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Hypothesis The shear stress of the axisymmetric flow field triggers a nonuniform distribution of the surfactants at the surface of a rising bubble, known as stagnant cap. The formation of the stagnant cap gives rise to Marangoni stresses that reduce the mobility of the interface, which in return reduces the rising velocity. However, the conditions in technological processes usually deviate from the linear rise of a single bubble in a quiescent unbounded liquid. Asymmetric shear can act on the bubble surface e.g. due to the vorticity in the surrounding flow, bubble-bubble interactions, or influence of the reactor wall. A different surfactant distribution at the interface is expected under asymmetric shear, which can change the hydrodynamic behavior of the interface drastically. Experiments Here we conduct model experiments with a bubble or a drop at the tip of a capillary placed in a defined flow field. Thereby we investigate the influence of asymmetric shear forces on the interface in the presence of surfactants. Microscopic particle tracking velocimetry is employed to measure the velocity of the surfactant-laden interface for different degrees of asymmetry in the surrounding liquid flow. Findings We show a direct experimental observation of the circulating flow at the interface under asymmetric shear, which prevents the formation of the typical stagnant cap. Additionally, we reveal that the interface remains mobile regardless of the surfactant concentration. Our results confirm that increasing the degree of asymmetry increases the shear forces and thus the interfacial velocity.

Hypothesis The shear stress of the axisymmetric flow field triggers a nonuniform distribution of the surfactants at the surface of a rising bubble, known as stagnant cap. The formation of the stagnant cap gives rise to Marangoni stresses that reduce the mobility of the interface, which in return reduces the rising velocity. However, the conditions in technological processes usually deviate from the linear rise of a single bubble in a quiescent unbounded liquid. Asymmetric shear can act on the bubble surface e.g. due to the vorticity in the surrounding flow, bubble-bubble interactions, or influence of the reactor wall. A different surfactant distribution at the interface is expected under asymmetric shear, which can change the hydrodynamic behavior of the interface drastically. Experiments Here we conduct model experiments with a bubble or a drop at the tip of a capillary placed in a defined flow field. Thereby we investigate the influence of asymmetric shear forces on the interface in the presence of surfactants. Microscopic particle tracking velocimetry is employed to measure the velocity of the surfactant-laden interface for different degrees of asymmetry in the surrounding liquid flow. Findings We show a direct experimental observation of the circulating flow at the interface under asymmetric shear, which prevents the formation of the typical stagnant cap. Additionally, we reveal that the interface remains mobile regardless of the surfactant concentration. Our results confirm that increasing the degree of asymmetry increases the shear forces and thus the interfacial velocity.

The shear stress of an axisymmetric flow field triggers a nonuniform distribution of the surfactants at the surface of a rising bubble, known as stagnant cap. This nonuniform surfactant distribution creates a surface tension gradient that counteracts the viscous shear stress of the flow and thus reduces the mobility of the interface. However, in technological processes the flow field often is asymmetric e.g. due to the vorticity in the flow. Under such conditions, the interface experiences an unbalanced shear stress that is not curl-free. Thus, it cannot be compensated by the redistribution of the surfactants at the interface [1]. Here, we conduct model experiments with a bubble at the tip of a capillary placed in a defined asymmetric flow field. Thereby, we investigate the mobility of the interface in the presence of surfactants and nanoparticles using microscopic particle tracking velocimetry. Compared to surfactants, nanoparticles have substantially higher desorption energy, leading to irreversible adsorption. Thus, a different interaction between the bulk flow and the interface is expected for different types of adsorbed materials. In this study, we show a direct experimental observation of the circulating flow at the interface under asymmetric shear stress. The results indicate that the interface remains mobile regardless of the surfactant concentration [2]. Additionally, we show that the nanoparticle-laden interface adopts a solid-like state and resists the interfacial flow upon surface compression. Our results imply that the immobilization of the interface can be described by the ratio of the interfacial elasticity to the bulk viscous forces.

With the aim of a generalized model framework for two-phase flows, cases with large scale interfaces are modeled by means of a two-fluid model in the manner of large-eddy simulations. In this context a number of unclosed terms due to the filtering operation arise. One of them is the classical convective sub-grid scale turbulence stress term. Different closure models for the convective sub-grid scale term are adapted to the presented model framework and a-posteriori investigations are carried out in order to compare the influence of the different modeling approaches.

With the aim of a generalized model framework for two-phase flows, cases with large scale interfaces are modeled by means of a two-fluid model in the manner of large-eddy simulations. In this context a number of unclosed terms due to the filtering operation arise. One of them is the classical convective sub-grid scale turbulence stress term. Different closure models for the convective sub-grid scale term are adapted to the presented model framework and a-posteriori investigations are carried out in order to compare the influence of the different modeling approaches.

With the aim of a generalized model framework for two-phase flows, cases with large scale interfaces are modeled by means of a two-fluid model in the manner of large-eddy simulations. In this context a number of unclosed terms due to the filtering operation arise. One of them is the classical convective sub-grid scale turbulence stress term. Different closure models for the convective sub-grid scale term are adapted to the presented model framework and a-posteriori investigations are carried out in order to compare the influence of the different modeling approaches.

