The motion of microswimmers in complex flows is ruled by the interplay between swimmer propulsion and the dynamics induced by the fluid velocity field. Here we study the motion of a chiral microswimmer whose propulsion is provided by the spinning of
a helical tail with respect to its body in a simple shear flow. Thanks to an efficient computational strategy that allowed us to simulate thousands of different trajectories, we show that the tail shape dramatically affects the swimmers motion. In the shear dominated regime, the swimmers carrying an elliptical helical tail show several different Jeffery-like (tumbling) trajectories depending on their initial configuration. As the propulsion torque increases, a progressive regularization of the motion is observed until, in the propulsion dominated regime, the swimmers converge to the same final trajectory independently on the initial configuration. Overall, our results show that elliptical helix swimmer presents a much richer variety of trajectories with respect to the usually studied circular helix tails.
We demonstrate that the multi-phase lattice Boltzmann method (LBM) yields a curvature dependent surface tension $sigma$ by means of three-dimensional hydrostatic droplets/bubbles simulations. Such curvature dependence is routinely characterized, at t
he first order, by the so-called {it Tolman length} $delta$. LBM allows to precisely compute $sigma$ at the surface of tension $R_s$, i.e. as a function of the droplet size, and determine the first order correction. The corresponding values of $delta$ display universality in temperature for different equations of state, following a power-law scaling near the critical point. The Tolman length has been studied so far mainly via computationally demanding molecular dynamics (MD) simulations or by means of density functional theory (DFT) approaches. It has proved pivotal in extending the classical nucleation theory and is expected to be paramount in understanding cavitation phenomena. The present results open a new hydrodynamic-compliant mesoscale arena, in which the fundamental role of the Tolman length, alongside real-world applications to cavitation phenomena, can be effectively tackled.
We develop a multicomponent lattice Boltzmann (LB) model for the 2D Rayleigh--Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. In the immiscible case this method is able to accurately overcome the inherent numerical complexity
caused by the complicated structure of the interface that appears in the fully developed turbulent regime. Accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion we analyze the balance between different terms describing variations of the kinetic and potential energies. Then, we analyze the role of interface in the energy balance, and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to 3D immiscible Rayleigh-Taylor turbulence.
We systematically analyze the tensorial structure of the lattice pressure tensors for a class of multi-phase lattice Boltzmann models (LBM) with multi-range interactions. Due to lattice discrete effects, we show that the built-in isotropy properties
of the lattice interaction forces are not necessarily mirrored in the corresponding lattice pressure tensor. This finding opens a different perspective for constructing forcing schemes, achieving the desired isotropy in the lattice pressure tensors via a suitable choice of multi-range potentials. As an immediate application, the obtained LBM forcing schemes are tested via numerical simulations of non-ideal equilibrium interfaces and are shown to yield weaker and less spatially extended spurious currents with respect to forcing schemes obtained by forcing isotropy requirements only. From a general perspective, the proposed analysis yields an approach for implementing forcing symmetries, never explored so far in the framework of the Shan-Chen method for LBM. We argue this will be beneficial for future studies of non-ideal interfaces.
We studied turbulence induced by the Rayleigh-Taylor (RT) instability for 2D immiscible two-component flows by using a multicomponent lattice Boltzmann method with a Shan-Chen pseudopotential implemented on GPUs. We compare our results with the exten
sion to the 2D case of the phenomenological theory for immiscible 3D RT studied by Chertkov and collaborators ({it Physical Review E 71, 055301, 2005}). Furthermore, we compared the growth of the mixing layer, typical velocity, average density profiles and enstrophy with the equivalent case but for miscible two-component fluid. Both in the miscible and immiscible cases, the expected quadratic growth of the mixing layer and the linear growth of the typical velocity are observed with close long-time asymptotic prefactors but different initial transients. In the immiscible case, the enstrophy shows a tendency to grow like $propto t^{3/2}$, with the highest values of vorticity concentrated close to the interface. In addition, we investigate the evolution of the typical drop size and the behavior of the total length of the interface in the emulsion-like state, showing the existence of a power law behavior compatible with our phenomenological predictions. Our results can also be considered as a first validation step to extend the application of lattice Boltzmann tool to study the 3D immiscible case.
