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Self-rewetting fluids (SRFs) (e.g., aqueous solutions of long-chain alcohols) show anomalous nonlinear (quadratic) variations of surface tension with temperature involving a positive gradient, leading to different thermocapillary convection compared to normal fluids (NFs). Moreover, surface-active materials or surfactants can significantly alter interfacial dynamics by their adsorption on fluid interfaces. The coupled effects of temperature- and surfactant-induced Marangoni stresses on migration bubbles in SRFs remain unexplored. We use a robust lattice Boltzmann (LB) method based on central moments to simulate the two-fluid motions, capture interfaces, and compute the transport of energy and surfactant concentration fields, and systematically study the surfactant-laden bubble dynamics in SRFs. When compared to motion of bubbles in normal fluids, in which they continuously migrate without a stationary behavior, our results show that they exhibit dramatically different characteristics in SRFs. Not only is the bubble motion directed from the hot to the cold sides in SRFs, which is opposite to that in NFs, but, more importantly, the bubble attains an equilibrium position. In the absence of surfactants, such an equilibrium position arises at the reference temperature occurring at the center of the domain. The addition of surfactants moves the equilibrium location further upstream, which is controlled by the magnitude of the Gibbs elasticity parameter that determines the magnitude of the surface tension variation with surfactants. The quadratic sensitivity coefficient of surface tension on temperature associated with the SRF modulates this behavior. The lower this quantity, the greater is the role of surfactants modifying the equilibrium position of the bubble in SRF. These findings provide new means to potentially manipulate the bubble dynamics, and especially to tune its equilibrium states., Comment: 50 pages, 26 figures. arXiv admin note: text overlap with arXiv:2210.07501

Self-rewetting fluids (SRFs), such as aqueous solutions of long-chain alcohols, exhibit anomalous quadratic dependence of surface tension on temperature having a minimum and with a positive gradient. When compared to the normal fluids (NFs), the SRFs can be associated with significantly modified interfacial dynamics, which have recently been exploited to enhance flow and thermal transport in various applications (e.g., microgravity and microscale transport systems). In this work, first, we develop a new analytical solution of thermocapillary convection in superimposed two SRF layers confined within a microchannel that is sinusoidally heated on one side and maintained at a uniform temperature on the other side under the creeping flow regime. Then, a robust central moment lattice Boltzmann method using the Allen-Cahn equation for interface tracking, two-fluid motion, and the energy transport for numerical simulations of SRFs is constructed. The analytical and computational techniques are generally shown to be in good quantitative agreement with one another. Moreover, the effect of the various characteristic parameters on the magnitude and the distribution thermocapillary-driven motion is studied. The thermocapillary flow patterns in SRFs are shown to be strikingly different when compared to the NFs: For otherwise the same conditions, the SRFs result in eight periodic counterrotating thermocapillary convection rolls, while the NFs exhibit only four such vortices. Moreover, the direction of the circulating fluid motion in such vortical structures for the SRFs is found to be towards the hotter zones on the interfaces, which is opposite to that in NFs. By tuning the sensitivity coefficients of the surface tension on temperature, it is shown that the magnitude as well the overall thermocapillary flow patterns can be significantly manipulated., Comment: 55 pages, 29 figures

Computation of vorticity in conjunction with the strain rate tensor, plays an important role in fluid mechanics in vortical structure identification and in the modeling of various complex fluids. For the simulation of flows accompanied by the advection-diffusion transport of a scalar field, double distribution functions (DDF) based lattice Boltzmann methods (LBMs) are commonly used. We present a new local vorticity computation approach by introducing an intensional anisotropy of the scalar flux in the third order, off-diagonal moment equilibria of the LB scheme for the scalar field, and then combining the second order non-equilibrium components of both the LBMs. As such, any pair of lattice sets in the DDF formulation that can independently support the third order off-diagonal moments would enable local determination of the complete flow kinematics, with the LBMs for the fluid motion and the transport of the passive scalar respectively providing the necessary moment relationships to determine the symmetric and skew-symmetric components of the velocity gradient tensor. Since the resulting formulation is completely local and do not rely on finite difference approximations for velocity derivatives, it is by design naturally suitable for parallel computation. As an illustration of our approach, we formulate a DDF-LB scheme for local vorticity computation using a pair of multiple relaxation times (MRT) based collision approaches on two-dimensional, nine velocity (D2Q9) lattices, where the necessary moment relationships to determine the velocity gradient tensor and the vorticity are established via a Chapman-Enskog analysis. Simulations of various benchmark flows demonstrate good accuracy of the predicted vorticity fields, with a second order convergence. Furthermore, extensions of our formulation for a variety of collision models to enable local vorticity computation are presented., Comment: 48 pages, 6 figures; A three-dimensional version of the local vorticity computation approach in double distribution functions-based LB models on standard lattices using different collision models was presented at the 16th International Conference on Mesoscopic Methods in Engineering Science (ICMMES 2019) in Edinburgh, UK which will be reported separately

Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third order diagonal moments on the first order moments for standard lattices, and strategies have recently been introduced to restore GI without such errors using a modified collision operator involving either corrections to the relaxation times or to the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that alleviates the numerical stiffness. In the present study, we present a GI formulation of the preconditioned cascaded central moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. Improvements in accuracy and convergence acceleration are demonstrated., Comment: 43 pages, 14 figures

Operator split forcing schemes exploiting a symmetrization principle, i.e. Strang splitting, for cascaded lattice Boltzmann (LB) methods in two- and three-dimensions for fluid flows with impressed local forces are presented. Analogous scheme for the passive scalar transport represented by a convection-diffusion equation with a source term in a novel cascaded LB formulation is also derived. They are based on symmetric applications of the split solutions of the changes on the scalar field/fluid momentum due to the sources/forces over half time steps before and after the collision step. The latter step is effectively represented in terms of the post-collision change of moments at zeroth and first orders, respectively, to represent the effect of the sources on the scalar transport and forces on the fluid flow. Such symmetrized operator split cascaded LB schemes are consistent with the second-order Strang splitting and naturally avoid any discrete effects due to forces/sources by appropriately projecting their effects for higher order moments. All the force/source implementation steps are performed only in the moment space and they do not require formulations as extra terms and their additional transformations to the velocity space. These result in particularly simpler and efficient schemes to incorporate forces/sources in the cascaded LB methods unlike those considered previously. Numerical study for various benchmark problems in 2D and 3D for fluid flow problems with body forces and scalar transport with sources demonstrate the validity and accuracy, as well as the second-order convergence rate of the symmetrized operator split forcing/source schemes for the cascaded LB methods., Comment: 41 pages, 9 figures

A cascaded lattice Boltzmann (LB) approach based on central moments and multiple relaxation times to simulate thermal convective flows, which are driven by buoyancy forces and/or swirling effects, in the cylindrical coordinate system with axial symmetry is presented. In this regard, the dynamics of the axial and radial momentum components along with the pressure are represented by means of the 2D Navier-Stokes equations with geometric mass and momentum source terms in the pseudo Cartesian form, while the evolutions of the azimuthal momentum and the temperature field are each modeled by an advection-diffusion type equation with appropriate local source terms. Based on these, cascaded LB schemes involving three distribution functions are formulated to solve for the fluid motion in the meridian plane using a D2Q9 lattice, and to solve for the azimuthal momentum and the temperature field each using a D2Q5 lattice. The geometric mass and momentum source terms for the flow fields and the energy source term for the temperature field are included using a new symmetric operator splitting technique, via pre-collision and post-collision source steps around the cascaded collision step for each distribution function. These result in a particularly simple and compact formulation to directly represent the effect of various geometric source terms consistently in terms of changes in the appropriate zeroth and first order moments. Simulations of several complex buoyancy-driven thermal flows and including rotational effects in cylindrical geometries using the new axisymmetric cascaded LB schemes show good agreement with prior benchmark results for the structures of the velocity and thermal fields as well as the heat transfer rates given in terms of the Nusselt numbers., Comment: 49 pages,12 figures

Fluid motion driven by thermal effects, such as that due to buoyancy in differentially heated three-dimensional (3D) enclosures, arise in several natural settings and engineering applications. It is represented by the solutions of the Navier-Stokes equations (NSE) in conjunction with the thermal energy transport equation represented as a convection-diffusion equation (CDE) for the temperature field. In this study, we develop new 3D lattice Boltzmann (LB) methods based on central moments and using multiple relaxation times for the three-dimensional, fifteen velocity (D3Q15) lattice, as well as it subset, i.e. the three-dimensional, seven velocity (D3Q7) lattice to solve the 3D CDE for the temperature field in a double distribution function framework. Their collision operators lead to a cascaded structure involving higher order terms resulting in improved stability. In this approach, the fluid motion is solved by another 3D cascaded LB model from prior work. Owing to the differences in the number of collision invariants to represent the dynamics of flow and the transport of the temperature field, the structure of the collision operator for the 3D cascaded LB formulation for the CDE is found to be markedly different from that for the NSE. The new 3D cascaded (LB) models for thermal convective flows are validated for natural convection of air driven thermally on two vertically opposite faces in a cubic cavity enclosure at different Rayleigh numbers against prior numerical benchmark solutions. Results show good quantitative agreement of the profiles of the flow and thermal fields, and the magnitudes of the peak convection velocities as well as the heat transfer rates given in terms of the Nusselt number., Comment: 38 pages, 4 figures; typos corrected & figures 3 and 4 modified