The deformation of a hydrogen microbubble line and/or mesh in a viscoelastic fluid around a rising bubble was tracked from the original static position in order to discuss the mechanism of the typical phenomena such as the negative wake or the cusp shape. This new experimental method is essentially important because of the hysteresis-dependent nature of the viscoelastic fluid. This new method makes this study distinctive from a number of conventional studies of viscoelastic fluids focusing on the non-Newtonian properties and/or the instantaneous flow field. According to our experimental results, the flow mechanism responsible for the negative wake or cusp shape was attributed to the accumulation and release of the shear strain energy. Some residual displacements were observed after the bubble rising, which were almost completely reproduced as the internal dissipations in a Maxwell model modified with a non-linear spring.

A lattice Boltzmann method (LBM) for two-phase viscoelastic fluid flows is proposed. The method is mainly an extension of the LBM for two-phase flows with large density differences proposed by Inamuro et al. [Journal of Computational Physics Vol.198, No.2 (2004), pp.628–644]. The viscoelastic effects are introduced by the constitutive equation based on the Maxwell model, which has a spring and a dashpot connected with each other in series. The method is applied to simulations of a drop under shear flow in viscoelastic fluids and of a bubble rising in viscoelastic fluids. In the simulation of drop deformation under shear flows, the effects of viscoelasticity on the deformation and orientation angle are evaluated. In the simulation of bubble rising in viscoelastic fluids, a cusp configuration at the trailing edge is investigated and compared with the theoretical prediction and other numerical results.

The numerical simulation of a rising bubble in liquid and falling droplet is presented. The two- and three-dimensional incompressible Navier-Stokes equations are used to solve the gas-liquid two phases flow system with free surfaces. A sharp interface separates fluids of different density and viscosity. The interface between gas and liquid is described as the zero level set of a smooth function. In order to maintain the level set function as a smooth signed distance function from the interface, a reinitialization operation is required. We also apply a constraint to improve the conservation of mass significantly. A WENO scheme for space derivatives and third-order Runge-Kutta scheme for the time discretization are used to solve the level set equation. The projection method are used to derive a pressure Poisson equation to ensure the satisfaction of continuity equation. The velocity field can be obtained by second-order explicit Adams-Bashforth scheme, while the pressure is solved. The staggered grid system is used in the numerical model. The model allows us to simulate a wide range of flow regimes and surface tension effect can be consideration. The effect of deformation and motion of a riging bubble is investigated by changing the Reynolds numbers and Weber numbers. A droplet falls into a tank of a quiescent fluid is also simulated. Complex numerical simulations show the capability of our numerical model. Our model can be used to simulate a number of problems and to investigate many physical phenomena involving multi-fluid flows that consider the free surfaces.

The numerical simulation of a rising bubble in liquid and falling droplet is presented. The two- and three-dimensional incompressible Navier-Stokes equations are used to solve the gas-liquid two phases flow system with free surfaces. A sharp interface separates fluids of different density and viscosity. The interface between gas and liquid is described as the zero level set of a smooth function. In order to maintain the level set function as a smooth signed distance function from the interface, a reinitialization operation is required. We also apply a constraint to improve the conservation of mass significantly. A WENO scheme for space derivatives and third-order Runge-Kutta scheme for the time discretization are used to solve the level set equation. The projection method are used to derive a pressure Poisson equation to ensure the satisfaction of continuity equation. The velocity field can be obtained by second-order explicit Adams-Bashforth scheme, while the pressure is solved. The staggered grid system is used in the numerical model. The model allows us to simulate a wide range of flow regimes and surface tension effect can be consideration. The effect of deformation and motion of a riging bubble is investigated by changing the Reynolds numbers and Weber numbers. A droplet falls into a tank of a quiescent fluid is also simulated. Complex numerical simulations show the capability of our numerical model. Our model can be used to simulate a number of problems and to investigate many physical phenomena involving multi-fluid flows that consider the free surfaces.

The numerical simulation of a rising bubble in liquid and falling droplet is presented. The two- and three-dimensional incompressible Navier-Stokes equations are used to solve the gas-liquid two phases flow system with free surfaces. A sharp interface separates fluids of different density and viscosity. The interface between gas and liquid is described as the zero level set of a smooth function. In order to maintain the level set function as a smooth signed distance function from the interface, a reinitialization operation is required. We also apply a constraint to improve the conservation of mass significantly. A WENO scheme for space derivatives and third-order Runge-Kutta scheme for the time discretization are used to solve the level set equation. The projection method are used to derive a pressure Poisson equation to ensure the satisfaction of continuity equation. The velocity field can be obtained by second-order explicit Adams-Bashforth scheme, while the pressure is solved. The staggered grid system is used in the numerical model. The model allows us to simulate a wide range of flow regimes and surface tension effect can be consideration. The effect of deformation and motion of a riging bubble is investigated by changing the Reynolds numbers and Weber numbers. A droplet falls into a tank of a quiescent fluid is also simulated. Complex numerical simulations show the capability of our numerical model. Our model can be used to simulate a number of problems and to investigate many physical phenomena involving multi-fluid flows that consider the free surfaces.