPD solutions are shown to satisfy the condition on the wavelength of an axial disturbance leading to the pinch-off of a cylindrical liquid thread; correctly, no pinch-off occurs below the cutoff wavelength. Moreover, in an example that illustrates the cascade of fluid dynamics behaviors from potential to inertial-viscous to stochastic flow, the dynamics of the jet radius is consistent with the power law predictions of asymptotic analysis. To model interaction with a solid wall, MDPD is augmented by a set of bell-shaped weight functions; hydrophilic and hydrophobic behaviors, including the occurrence of slip in the latter, are reproduced using a modification in the weight function that avoids particle clustering. The dynamics of droplets entering an inverted Y-shaped fracture junction is shown to be correctly captured in simulations parametrized by the Bond number, confirming the flexibility of MDPD in modeling interface-dominated flows.

A low-dimensional model for the red blood cell

The red blood cell (RBC) is an important determinant of the rheological properties of blood because of its predominant number density, special mechanical properties and dynamics. Here, we develop a new low-dimensional RBC model based on dissipative particle dynamics (DPD). The model is constructed as a closed-torus-like ring of 10 colloidal particles connected by wormlike chain springs combined with bending resistance. Each colloidal particle is represented by a single DPD particle with a repulsive core. The model is able to capture the essential mechanical properties of RBCs, and allows for economical exploration of the rheology of RBC suspensions. Specifically, we find that the linear and non-linear elastic deformations of healthy and malaria-infected cells match those obtained in optical tweezers experiments. Through simulations of some key features of blood flow in vessels, i.e., the cell-free layer (CFL), the Fahraeus effect and the Fahraeus-Lindqvist effect, we verify that the new model captures the essential shear flow properties of real blood, except for capillaries of sizes comparable to the cell diameter. Finally, we investigate the influence of a geometrical constriction in the flow on the enhancement of the downstream CFL. Our results are in agreement with recent experiments.

Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media

Smoothed particle hydrodynamics (SPH) is a Lagrangian method based on a meshless discretization of partial differential equations. In this review, we present SPH discretization of the Navier-Stokes and advection-diffusion-reaction equations, implementation of various boundary conditions, and time integration of the SPH equations, and we discuss applications of the SPH method for modeling pore-scale multiphase flows and reactive transport in porous and fractured media.

Single-particle hydrodynamics in DPD: A new formulation

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 (Phys. Rev. E, 57 (1998) 2930) and it has the computational and implementation simplicity of the standard DPD approach.

Predicting dynamics and rheology of blood flow: A comparative study of multiscale and low-dimensional models of red blood cells

We compare the predictive capability of two mathematical models for red blood cells (RBCs) focusing on blood flow in capillaries and arterioles. Both RBC models as well as their corresponding blood flows are based on the dissipative particle dynamics (DPD) method, a coarse-grained molecular dynamics approach. The first model employs a multiscale description of the RBC (MS-RBC), with its membrane represented by hundreds or even thousands of DPD-particles connected by springs into a triangular network in combination with out-of-plane elastic bending resistance. Extra dissipation within the network accounts for membrane viscosity, while the characteristic biconcave RBC shape is achieved by imposition of constraints for constant membrane area and constant cell volume. The second model is based on a low-dimensional description (LD-RBC) constructed as a closed torus-like ring of only 10 large DPD colloidal particles. They are connected into a ring by worm-like chain (WLC) springs combined with bending resistance. The LD-RBC model can be fitted to represent the entire range of nonlinear elastic deformations as measured by optical-tweezers for healthy and for infected RBCs in malaria. MS-RBCs suspensions model the dynamics and rheology of blood flow accurately for any vessel size but this approach is computationally expensive for vessel diameters above 100μm. Surprisingly, the much more economical suspensions of LD-RBCs also capture the blood flow dynamics and rheology accurately except for small-size vessels comparable to RBC diameter. In particular, the LD-RBC suspensions are shown to properly capture the experimental data for the apparent viscosity of blood and its cell-free layer (CFL) in tube flow. Taken together, these findings suggest a hierarchical approach in modeling blood flow in the arterial tree, whereby the MS-RBC model should be employed for capillaries and arterioles below 100μm, the LD-RBC model for arterioles, and the continuum description for arteries.

Smoothed particle hydrodynamics non-Newtonian model for ice-sheet and ice-shelf dynamics

We propose a new three-dimensional smoothed particle hydrodynamics (SPH) non-Newtonian model to study coupled ice-sheet and ice-shelf dynamics. Most existing ice-sheet numerical models use grid-based Eulerian discretizations, and are usually restricted to shallow ice-sheet and ice-shelf approximations of the momentum- conservation equation. SPH, a fully Lagrangian particle method, solves the full momentum-conservation equation. Numerical accuracy of the proposed SPH model is first verified by simulating Poiseuille flow, a plane shear flow with a free surface and the propagation of a blob of ice along a horizontal surface. Next, the SPH model is used to investigate the grounding-line dynamics of a ice sheet/shelf. The steady position of the grounding line, obtained from our SPH simulations, is in good agreement with laboratory observations for a wide range of bedrock slopes, ice-to-fluid density ratios, and flux. We examine the effect of non-Newtonian behavior of ice on the grounding-line dynamics. The non-Newtonian constitutive model is based on Glens law for a creeping flow of a polycrystalline ice. Finally, we investigate the effect of a bedrock geometry on a steady-state position of the grounding line.

Smoothed particle hydrodynamics continuous boundary force method for Navier-Stokes equations subject to a Robin boundary condition

A Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel continuous boundary force (CBF) method is proposed for solving the Navier-Stokes equations subject to the Robin boundary condition. In the CBF method, the Robin boundary condition is replaced by the homogeneous Neumann boundary condition and a volumetric force term added to the momentum conservation equation.Smoothed particle hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two- and three-dimensional flows subject to various forms of the Robin boundary condition in domains bounded by flat and curved boundaries. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite-element method. Considering the no-slip boundary condition as a special case of the slip boundary condition, we demonstrate that the SPH-CBF method accurately describes both the no-slip and slip conditions.

Discrete-element model for the interaction between ocean waves and sea ice

We present a discrete-element method (DEM) model to simulate the mechanical behavior of sea ice in response to ocean waves. The interaction of ocean waves and sea ice potentially can lead to the fracture and fragmentation of sea ice depending on the wave amplitude and period. The fracture behavior of sea ice explicitly is modeled by a DEM method where sea ice is modeled by densely packed spherical particles with finite sizes. These particles are bonded together at their contact points through mechanical bonds that can sustain both tensile and compressive forces and moments. Fracturing naturally can be represented by the sequential breaking of mechanical bonds. For a given amplitude and period of incident ocean waves, the model provides information for the spatial distribution and time evolution of stress and microfractures and the fragment size distribution. We demonstrate that the fraction of broken bonds α increases with increasing wave amplitude. In contrast, the ice fragment size l decreases with increasing amplitude. This information is important for the understanding of the breakup of individual ice floes and floe fragment size.