The dynamics of a vesicle in a wall-bound shear flow

Zhao, Hong; Spann, Andrew; Shaqfeh, Eric S. G.

doi:10.1063/1.3669440

Cited by 56 publications

(71 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The normal n a points outwards as long as the approximate normalñ a = ξ a × η a points outwards. Once the curvatures are calculated for every vertex, we find ∂ α H α and ∂ αβ H a by a fitting procedure analogous to (10). The Laplace-Beltrami operator is then calculated as…”

Section: Membrane Forcementioning

confidence: 99%

“…Several approaches are used to calculate curvature and differential operators on triangular mesh: trigonometrical formulae [9,5], direct variation of the energy [10], and quadratic interpolation [15]. It must be noted that only curvatures were calculated by quadratic interpolation in [15] while the trigonometric formulae similar to [9,5] were used for the Laplace-Beltrami operator of the curvature.…”

Section: Membrane Forcementioning

confidence: 99%

“…For each vertex a, all mesh triangles are divided into two groups: the "singular triangles", which contain the vertex a and the remaining "non-singular triangles". The integration over non-singular triangles can then be performed by a simple quadrature rule, while the integration over singular triangles is performed by exact analytical calculation [9], or in polar coordinates [5], or by a map from a square [16,10], assuming linear interpolation of the forces and the shape over the triangle. It is easy to show that this rule has a numerical error of order O(h) : Indeed, for a simple 3 point quadrature rule, the error of integration over one triangle is of order of the second derivative of the integrand times the size of the triangle to the power 4 (i.e., O(h 4 )).…”

Section: Exact Identitiesmentioning

confidence: 99%

“…Several studies of dynamics of vesicles under flow using BI method on triangular mesh already exist in literature [8,5,9,10]. Of these studies only [9] calculated BI with error O(h 2 ), while the others are limited to the error of order O(h).…”

Section: Introductionmentioning

confidence: 99%

“…As noted in [10], the linear operators (45) and (49) can be considered adjoint. We can see from (44) that…”

mentioning

confidence: 99%

See 4 more Smart Citations

3D numerical simulations of vesicle and inextensible capsule dynamics

Farutin

Biben

Misbah

2014

Journal of Computational Physics

View full text Add to dashboard Cite

Vesicles are locally-inextensible fluid membranes while inextensible capsules are in addition endowed with in-plane shear elasticity mimicking the cytoskeleton of red blood cells (RBCs). Boundary integral (BI) methods based on the Green's function techniques are used to describe their dynamics, that falls into the category of highly nonlinear and nonlocal dynamics. Numerical solutions raise several obstacles and challenges that strongly impact the results. Of particular complexity is (i) the membrane inextensibility, (ii) the mesh stability and (iii) numerical precisions for evaluation of the boundary integral equations. Despite intense research these questions are still a matter of debate.We regularize the single layer integral by subtraction of exact identities for the terms involving the normal and the tangential components of the force. In addition, the regularized kernel remains explicitly self-adjoint. The stability and precision of BI calculation is enhanced by taking advantage of additional quadrature nodes located in vertices of an auxiliary mesh, constructed by a standard refinement procedure from the main mesh. We extend the partition of unity technique to boundary integral calculation on triangular meshes: We split the calculation of the boundary integral between the original and the auxiliary mesh using a smooth weight function, which takes the distance between the source and the target as the argument and falls to zero beyond a certain cut-off distance. We provide an efficient lookup algorithm that allows us to discard most of the vertices of the auxiliary mesh lying beyond the cut-off distance from a given point without actually calculating the distances to them. The proposed algorithm offers the same treatment of near-singular integration regardless if the source and the target points belong to the same surface or not.Additional innovations are used to increase the stability and precision of the method: The bending forces are calculated by differential geometry expressions using local coordinates defined in vicinity of each vertex. The approximation of the surface in vicinity of a vertex is obtained by fitting with a second-degree polynomial of local coordinates.We solve for the Lagrange multiplier associated with membrane incompressibility using two penalization parameters per suspended entity: one for deviation of the global area from prescribed value and another for the sum of squares of local strains defined on each vertex. The proposed advancement is to vary the penalization parameters at each time step in such a way, that the global area of each membrane be conserved and the sum of squares of local strains be at minimum. This optimization is achieved by solving a linear system of rank three times the number of entities involved in the simulation. If no auxiliary mesh is used, the method reduces to steepest descent method thanks to the explicit self-adjointness of the regularized single-layer kernel in the boundary integral equation.Inextensible capsules, a model of RBC, are studied ...

show abstract

Section: Membrane Forcementioning

confidence: 99%

Section: Membrane Forcementioning

confidence: 99%

Section: Exact Identitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…As noted in [10], the linear operators (45) and (49) can be considered adjoint. We can see from (44) that…”

mentioning

confidence: 99%

See 3 more Smart Citations

3D numerical simulations of vesicle and inextensible capsule dynamics

Farutin

Biben

Misbah

2014

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

Dynamic and rheological properties of soft biological cell suspensions

Yazdani

Karniadakis

2015

Rheol Acta

View full text Add to dashboard Cite

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.

show abstract

On the volume conservation of emulsion drops in boundary integral simulations

Siqueira

Rebouças

Cunha

et al. 2017

J Braz. Soc. Mech. Sci. Eng.

View full text Add to dashboard Cite

Boundary Integral simulations are very common to study the microhydrodynamics of viscous drops and predict the rheology of emulsions. The standard boundary integral formulation for the velocity field at the drop surface is given by surface integrals of singular Green's functions in space and depends on geometric quantities of the mesh, as the local mean curvature and the unitary exterior normal vector. Typically, the drops deform and rotate under the flow action, which leads to a great distortion of the computational mesh and, therefore, might produce several numerical errors in the surface velocity calculation. In this work, we investigate the numerical errors in the calculation of the surface velocity in boundary integral simulations of a viscous drop in simple shear flows. Assuming that the flow is incompressible, such that the total volume of the drops must remain constant, we use the net flow rate across the drop surface as a measure of the numerical errors in the simulations. For both small and moderate regimes of drop surface deformation, we show that the net mass flow rate across the drop surface is positive, and strongly depends on the drop-to-basis fluid viscosity ratio, capillary number of the flow, and mesh refinement. These results indicate that the volume of the drops increases continuously during the simulations. To remove the spurious mass flow rate from the simulations, we present a mesh convergence study based on an extrapolation procedure to an almost continuous mesh, so that the results become independent of mesh refinement and recover the theoretical prediction of a null net flow rate and constant drop volume in incompressible flows. The extrapolation method proposed here can be straightforwardly implemented to improve the accuracy of BI simulations used to study drop microhydrodynamics and emulsion rheology. As a matter of example, we applied the method to predict the surface deformation of a high-viscosity emulsion drop, and the result is compared in very good agreement with asymptotic theories available in the related literature.

show abstract

The dynamics of a vesicle in a wall-bound shear flow

Cited by 56 publications

References 42 publications

3D numerical simulations of vesicle and inextensible capsule dynamics

3D numerical simulations of vesicle and inextensible capsule dynamics

Dynamic and rheological properties of soft biological cell suspensions

On the volume conservation of emulsion drops in boundary integral simulations

Contact Info

Product

Resources

About