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In this paper, we propose a phase field-lattice Boltzmann (LB) model with an equation of state (EOS) inputting for two-phase flow containing soluble surfactants. In this model, both the order parameter for the phase field and the surfactant concentration are described by second-order partial differential equations, along with Navier–Stokes equations for the flow field. Changes in surfactant concentration do not affect the order parameter distribution; hence, an unwanted sharpening effect cannot arise. Most importantly, in the existing models, the EOS of surface tension is determined by posterior simulation tests instead of being directly set as an input parameter before the simulations. Hence, it is difficult to determine the model parameters in practical applications. To address this issue, we systematically develop a fully analytical EOS for surface tension based on the Gibbs–Duhem equation. Subsequently, an approximate explicit form for EOS is provided by utilizing the Jacobi–Gauss quadrature rule. Furthermore, a multiple-relaxation-time LB scheme is utilized to numerically solve the governing equations of three physical fields. Two benchmark examples are simulated to validate the accuracy of the present model. The consistency between the numerical results and the analytical EOS is verified. Moreover, the dynamics of droplets with surfactant in simple shear flow is investigated, unveiling the profound impact of various factors, such as surfactant bulk concentration, capillary number, and viscosity ratio, on single droplet deformation and two equal-sized droplets interaction. A detailed exploration of the fluid mechanism involved in two-phase flow with soluble surfactants is presented. [ABSTRACT FROM AUTHOR]

This study numerically examines the Rosensweig instability of a ferrofluid-infused surface (FIS), which is an overlayer surface formed on the top of a porous substrate into which the ferrofluid is infused. FIS inherits the lubricating property of liquid-infused surfaces and the magnetic property of the ferrofluid, allowing an external control by a magnetic field. Currently, the evolution mechanisms of the Rosensweig instability of the FIS remain unclear. By using the recently developed coupled numerical scheme, which consists of the simplified multiphase lattice Boltzmann method and the self-correcting method for the Maxwell magnetic field equations, the intriguing mechanism and evolution dynamics of the ferrofluid spikes on the FIS are investigated systematically by examining the effects of overlayer thickness, substrate pore size, and magnetic field strength. The results are also analyzed by the Rosensweig instability theory. This study provides a theoretical and numerical basis for the magnetic field control of droplet or bubble motions on the FIS. [ABSTRACT FROM AUTHOR]

An experimental study is carried out to investigate the effects of microglass fiber suspensions in the non-Newtonian fluids in a gap between an inner rotating sphere and an outer whole stationary sphere. In the experiments, the microglass fibers with different aspect ratios are mixed with a macromolecule polymeric fluid to obtain different suspension fluids. For comparison, a Newtonian fluid and the non-Newtonian polymeric fluid are also studied. The stationary torques of the inner sphere that the test fluids acted on are measured under conditions of various concentric spherical gaps and rotational Reynolds numbers. It is found that the polymeric fluid could be governed by the Couette flow at a gap ratio of less than 0.42 and the Reynolds number of less than 100, while the fiber-suspended polymeric fluids could expand the Couette flow region more than the Reynolds number of 100 at the same gap ratios. [DOI: 10.1115/1.4001491] Keywords: fiber suspension, sphere Couette flow, viscoelastic fluid