Accuracy of the toroidal approximation for the calculus of concave and convex liquid bridges between particles

In situations and processes where finely divided solids are in contact with small amounts of liquid, capillary effects influence the behavior of such systems. If the quantity of liquid is rather limited, it arranges as individual liquid bridges connecting the solid particles just wetting a portion of the solids surface. These bridges develop forces which drive the cohesion and motion of the solid particles, further determining in many times the final structure or even the quality of the material. Since the liquid is not able to fully cover the solid particles like in a proper suspension, this liquid adopts a shape which is determined by the principle of constant mean curvature. A rigorous determination of such a shape, which in turn determines the capillary forces, must be carried out by solving the Young-Laplace equation. Due to the difficulties in such calculation, it was proposed to approximate the meniscus profile by an arc-of-circumference, the so-called toroidal approximation. Here it is quantitatively studied the suitability of such approximation for the most general geometry of liquid bridges, finding that the error of the approximation is below 10% for concave menisci and 30% for convex one

Viscosity of a Newtonian fluid calculated from the deformation of droplets covered with a surfactant under a linear shear flow

The viscosity of small fluid droplets covered with a surfactant is determined using drop deformation techniques. This method, proposed by Hu and Lips, is here extended to the case of the presence of a surface-active adsorpted at the liquid-liquid interface, to consider more general scenarios. In these experiments, a droplet is sheared by another immiscible fluid of known viscosity, both Newtonian liquids. From the steady-state deformation and retraction mechanisms, the droplet viscosity is calculated using an equation derived from the theories of Taylor and Rallison. Although these theories were expressed for surfactant-free interfaces, they can be applied when a surfactant is present in the system if the sheared droplet reaches reliable steady-state deformations and the surfactant attains its equilibrium adsorption concentration. These determinations are compared to bulk viscosities measured in a rheometer for systems with different viscosity ratios and surfactant concentrations. Very good agreement between both determinations is found for drops more viscous than the continuous phas

Capillary and van der Waals forces between uncharged colloidal particles linked by a liquid bridge

This work presents a theoretical study of the forces established between colloidal particles connected by means of a concave liquid bridge, where the solid particles are partially wetted by a certain amount of liquid also possessing a dry portion of their surfaces. In our analysis, we adopt a two-particle model assuming that the solids are spherical and with the same sizes and properties and that the liquid meniscus features an arc-of-circumference contour. The forces considered are the typical capillary ones, namely, wetting and Laplace forces, as well as the van der Waals force, assuming the particles uncharged. We analyze different parameters which govern the liquid bridge: interparticle separation, wetting angle, and liquid volume, which later determine the value of the forces. Due to the dual characteristic of the particles' surfaces, wet and dry, the forces are to be determined numerically in each case. The results indicate that the capillary forces are dominant in most of the situations meanwhile the van der Waals force is noticeable at very short distances between the particle

Accuracy of the toroidal approximation for the calculus of concave and convex liquid bridges between particles

ISSN:1434-5021ISSN:1434-763

Viscosity of a Newtonian fluid calculated from the deformation of droplets covered with a surfactant under a linear shear flow

ISSN:0035-4511ISSN:1435-152

Capillary and van der Waals forces between uncharged colloidal particles linked by a liquid bridge (vol 288, pg 133, 2010)

ISSN:0303-402XISSN:1435-153

Capillary and van der Waals forces between uncharged colloidal particles linked by a liquid bridge

ISSN:0303-402XISSN:1435-153

Simulation and experiments of droplet deformation and orientation in simple shear flow with surfactants

The deformation and orientation behavior of three-dimensional (3D) viscous droplets with and without surfactants is studied in simple shear flow using simulations and experiments. Two added amounts of surfactants are considered, along with a range of viscosity ratios and capillary numbers. The numerical method couples the boundary integral method for interfacial velocity, a second-order Runge-Kutta method for interface evolution, and a finite element method for surfactant concentration. The algorithm assumes a bulk-insoluble, nonionic surfactant, and uses a linear equation of state to model the relationship between the interfacial tension and the surfactant concentration on the drop surface. The algorithm was validated by comparison with other numerical results and good agreement was found. The experiments are performed in a parallel-band apparatus with full optical analysis of the droplet. The simulated and measured 3D steady-state shape of the ellipsoidal drops and their orientation are in reasonably good agreement. It was found that the surfactants have a greater effect on drop geometry for smaller viscosity ratios and that the deformation increases as the transport of surfactant becomes more convection dominated. It was also found that surfactants cause the drops to align more in the flow direction and that, for both clean and surfactant-covered drops, this alignment increases with viscosity ratio. Finally, simulations showed a wider distribution of surfactant on the interface for smaller viscosity ratios. © 2007 Elsevier Ltd. All rights reserved

Droplet deformation under simple shear investigated by experiment, numerical simulation and modeling

The deformation and break-up of droplets in complex flow fields is encountered in many engineering applications such as mixing and dispersing processes. To manipulate and control such operations, rheological, interfacial and dynamical properties of the multiphase fluid as well as their interaction have to be known. In the present work, the deformation of droplets is studied experimentally in simple shear flow and compared with numerical calculations and modeling. For this purpose, a computer-controlled parallel band apparatus equipped with a digital camera records the time evolution of the sheared droplet and thus, analyzes digitally its shape. Numerical simulations are performed to calculate the drop deformation in three-dimensional space, although only two dimensions available experimentally (plane of shear) are considered for comparison. The simulations use a boundary integral method to determine drop deformation from the mass and momentum balance equations. Furthermore, a simple phenomenological model in terms of a droplet shape tensor is proposed to describe droplet deformation in homogeneous flow. © 2004 Elsevier B.V. All rights reserved