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Non-Linear, Granular, and Fluid Physics
Published in Walter Fox Smith, Experimental Physics, 2020
Because making a surface smaller will lower its interfacial energy, surface tension exerts forces and can do work. It’s often useful to model this effect as Laplace pressure – a pressure exerted on a fluid by its interface. This is pLaplace = γκ, where γ is the surface tension, and κ is the mean curvature of the surface. For example, a liquid-filled sphere of radius R has κ = 1/R; its contents are always under Laplace pressure γ/R, in addition to pressure from the outside atmosphere and hydrostatic pressure. As the sphere gets smaller, the contents are under greater pressure. A cylinder of radius R has mean curvature κ=121R, because its surface only curves in one direction.
Nanoemulsions in Non-Invasive Drug Delivery Systems
Published in Bhaskar Mazumder, Subhabrata Ray, Paulami Pal, Yashwant Pathak, Nanotechnology, 2019
Ratna Jyoti Das, Subhabrata Ray, Paulami Pal, Anup Kumar Das, Bhaskar Mazumder
As tremendous shear must be applied to overcome the Laplace pressure for the purpose of breaking the larger droplets into nano-size droplets, the formation of nanoemulsion is impossible with traditional emulsification systems. Typically, different homogenizing technologies such as ultrasonication, high speed agitation, colloidal mills, static mixers, and high shear mixers have been employed to produce nanoemulsions. Both the physicochemical and organoleptic properties of nanoemulsions are a function of the method used to produce it, such as their stability, surface morphology, texture, and rheological behavior, which are significantly affected by the droplet size and its distribution in the nanoemulsion. It has been observed that the smaller the particle size the better the formulation comes out, e.g., a creamier mouth feel and higher stability in terms of shelf-life (Overbeek, 1978).
Stability and Viability of Food Nanoparticles
Published in C. Anandharamakrishnan, S. Parthasarathi, Food Nanotechnology, 2019
S. Parthasarathi, C. Anandharamakrishnan
Laplace pressure is the internal overpressure among the emulsion droplets due to interfacial tension. ΠLaplace=4.γd
Stability of nanoparticle stabilized oil-in-water Pickering emulsion under high pressure and high temperature conditions: comparison with surfactant stabilized oil-in-water emulsion
Published in Journal of Dispersion Science and Technology, 2021
Ganesh Kumar, Abhijit Kakati, Ethayaraja Mani, Jitendra S. Sangwai
Ostwald ripening is another important phenomenon that results in destabilization and phase separation of oil-in-water emulsions. Ostwald ripening is the process where small droplets of emulsions diffuse into larger emulsion droplets through dissolution and deposition. This phenomenon is driven by the difference in solubility between the small and the large droplets.[65] The smaller droplets in emulsion are more soluble which has a larger radius of curvature (leads to a higher Laplace pressure) than the larger droplets with a smaller radius of curvature. This difference in Laplace pressure between small and large emulsion droplets causes the transfer of small emulsion droplets to the larger ones.[66] The silica nanoparticles attached at the oil–water interface of the droplets are difficult to displace due to the higher free energy of adsorption associated with them. Moreover, the nanoparticles form an insoluble barrier which jammed around the interfaces of shrinking emulsion droplets and develops the interface in such a manner to have nearly zero mean radius of curvature.[67] On the other hand, surfactant molecules cannot provide a strong insoluble barrier like the nanoparticles. Therefore, nanoparticles stabilized emulsions can arrest the Ostwald ripening process to a great extent and prevent the destabilization of oil-water emulsion system.
Effects of Nanobubbles on Froth Stability in Flotation Column
Published in International Journal of Coal Preparation and Utilization, 2019
Coalescence of two bubbles in water is thermodynamically favorable to form a larger, single bubble. The force generated by Laplace pressure drains the water between the approaching bubbles, which is sufficient to deform the bubbles surfaces as illustrated in Figure 4, and in sequence, the thin draining film joining the two bubbles ruptures (Pashley and Karaman 2005). The pressure difference given by Laplace equation: (where γ is the surface tension and R is the curvature radius) across a flat interface A-B is zero, while there is a pressure difference where the interface is curved at A-C. Thus, the drainage of the liquid from the laminar part of the thin film (B) is governed by the pressure of the liquid in this region compared with that of the liquid in the Plateau borders (C) or in the bulk liquid. The film may either thin continuously and eventually rupture, or attain an equilibrium thickness depending on the balance of the forces which favor film thinning such as van der Waals attractive forces and a capillary pressure and the forces which resist film thinning similar to overlapping of similar charged electric double layers (Shaw 1992). The thinning of the inter-bubble layer of liquid takes place at first by drainage under gravitational forces and is then followed by movement of the liquid within the lamella by capillary pressure (Sagert, 1976).
Microextractors applied in nuclear-spent fuel reprocessing: Micro/mini plants and radiochemical analysis
Published in Critical Reviews in Environmental Science and Technology, 2018
Tao Wang, Tingliang Xie, Cong Xu
In the back-pressure control method, a pressure controller is applied to add an extra back pressure at the output of one of the phases (usually the aqueous phase) to maintain the pressure balance (Aota et al., 2009). Jasmin et al. (2017) proposed a similar method to center and stabilize the interface by adjusting the length of the outlet capillaries, which allows to optimize the back pressure drop (Jasmin et al., 2017). Alternatively, a microchannel with an asymmetrical cross-section and partial surface modification is responsible for adjusting the Laplace pressure with the hydrodynamic pressure (Hellé et al., 2015). Compared to the surface modification method, the pressure control method is more robust but imprecise. Therefore, the partial surface modification method is more commonly applied and a combination of the two methods is an ideal choice for phase separation in laminar flow microextractors.