Session R45: Suspensions: Numerical Simulations

Fully resolved particulate Rayleigh-Benard convection

Simplified models show that Rayleigh-Benard convection is relatively inefficient at maintaining particles in suspension (Solomatov & Stevenson, J. Geophys. Res. 98 5375 1993). In this work the behavior of heavy particles suspended in Rayleigh-Benard convection is investigated using particle-resolved simulations. The particle weight and the downward plumes cause a tendency for particles to deposit on the bottom wall. The key physical process to maintain a significant fraction of particles suspended is therefore the lifting of the deposited particles, a process that it is difficult to describe with a point-particle model. We focus on this aspect of the problem by means of the simulation of few particles in a slender domain with a square cross section in the vertical direction. The results show that the particle lift is primarily due to the plume generated by the particle itself. We also perform simulations in a cubic cell with up to 500 particles and  3.27% volume fraction finding that interaction with other particles increases the resuspension of deposited particles. As the total particle load increases (by increasing volume fraction or weight), a greater fraction of particles resides for a longer and longer time on the bottom of the domain.    

Numerical analysis of non-spherical particles moment arm in particle-particle interactions and its impact on rotational motion

The particle-particle interaction of three-dimensional, non-spherical particles is thoroughly investigated using the sharp-interface curvilinear immersed boundary (CURVIB) method. Kinematic motion equations govern particle progression through a channel with particle-wall and particle-particle interactions. A threshold algorithm is used where a collision has occurred when the distance between the particle's surface nodes or the wall is less than the set threshold value. At the collision, the nodes less than the threshold are considered the contact points, where the average contact point locations and relative velocities are used to determine the moment arm and the rebounding translational and rotational velocity. Verification is achieved using a coefficient of restitution equal to one, confirming the constant total energy of interactions for the particles and wall collisions. Particle shapes include cubes, spheres, doughnuts, and irregular shapes. One particle is initially stationary in the middle of the channel, while a second and third particle is set with an arbitrary initial velocity to cause the particles to interact with the stationary particle. A series of simulations demonstrate the influence of the moment arm on the rotational motion of non-spherical particle-particle collisions. Knowing the effect of the moment arm on the rotational motion can lead to more precise predictions and control of particle behavior in fluid mechanics applications.   

Optimization of complex fluids flows using end to end differentiable immersed boundary algorithm

Inverse design of fluid flows of complex fluids is important in several applications such as controlling the fluid rheological response, optimizng the design of microfluidic devices, etc. Solving a PDE-constrained optimization problem using direct optimization approaches where the jacobian is calcualted from a forward simulation is easy to implement and flexible but is prohibitively computationally expensive. Automatic differentiation which is the key driver to train deep neural networks alllows for efficient computation of the Jacobian making it possible to use direct optimization approaches to tackle inverse flow problems. In this work, we demonstrate how auomatic differentation can be used to solve high-dimensional optimization problems related to complex flows. We developed a differentiable solver that implements the immersed boundary method. By differentiating through the solver, we optimize the flow of a couple of canonical problems such as flow in porous media, swimming of active matter, and mixing in low Reynolds numbers.   

Space- and time-resolved stress fluctuations in discontinuous shear thickening suspensions

Discontinuous shear thickening (DST) is associated with a sharp rise of a suspension's viscosity with increasing applied shear rate. A key signature of DST, highlighted in recent studies, is the very large fluctuations of the measured stress as the suspension thickens. Recent work has suggested that these fluctuations are due to the flow-induced growth and percolation of constrained particle networks within the suspension, but the specific localization of these processes are not well understood. To illuminate this connection, we combine simulations of sheared dense frictional suspensions with a local, spatially-resolved analysis derived from experimental boundary stress microscopy measurements. Our study investigates how the microstructural stress fluctuations are non-uniform throughout the sample, and move spatially with respect to time.   

