The effect of a few relatively large bubbles injected near the walls on the wall drag in the “minimum turbulent channel” is examined by direct numerical simulations. A front-tracking/finite-volume method is used to fully resolve all flow scales including the bubbles and the flow around them. The Reynolds number, using the friction velocity and the channel half-height, is 135 and the bubbles are 54 wall units in diameter. The results show that deformable bubbles can lead to significant reduction of the wall drag by suppression of streamwise vorticity. Less deformable bubbles, on the other hand, are slowed down by the viscous sublayer and lead to a large increase in drag.

Numerical simulations are used to examine the effect of an electrostatic field on an emulsion of drops in a channel. The leaky-dielectric theory of Taylor is used to find the electric field, the charge distribution on the drop surface, and the resulting forces. The Navier-Stokes equations are solved using a front-tracking/finite-volume technique. Depending on the ratios of conductivity and permittivity of the drop fluid and the suspending fluid the drops can become oblate or prolate. In addition to normal forces that deform the drops, tangential forces can induce a fluid motion either from the poles of the drops to their equator or from the equator to the poles. In this paper we focus on oblate drops, where both the dielectrophoretic and the electrohydrodynamic interactions of the drops work together to "fibrate" the emulsion by lining the drops up into columns parallel to the electric field. When the flow through the channel is slow, the fibers can extend from one wall to the other. As the flow rate is increased the fibers are broken up and drops accumulate at the channel walls. For high enough flow rate, when the drop interactions are dominated by the fluid shear, the drops remain in suspension. Only two-dimensional systems are examined here, but the method can be used for fully three-dimensional systems as well.

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Direct numerical simulations of the motion of bubbles in turbulent flows are being carried out, using a finite volume/front tracking technique that accounts fully for the effect of fluid inertia, viscosity, bubble deformability, and surface tension. The objective of the simulations is both to address the fundamental interaction mechanisms between the bubbles and the flow and how the bubbles modify the wall turbulent structures, as well as to provide data for validation of simplified models. Results for bubbles placed in the so-called “minimum turbulent channel” show significant drag reduction as the bubbles disrupt the near-wall turbulent flow.

Direct numerical simulation is used to examine the rheological properties of an emulsion of leaky dielectric fluids when an electric field is applied to the system. The emulsion consisting of neutrally buoyant drops is immersed in a simple shear flow where an electric potential difference is applied between the plates. It is assumed that drops are more conductive than the suspending fluid and that the electrical conductivity ratio between the drops and the suspending fluid, R=σi∕σo, is larger than the dielectric permittivity ratio, S=εo∕εi. If a single leaky dielectric drop is immersed in an electric field, this combination of properties leads to a viscous fluid motion from the equator to the poles. The response of an emulsion depends on the competition between the electrical forces and the fluid shear. This relation is quantified by the Mason number, Mn=(3λ+2)μγ̇∕6(λ+1)ε0β2E∞2. The significance of drop deformability is measured through the electric capillary number, Ce=ε0β2E∞2a∕γ. The microstructure and properties of an emulsion depend mainly on Mn, Ce, and R. An emulsion immersed in an electric field exhibits three different regimes for increasing Mn. When the electrical forces are substantially larger than the fluid shear, Mn<0.02, the drops aggregate in structures oriented parallel to the electric field that dictate the response of the system. At intermediate shear rates, 0.02<Mn<0.2, the competition between the electrical forces and the fluid shear results in a continuous rearrangement of the aggregated structures. When the shear rate is increased further, Mn>0.2, the aggregated structures are broken up, and the effect of the electrical interaction weakens. The application of an electric field leads electrorheological emulsions to exhibit an increase in their effective viscosity for the range of properties examined here, 0.001<Mn<10.0. However, this variation is strongly nonlinear and depends on the microstructure of the emulsion. The deformation and aggregation of the drops caused by the electric field also modifies the elastic properties of the systems. When the strength of the electrical forces is larger than that of the viscous forces, Mn<O(1), the electrorheological emulsions exhibit negative values for the first normal stress difference. The electric field causes the drops to deform into a prolate shape in the direction parallel to the electric field. The prolate deformation leads to stronger interfacial stresses in the direction normal to the applied shear, which results in negative values of the first normal stress difference. The dependency of the microstructure and rheological properties on the drop deformability, the electrical conductivity ratio, and the drop volumetric fraction is also discussed. Results for emulsions with a drop volumetric fraction of up to 0.56 are presented.

Direct numerical simulations of the effects of an electric field on an emulsion of drops are presented. A simple shear flow configuration is adopted where the electric field is applied perpendicular to the sliding plates. Both the drops and the suspending fluid are assumed to behave as leaky dielectric fluids. Here, drops less conductive than the suspending fluid with an electrical conductivity ratio smaller than the dielectric permittivity ratio are considered. This combination of electrical properties leads to a viscous fluid motion from the poles to the equator. The response of an emulsion is governed by the competition between the electrical forces, the fluid shear, and the capillary forces. The Mason number [Mn=(3λ+2)μγ̇∕6(λ+1)ε0β2E∞2] and the electric capillary number [Ce=ε0β2E∞2a∕γ] are used to describe the response of the systems. As previously observed in experiments at low shear rates, Mn<0.2, the drops aggregate in chains that tilt under a shear. The competition between the electrical forces and the fluid shear results in shorter chains at intermediate shear rates, 0.2<Mn<2.0. As the fluid shear becomes stronger than the electrical attraction, Mn>2.0, the chains of drops break up. The rheological properties mainly depend on the emulsion microstructure. The effective viscosity exhibits a strong shear-thinning response because the chains of drops, which appear at low shear rates, increase the resistance of the system to shear. As the chains shorten and break up, the effective viscosity decreases. The elastic properties of the emulsion are also affected by the presence of the electric field. Normal stress differences arise as a consequence of the deformation of the drops and the surface tension acting on the interface between the fluids. The shape of the drops is determined by the deformation caused by the viscous forces and the deformation due to the electric stresses. At low shear rates, the electric effects are predominant and the application of an electric field leads the drops to deform into oblate shapes. The oblate deformation results in higher stresses in the direction parallel to the shearing motion than perpendicular to it, which results in a significant increase in the first normal stress difference. As the shear rate is increased, the oblate deformation is supplemented by the deformation due to the fluid shear. The deformation caused by the electric field is also responsible for the negative magnitude of the second normal stress difference in three-dimensional emulsions.

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