Couette flow obtained by utilization of the Lees–Edwards boundary condition. The solid line is the theoretical prediction, is the position (perpendicular to the vorticity and flow direction) in the simulation cell and the circles are data representing local flow field from the simulation, averaged over 100 time steps.
Poiseuille flow obtained by applying a body force to the DPD fluid. An effective no-slip boundary condition is imposed at the walls. is the position relative to the center of the cell. The circles are data representing the average local flow field from the simulation. The value of viscosity determined from a theoretical fit (solid line) for Poiseuille flow was consistent with direct calculation of the stress tensor from the Couette flow simulation in Fig. 1.
Determination of the intrinsic viscosity ( intercept) and Huggins coefficient (slope) for a semidilute suspension. The solid circles represent simulation data and the +'s are derived from experiment. The lines correspond to a Huggins coefficient of 7 (solid) and 5 (dashed). Statistical uncertainties in the simulation data were approximately 10% or smaller.
Comparison of simulation predictions and experimental data for high volume fraction effective hard sphere systems. Here . The open circles are results from Stokesian dynamics simulations [Foss and Brady (2000)], open triangles are from DPD simulations without lubrication forces and open squares are from DPD simulations with lubrication forces. The open diamonds are results from the DPD simulation where a constant stress was applied instead of the Lees–Edwards boundary condition. The solid and dashed lines are experimental data from sheared suspensions of silica particles [Bender and Wagner (1996)].
Calculated values of relative viscosity as a function of integrated strain rate. The dashed line corresponds to data from a constant stress driven system. The solid line is from a simulation with constant strain rate (Lees–Edwards boundary condition). Note the large temporal fluctuations in relative viscosity for the constant strain rate case as spheres must respond to an unyielding motion resulting from such boundary condition.
Constant stress driven shear. The velocity difference of the two parallel regions where the force is applied is given by . To set the velocity scale, corresponds to . For this system . There were moderate fluctuations in as the simulation progressed.
Suspension of polydisperse spheres with and .
Suspension of polydisperse spheres with and .
Relative viscosity of polydisperse suspensions. Shown are simulation data for , 0.2, 0.4, 0.6, 0.8, and 1.0. Solid lines are fits of data to Krieger–Doughtery equation. Curves offset to the right correspond to increasing . Statistical uncertainties in the simulation data were approximately 10% or smaller.
Fit of same data in Fig. 8 to Eq. (21) with and terms up to retained. Statistical uncertainties in the simulation data were approximately 10% or smaller.
Comparison of DPD simulation (dashed line) to predictions from theory (solid line) for rotation of prolate spheroid under shear. Here, is the angle of orientation, is the time, and is the period of rotation [Eq. (23)].
Relative viscosity for spheroid systems. Shown are data for oblate (dashed line), spherical (filled circles), and prolate (solid line) spheroids. Note that at of rate of increase of relative viscosity with for the oblate spheroid decreases, indicative of the onset of an apparent nematic phase. A nematic phase for the prolate spheroids occurs at somewhat higher . Statistical uncertainties in the simulation data were approximately 10% or smaller.
Evidence of an apparent nematic phase for the oblate spheroid system with . The particles initial orientation was such that the axis of symmetry was in the vorticity direction (perpendicular to the page). Here, the Jeffery’s orbits were suppressed.
Flow through rebars: Case A. A suspension of spheres was subject to a body force downward. The sphere’s diameter was about the gap spacing between the rebars (the four smaller radii objects represent cylinders). The volume fraction was . After a short period, the flow came to a stop as the spheres became jammed between the rebars.
Flow through rebars: Case B. Here the sphere diameters were about the gap spacing. The volume fraction was . The spheres continued to flow throughout the simulation, which ran several times longer in time than in case A. There was no indication of jamming (note, lubrication forces were not included in this simulation).
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