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1. Onset of thermal convection in non-colloidal suspensions

   https://doi.org/10.1017/jfm.2021.59  

   Kang, Changwoo ; Yoshikawa, Harunori N. ; Mirbod, Parisa ( May 2021 , Journal of Fluid Mechanics)

   null (Ed.)

   This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin ( J. Fluid Mech. , vol. 724, 2013, pp. 527–552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number ( Pe ) and the particle volume fraction ( ϕ ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions $({\phi _b})$ ranging from 0 to 0.3. The critical Rayleigh number $(R{a_c})$ grows gradually by increasing ${\phi _b}$ from the critical value $(R{a_c} = 1708)$ for a pure Newtonian fluid, while the critical wavenumber $({k_c})$ remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid $({\phi _b} = 0)$ . The heat transfer in moderately dense suspensions $({\phi _b} = 0.2\text{--}0.3)$ is significantly enhanced by convection rolls for small Rayleigh number ( Ra ) close to $R{a_c}$ . We also found a power-law increase of the Nusselt number ( Nu ) with Ra , namely, $Nu\sim R{a^b}$ for relatively large values of Ra where the scaling exponent b decreases with ${\phi _b}$ . Finally, it turns out that the shear-induced migration of particles can modify the heat transfer. 

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2. Dependency of active pressure and equation of state on stiffness of wall

   https://doi.org/10.1038/s41598-021-01605-8  

   Pirhadi, Emad ; Cheng, Xiang ; Yong, Xin ( November 2021 , Scientific Reports)

   Autonomous motion and motility are hallmarks of active matter. Active agents, such as biological cells and synthetic colloidal particles, consume internal energy or extract energy from the environment to generate self-propulsion and locomotion. These systems are persistently out of equilibrium due to continuous energy consumption. It is known that pressure is not always a state function for generic active matter. Torque interaction between active constituents and confinement renders the pressure of the system a boundary-dependent property. The mechanical pressure of anisotropic active particles depends on their microscopic interactions with a solid wall. Using self-propelled dumbbells confined by solid walls as a model system, we perform numerical simulations to explore how variations in the wall stiffness influence the mechanical pressure of dry active matter. In contrast to previous findings, we find that mechanical pressure can be independent of the interaction of anisotropic active particles with walls, even in the presence of intrinsic torque interaction. Particularly, the dependency of pressure on the wall stiffness vanishes when the stiffness is above a critical level. In such a limit, the dynamics of dumbbells near the walls are randomized due to the large torque experienced by the dumbbells, leading to the recovery of pressure as a state variable of density.

    

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3. The effect of shear flow on the rotational diffusion of a single axisymmetric particle

   https://doi.org/10.1017/jfm.2015.186  

   Leahy, Brian D. ; Koch, Donald L. ; Cohen, Itai ( June 2015 , Journal of Fluid Mechanics)

   Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion: $D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$ , where $p$ is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio $p$ , as $1/D_{0}^{r}p^{4}$ and as $1/D_{0}^{r}p^{2}$ for $p\gg 1$ . For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of ${\approx}2$ and the rotational diffusion by a factor of ${\approx}40$ . 

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4. Clustering of inertial particles in turbulent flow through a porous unit cell

   https://doi.org/10.1017/jfm.2022.100  

   Apte, Sourabh V. ; Oujia, Thibault ; Matsuda, Keigo ; Kadoch, Benjamin ; He, Xiaoliang ; Schneider, Kai ( April 2022 , Journal of Fluid Mechanics)

   Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ( $St = 0.01, 0.1, 0.5, 1, 2$ ) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers. 

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5. Clustering of inertial particles in turbulent flow through a porous unit cell

   Apte, SV ; Oujia, T ; Matsuda, K ; Kadoch, B ; He, X ; Schneider, K ( February 2022 , Journal of fluid mechanics)

   Direct numerical simulation is used to investigate effects of turbulent flow in the confined geometry of a face-centred cubic porous unit cell on the transport, clustering and deposition of fine particles at different Stokes numbers ( 𝑆𝑡=0.01,0.1,0.5,1,2 ) and at a pore Reynolds number of 500. Particles are advanced using one-way coupling and the collision of particles with pore walls is modelled as perfectly elastic with specular reflection. Tools for studying inertial particle dynamics and clustering developed for homogeneous flows are adapted to take into account the embedded, curved geometry of the pore walls. The pattern and dynamics of clustering are investigated using the volume change of Voronoi tesselation in time to analyse the divergence and convergence of the particles. Similar to the case of homogeneous, isotropic turbulence, the cluster formation is present at large volumes, while cluster destruction is prominent at small volumes and these effects are amplified with the Stokes number. However, unlike homogeneous, isotropic turbulence, the formation of a large number of very small volumes was observed at all Stokes numbers and attributed to the collision of particles with the pore wall. Multiscale wavelet analysis of the particle number density indicates that the peak of the energy density spectrum, representative of enhanced particle clustering, shifts towards larger scales with an increase in the Stokes number. Scale-dependent skewness and flatness quantify the intermittent void and cluster distribution, with cluster formation observed at small scales for all Stokes numbers, and void regions at large scales for large Stokes numbers. 

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