We study the motion of a spherical particle driven by a constant volume force in a confined channel with a fixed square cross-section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. We use the lattice Bo
ltzmann method to simulate a fluctuating multicomponent fluid in the mixed-phase, and particle-fluid interactions are tuned to reproduce different wetting properties at the particle surface. The numerical set-up is first validated in the absence of thermal fluctuations; to this aim, we quantitatively compute the drift velocity at changing the particle radius and compare it with previous experimental and numerical data. In the presence of thermal fluctuations, we study the fluctuations in the particles velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean drift velocity is quantitatively assessed, especially in comparison to unconfined situations. Results show that confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the lattice Boltzmann simulations in concrete applications involving the motion of colloidal particles in a highly confined environment in the presence of thermal fluctuations.
We study the effects of thermally induced capillary waves in the fragmentation of a liquid ligament into multiple nano-droplets. Our numerical implementation is based on a fluctuating lattice Boltzmann (LB) model for non-ideal multicomponent fluids,
including non-equilibrium stochastic fluxes mimicking the effects of molecular forces at the nanoscales. We quantitatively analyze the statistical distribution of the break-up times and the droplet volumes after the fragmentation process, at changing the two relevant length scales of the problem, i.e., the thermal length-scale and the ligament size. The robustness of the observed findings is also corroborated by quantitative comparisons with the predictions of sharp interface hydrodynamics. Beyond the practical importance of our findings for nanofluidic engineering devices, our study also explores a novel application of LB in the realm of nanofluidic phenomena.
We study small-scale and high-frequency turbulent fluctuations in three-dimensional flows under Fourier-mode reduction. The Navier-Stokes equations are evolved on a restricted set of modes, obtained as a projection on a fractal or homogeneous Fourier
set. We find a strong sensitivity (reduction) of the high-frequency variability of the Lagrangian velocity fluctuations on the degree of mode decimation, similarly to what is already reported for Eulerian statistics. This is quantified by a tendency towards a quasi-Gaussian statistics, i.e., to a reduction of intermittency, at all scales and frequencies. This can be attributed to a strong depletion of vortex filaments and of the vortex stretching mechanism. Nevertheless, we found that Eulerian and Lagrangian ensembles are still connected by a dimensional bridge-relation which is independent of the degree of Fourier-mode decimation.
We compute the continuum thermo-hydrodynamical limit of a new formulation of lattice kinetic equations for thermal compressible flows, recently proposed in [Sbragaglia et al., J. Fluid Mech. 628 299 (2009)]. We show that the hydrodynamical manifold i
s given by the correct compressible Fourier- Navier-Stokes equations for a perfect fluid. We validate the numerical algorithm by means of exact results for transition to convection in Rayleigh-Benard compressible systems and against direct comparison with finite-difference schemes. The method is stable and reliable up to temperature jumps between top and bottom walls of the order of 50% the averaged bulk temperature. We use this method to study Rayleigh-Taylor instability for compressible stratified flows and we determine the growth of the mixing layer at changing Atwood numbers up to At ~ 0.4. We highlight the role played by the adiabatic gradient in stopping the mixing layer growth in presence of high stratification and we quantify the asymmetric growth rate for spikes and bubbles for two dimensional Rayleigh- Taylor systems with resolution up to Lx times Lz = 1664 times 4400 and with Rayleigh numbers up to Ra ~ 2 times 10^10.
We present an investigation of the statistics of velocity gradient related quantities, in particluar energy dissipation rate and enstrophy, along the trajectories of fluid tracers and of heavy/light particles advected by a homogeneous and isotropic t
urbulent flow. The Refined Similarity Hypothesis (RSH) proposed by Kolmogorov and Oboukhov in 1962 is rephrased in the Lagrangian context and then tested along the particle trajectories. The study is performed on state-of-the-art numerical data resulting from numerical simulations up to Re~400 with 2048^3 collocation points. When particles have small inertia, we show that the Lagrangian formulation of the RSH is well verified for time lags larger than the typical response time of the particle. In contrast, in the large inertia limit when the particle response time approaches the integral-time-scale of the flow, particles behave nearly ballistic, and the Eulerian formulation of RSH holds in the inertial-range.