Rheology of dense fiber suspensions: Origin of yield stress, shear thinning, and normal stress differences

We use high-fidelity computational model of fiber suspension to investigate suspension rheology. We investigate the interplay between the hydrodynamic, noncontact attractive and repulsive, and interfiber contact interactions. The shear-thinning viscosity and finite yield stress obtained from the Immerse Boundary Method simulations align quantitatively with experimental findings from the literature. The study demonstrates that attractive interactions lead to both yield stress and shear thinning behavior in rigid fiber suspensions. This discovery holds significance as it contributes to the ongoing debate on the source of yield stress in fiber suspensions. The proposed model is used to quantify normal stresses in addition to shear thinning and yield stress.   

Suspensions of viscoelastic capsules: effect of membrane viscosity on transient dynamics

Viscoelastic capsules consist of a liquid drop core enclosed by a thin membrane that can be engineered with tailored mechanical properties. While the mechanical and rheological properties of purely elastic capsules have been thoroughly studied, only a few studies have focused on understanding the effect of membrane viscosity (MV) on the dynamics of single capsules, and the understanding of its effect on the suspension of capsules is still lacking. This knowledge gap is particularly relevant in the context of blood, which can be considered a suspension of red blood cells (RBCs). Although the impact of MV on single RBCs has recently been investigated, little is known about dense suspensions of RBCs, which is crucial for improving our understanding of blood flow at the macroscale, with important implications for cardiovascular dynamics. 

In this contribution, we fill this gap by presenting a numerical investigation of the effect of MV on suspensions of viscoelastic capsules under simple shear flow, using a coupled immersed boundary-lattice Boltzmann implementation. We found that both the deformation and the loading time (i.e., the time it takes for the capsules to deform) are affected by the MV at varying values of the capillary number (Ca) and the volume fraction. Our simulations reveal the non-trivial role played by the MV in these systems. Specifically, while the effect of MV on the deformation and loading time is significant for dilute suspensions, it reduces as the volume fraction increases.   

Accelerated force-coupling method and applications

Microscale fluid-structure interactions are present in many biological and industrial processes. To accelerate the computation of these interactions, we develop a fast implementation of the force-coupling method (FCM) in which the action of the mobility matrix is split between a global, grid-based computation involving a modified FCM kernel, and a local pairwise correction. The approach is constructed to yield a sparse, local-correction matrix to limit the need for pairwise corrections and to ensure the positive definiteness of the global and local-correction matrices. In most physical configurations, we have observed that fast FCM surpasses regular FCM by a factor of 10 to 100. Moreover, it has the advantage of being more memory-efficient, enabling larger simulations to be conducted. We demonstrate the effectiveness of fast FCM in simulating rod sedimentation and active filament synchronisation, where we find that the hydrodynamic solve constitutes a small fraction of the total computation costs.   

Fingering Effects in Oil-Water Interfaces with Nanoparticles

Nanoparticles (NPs) influence the stability of interfaces especially in non-equilibrium situations. Attention has been primarily focused on the physical mechanism for fluid-fluid interfaces stabilized in bare oil-water systems without the presence of nanoparticles. Here, the dissipative particle dynamics (DPD) method [1-3] is applied to investigate the influence of nanoparticles and their wetting properties on the stability of two immiscible fluids; pure oil and water positioned adjacent to each other, resulting in the formation of a meniscus in a nanochannel. The NPs are placed at the oil-water interface. Our findings show that the meniscus stability is affected by the wettability of the nanoparticles, and two instabilities occur during water flooding: first, the formation of fingers, and second, the separation of oil from the channel wall. The presence of NPs allows for fingering at lower pressure drops than in pure oil and water. When considering different NPs, hydrophobic NPs can disrupt the formation of a stable water meniscus at lower flow rates when compared with Janus and hydrophilic nanoparticles. The second instability leads to the formation of a drop that propagates through the channel. The wettability of NPs does not influence the critical flow rate, resulting in the three-phase contact angle being the same when the detachment occurs.  The discussion will cover the computational methodology employed and its validation, as well as an analysis of how different types of nanoparticles stabilize the oil-water interface.

References

[1]        T. V. Vu and D. V. Papavassiliou, Journal of colloid and interface science 553, 50 (2019).

[2]        T. X. Nguyen, S. Razavi, and D. V. Papavassiliou, The Journal of Physical Chemistry B 126, 6314 (2022).

[3]        T. X. Nguyen, T. V. Vu, S. Razavi, and D. V. Papavassiliou, Polymers 14, 543 (2022).