A smoothed profile method for simulating charged colloidal dispersions

2005 ◽  
Vol 169 (1-3) ◽  
pp. 104-106 ◽  
Author(s):  
Kang Kim ◽  
Yasuya Nakayama ◽  
Ryoichi Yamamoto
Keyword(s):  
Colloidal Dispersions ◽  
Profile Method ◽  
Smoothed Profile Method

Rheological evaluation of colloidal dispersions using the smoothed profile method: formulation and applications

2016 ◽  
Vol 792 ◽  
pp. 590-619 ◽  
Author(s):  
John J. Molina ◽  
Kotaro Otomura ◽  
Hayato Shiba ◽  
Hideki Kobayashi ◽  
Masaki Sano ◽  
...  
Keyword(s):  
Shear Flow ◽  
Rheological Behaviour ◽  
Direct Calculation ◽  
Simulation Method ◽  
Colloidal Dispersions ◽  
Spherical Particles ◽  
Shear Stresses ◽  
Stokesian Dynamics ◽  
Profile Method ◽  
Smoothed Profile Method

The smoothed profile method is extended to study the rheological behaviour of colloidal dispersions under shear flow by using the Lees–Edwards boundary conditions. We start with a reformulation of the smoothed profile method, a direct numerical simulation method for colloidal dispersions, so that it can be used with the Lees–Edwards boundary condition, under steady or oscillatory-shear flow. By this reformulation, all the resultant physical quantities, including local and total shear stresses, become available through direct calculation. Three simple rheological simulations are then performed for (1) a spherical particle, (2) a rigid bead chain and (3) a collision of two spherical particles under shear flow. Quantitative validity of these simulations is examined by comparing the viscosity with that obtained from theory and Stokesian dynamics calculations. Finally, we consider the shear-thinning behaviour of concentrated colloidal dispersions.

Smoothed Profile Method for Particulate Two-Phase Flow

2008 ◽  
Author(s):  
Xian Luo ◽  
Martin R. Maxey ◽  
George E. Karniadakis
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Integration Scheme ◽  
Force Density ◽  
Step Size ◽  
Time Step ◽  
Element Discretization ◽  
Profile Method ◽  
Time Step Size ◽  
Smoothed Profile Method

We re-formulate and demonstrate a new method for particulate flows, the so-called “Smoothed Profile” method (SPM) first proposed in [1]. The method uses a fixed computational mesh, which does not conform to the geometry of the particles. The particles are represented by certain smoothed indicator profiles to construct a smooth body force density term added into the Navier-Stokes equations. The SPM imposes accurately and efficiently the rigid-body constraint inside the particles. In particular, while the original method employs a fully-explicit time-integration scheme, we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. We show that the modeling error of SPM has a non-monotonic dependence on the time step size Δt. The optimum time step size balances the thickness of the Stokes layer and that of the profile interface. Subsequently, we present several numerical simulations, including flow past three-dimensional complex-shaped particles and two interacting microspheres, which are compared against full direct numerical simulations and the force coupling method (FCM).

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