Stabilizing the thermal lattice Boltzmann method by spatial filtering

We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions

Two-Dimensional Decaying Elastoinertial Turbulence

We numerically simulate two-dimensional, decaying elastoinertial turbulence using the finitely extensible, nonlinear, elastic spring model. We vary the polymer concentration over seven decades, and observe two turbulent elastoinertial regimes. In the weakly coupled regime only the small scale structures change, while in the strongly coupled regime all structures change. This regime is dominated by elastoinertial shock waves with drag reduction properties; i.e., the energy decay rate decreases when the polymer concentration increases

Data assimilation method to de-noise and de-filter particle image velocimetry data

We present a variational data assimilation method in order to improve the accuracy of velocity fields v˜, that are measured using particle image velocimetry (PIV). The method minimises the space-time integral of the difference between the reconstruction u and v˜, under the constraint, that u satisfies conservation of mass and momentum. We apply the method to synthetic velocimetry data, in a two-dimensional turbulent flow, where realistic PIV noise is generated by computationally mimicking the PIV measurement process. The method performs optimally when the assimilation integration time is of the order of the flow correlation time. We interpret these results by comparing them to onedimensional diffusion and advection problems, for which we derive analytical expressions for the reconstruction erro

Probing Membrane Viscosity and Interleaflet Friction of Supported Lipid Bilayers by Tracking Electrostatically Adsorbed, Nano-Sized Vesicles

Particle tracking is used to measure the diffusional motion of nanosized (≈100 nm), lipid vesicles that are electrostatically adsorbed onto a solid supported lipid bilayer. It is found that the motion of membrane-adhering vesicles is Brownian and depends inversely on the vesicle size, but is insensitive to the vesicle surface charge. The measured diffusivity agrees well with the Evans–Sackmann model for the diffusion of inclusions in supported, fluidic membranes. The agreement implies that the vesicle motion is coupled to that of a nanoscopic lipid cluster in the upper leaflet, which slides over the lower leaflet. The diffusivity of membrane-adhering vesicles is therefore predominantly governed by the interleaflet friction coefficient, while the diffusivity of single lipids is mainly governed by the membrane viscosity. Combined with fluorescence recovery after photobleaching analysis, the interleaflet friction coefficient and the membrane viscosity are determined by applying the Evans–Sackmann model to the measured diffusivity of membrane adhering vesicles and that of supported membrane lipids. This approach provides an alternative to existing methods for measuring the interleaflet friction coefficient and the membrane viscosity

Effect of normal contact forces on the stress in shear rate invariant particle suspensions

We present a tensorial theory for the microstructure and the stress in shear rate invariant particle suspensions that includes hydrodynamic and normal but not tangential hard sphere interaction forces. The theory predicts that hydrodynamic forces produce a negligible first normal stress difference, while contact forces produce a positive first normal stress difference. The theory thereby provides a rationale for seemingly contradicting experimental observations in the literature. In addition, the theory captures the experimentally observed time dependence of the shear stress after shear reversal

Taylor Couette instability in disk suspensions

We study the stability of dilute suspensions of spheroids in Taylor Couette flow. We focus on axisymmetric perturbations and on the limiting cases of thin disks and long rods. It is found that in the non-Brownian limit, the rods have a negligible effect on the stability, while the disks are destabilizing. The instability is driven by a tilting of the disks, which draws energy from the base flow into azimuthal velocity fluctuations. The resulting instability mode has a wavelength which is smaller than the unstable Newtonian mode. These findings may serve to understand experiments using clay suspensions in the literature

Taylor-Couette instability in sphere suspensions

We employ a rheological theory to show that circular Taylor-Couette flow of a suspension of non-Brownian spheres is less stable than that of a Newtonian fluid, at equal effective viscosity. The destabilization is related to the preferred orientation of the separation vector of the closely interacting spheres, in the compressive direction of the base flow. The results agree qualitatively with experimental observations from the literature

Modelling Sphere Suspension Microstructure and Stress

We develop a model for the microstructure and the stress, in dense suspensions of non-Brownian, perfectly smooth spheres at vanishing particle Reynolds number. These quantities are defined in terms of the second-order moment a of the distribution function of the orientation unit vector between hydro-dynamically interacting particles. We show, from first principles, that the evolution equation of a contains a source term, that accounts for the association and the dissociation of interacting particle pairs. This term provides a microscopic explanation for typical non-Newtonian behaviour, observed in experiments in the literature, including normal stress differences in steady shear flow, as well as time-dependent stress after abruptly reversed shear flow and during oscillating shear flow

Vortex merging and splitting: A route to elastoinertial turbulence in Taylor-Couette flow

We report experimental evidence of a new merge-split transition (MST) to elastoinertial turbulence (EIT) in Taylor-Couette flows of viscoelastic polymer solutions, caused by merging and splitting of base Taylor vortices when crossed by elastic axial waves (rotating standing waves, RSW). These vortex merging and splitting events are not due to transient behavior, finite aspect ratio, or shear-thinning behavior. They are random in nature and increase in frequency with Re; when superimposed on a RSW flow state they cause abrupt changes in the axial spatial wavelength, leading to the transition from a RSW to the EIT state. We thus identify MST as an inertial feature solely triggered by elasticity and independent of any shear-thinning behavior

Disentangling bulk polymers from adsorbed polymers using the quartz crystal microbalance

At sufficient adhesion energy, polymers may adsorb irreversibly at an interface, with many adhesion sites per polymer and significant changes in their conformation. In addition to irreversibly adsorbed polymers there may be reversibly adsorbed polymers, which are in dynamic equilibrium with bulk polymers, and which have fewer adhesion sites per polymer and less significant conformational changes. In this work, we simultaneously determine the viscoelasticity of irreversibly adsorbed polymers, reversibly adsorbed polymers, and bulk polymers. To this end, we combine hydrodynamic modelling with quartz crystal microbalance-dissipation (QCM-D) measurements involving an adsorbing target surface and a non-adsorbing, i.e., passivated surface. We apply the method to polyethylene glycol adsorption at the water–silica interface. The results demonstrate that the viscoelasticity of the reversibly adsorbed polymers is similar to that of the bulk polymers, whereas the irreversibly adsorbed polymers are less elastic. This is the first approach to decouple these viscoelastic contributions, which provides a new analytical tool to quantify the kinetics and conformation of reversibly adsorbed polymers, shedding light on polymer dynamics near interfaces