Accelerated boundary integral method for multiphase flow in non-periodic geometries

An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the algorithm scales as O(N) or $O(N\log N$), where $N$ is proportional to the product of number of particles and the number of elements employed to discretize the particle. This technique is enabled by the use of an alternative boundary integral formulation in which the velocity field is expressed in terms of a single layer integral alone, even in problems with non-matched viscosities. The density of the single layer integral is obtained from a Fredholm integral equation of the second kind involving the double layer integral. Acceleration in this implementation is provided by the use of General Geometry Ewald-like method (GGEM) for computing the velocity and stress fields driven by a set of point forces in the geometry of interest. For the particular case of the slit geometry, a Fourier-Chebyshev spectral discretization of GGEM is developed. Efficient implementations employing the GGEM methodology are presented for the resulting single and the double layer integrals. The implementation is validated with test problems on the velocity of rigid particles and drops between parallel walls in pressure driven flow, the Taylor deformation parameter of capsules in simple shear flow and the particle trajectory in pair collisions of capsules in shear flow. The computational complexity of the algorithm is verified with results from several large scale multiparticle simulations.Comment: Journal of Computational Physics, to appea

Numerical simulation of a deformable cell in microchannels

The main goal of this work is to numerically investigate the behavior of a cell flowing in a microfluidic system. In particular, we want to model flow-induced deformations of an isolated cell to quantitatively evaluate the cell response when subjected to a representative range of flow rates in a realistic geometry, with specific interest in the case of cell trapping. This research will help optimize operating conditions as well as the design of cell manipulation/culture micro-devices, so as to guarantee cell viability and ultimately improve high-throughput performance

The motion of a deforming capsule through a corner

A three-dimensional deformable capsule convected through a square duct with a corner is studied via numerical simulations. We develop an accelerated boundary integral implementation adapted to general geometries and boundary conditions. A global spectral method is adopted to resolve the dynamics of the capsule membrane developing elastic tension according to the neo-Hookean constitutive law and bending moments in an inertialess flow. The simulations show that the trajectory of the capsule closely follows the underlying streamlines independently of the capillary number. The membrane deformability, on the other hand, significantly influences the relative area variations, the advection velocity and the principal tensions observed during the capsule motion. The evolution of the capsule velocity displays a loss of the time-reversal symmetry of Stokes flow due to the elasticity of the membrane. The velocity decreases while the capsule is approaching the corner as the background flow does, reaches a minimum at the corner and displays an overshoot past the corner due to the streamwise elongation induced by the flow acceleration in the downstream branch. This velocity overshoot increases with confinement while the maxima of the major principal tension increase linearly with the inverse of the duct width. Finally, the deformation and tension of the capsule are shown to decrease in a curved corner

An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces

Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier–Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressurecorrection approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces

Theory and simulation of polymer adsorption in flowing fluids

University of Minnesota Ph.D. dissertation. September 2014. Major: Chemical Engineering. Advisors: Kevin Dorfman, Satish Kumar. 1 computer file (PDF); viii, 117 pages.Adsorption and desorption of polymers in the presence of flowing fluids lies at the heart of many technological applications such as thin film deposition via layer-by-layer fabrication, development of surface coatings and responsive interfaces, stabilization of colloidal suspensions, and rheology modifiers. Adsorption under flow also constitutes a key step in many physiological mechanisms, e.g., formation of a platelet plug during hemostasis. Moreover, flow induced adsorption/desorption offers a rich source of problems from the point of view of fundamental polymer physics. However, despite its importance little is understood about the behavior of adsorbed polymers under flow, in contrast to the well-developed field of adsorption from a quiescent solution. Some experimental observations regarding the effect of flow on adsorption/desorption exist in the literature, but they are mutually conflicting and the underlying physics involved is yet to be explained. In this work, we provide new insight into the mechanism of adsorption/desorption under shear flow near a single planar wall using kinetic theory and Brownian dynamics (BD) simulations. We show that in the presence of shear flow accounting for hydrodynamic interactions (HI) between the polymer molecules and the wall is crucial to observe the experimentally obtained trends of the amount of adsorbed polymer with respect to shear rate and molecular weight. The amount adsorbed is governed by a balance between HI-induced repulsion and polymer-wall attraction. At a fixed molecular weight increasing shear rate increases HI, causing a reduction in the amount adsorbed. Moreover, if the shear rate is fixed the amount adsorbed decreases with an increase in molecular weight. These trends are in qualitative agreement with prior experimental observations of Lee and Fuller [J. Colloid Interface Sci. 103, 569 (1985)]. In the case of desorption, the trend for the amount adsorbed with respect to molecular weight depends on the polymer-wall interaction energy. We show that when adsorption is weak, desorption increases with an increase in molecular weight, but for strong adsorption the trend is reversed. We provide an explanation for this reversal in terms of the change in polymer conformations with increase in the interaction energy, thereby resolving the apparently conflicting experimental observations of Lee and Fuller and Soga and Granick [Langmuir 14, 4266 (1998)]