Turbulence in the Ott--Antonsen equation for arrays of coupled phase oscillators

In this paper we study the transition to synchrony in an one-dimensional array of oscillators with non-local coupling. For its description in the continuum limit of a large number of phase oscillators, we use a corresponding Ott-Antonsen equation, which is an integro-differential equation for the evolution of the macroscopic profiles of the local mean field. Recently, it has been reported that in the spatially extended case at the synchronization threshold there appear partially coherent plane waves with different wave numbers, which are organized in the well-known Eckhaus scenario. In this paper, we show that for Kuramoto-Sakaguchi phase oscillators the phase lag parameter in the interaction function can induce a Benjamin-Feir type instability of the partially coherent plane waves. The emerging collective macroscopic chaos appears as an intermediate stage between complete incoherence and stable partially coherent plane waves. We give an analytic treatment of the Benjamin-Feir instability and its onset in a codimension-two bifurcation in the Ott-Antonsen equation as well as a numerical study of the transition from phase turbulence to amplitude turbulence inside the Benjamin-Feir unstable region

Розробка моделі піноемульсійної системи та підтвердження ролі міцності міжфазних адсорбційних шарів в забезпеченні її утворення та стійкості

The model of the formation of the foam emulsion by the emulsion whipping was developed. It was experimentally proved that the yield stress shear of interfacial adsorption layers can be used as a criterion for evaluating the stability of foams, emulsions and foam-emulsion systems. It was found that the introduction of DATEM to the reconstituted skimmed milk increases the yield stress shear of interfacial adsorption layers and stability of foams and emulsions. The introduction of lecithin's or DATEM reduces the yield stress shear of interfacial adsorption layers and stability of foams and emulsions accordingly. Simultaneous use of milk proteins, LACTEM, lecithin's and DATEM provides 1.3 times higher yield stress shear of interfacial adsorption layers at the water-air interface than at the water-oil interface, which is a thermodynamic condition for the formation of the foam emulsion by the emulsion whipping. It was proved that homogenization of the emulsion based on cocoa butter, milk proteins and surfactants provides destabilization of the emulsion and creates conditions for the flotation of destabilized fat particles.The results allow justifying the parameters of the technology of the whipped semi-finished product based on cocoa butter, which is the emulsion whipping of which provides the foaming capacity of 450±22 %, the mechanical strength of the foam emulsion of 3200±160 Pa. It was confirmed that the whipping process can be divided into three stages: foaming, emulsion destabilization and adhesion of fat particles to air bubbles, providing high mechanical strength of the foam emulsion.Разработана модель образования пеноэмульсионной системы. Определены пути регулирования прочности межфазных адсорбционных слоев. Экспериментально подтверждено, что для создания пеноэмльсионной системы необходимо использовать белки молока и три низкомолекулярные поверхностно-активные вещества с высоким и низким гидрофильно-липофильным балансом. При реализации данных принципов получена пеноэмульсия, которая обладает высокой пенообразующей способностью, устойчивостью пены и механической прочностью.Розроблено модель утворення піноемульсійної системи. Визначено шляхи регулювання міцності міжфазних адсорбційних шарів. Експериментально підтверджено, що для створення піноемульсійної системи необхідно використовувати білки молока та три низькомолекулярні поверхнево-активні речовини з високим і низьким гідрофільно-ліпофільним балансом. За реалізації даних принципів одержано піноемульсію, яка володіє високою піноутворюючою здатністю, стійкістю піни та механічною міцністю

Розробка теоретичної моделі одержання піноемульсій з суміші сухої жировмісної та її експериментальне підтвердження

We developed a theoretical model of the Pickering-steric stabilization of whipped emulsions structure with a low fat content, obtained from a dry fat-containing mixture. It was experimentally proven that the yield shear stress of a whipped emulsion is determined by the degree of destabilization of fatty particles. It is shown that in order to ensure the full degree of destabilization of fatty particles, it is necessary that 5.0...7.0 g of oil is introduced with 3.0 g of distilled monoglycerides and 0.08…0.1 g of soy lecithin. The destabilized fatty particles are capable of adhesion to air bubbles thus providing for the Pickering-stabilization of a whipped emulsion. It was established that at low content of oil in the system (5.0...7.0 %), it is necessary to combine the Pickering stabilization with the steric stabilization. Steric stabilization in a whipped emulsion is implemented the complex formation of sodium caseinate and kappa-carrageenan, increasing the yield shear stress of the interface adsorption layers.Whipped emulsions with a large foaming capacity and yield shear stress are obtained from a dry fat-containing mixture. For this purpose, it is necessary to provide, during crystallization of the fatty phase, a contact with white sugar. This approach ensures formation of the interface adsorption layers and partial wetting the fatty particles (an edge angle of wetting is 25.0±2.0°). The proposed approach is named the quasi-emulsification. Introduction to sunflower oil of 30…37.5 % of distilled monoglycerides of fatty acids provides the obtaining of dry loose fat mixtures. New technology that we propose for obtaining the dry mixtures is characterized by energy efficiency because of the absence of operation of drying the emulsion. Using the developed technology makes it possible to receive whipped emulsions with the foaming capacity that is 1.7…2.0 times higher than that of the products-analogues available in the Ukrainian market.Разработана теоретическая модель Пикеринг-стерической стабилизации структуры пеноэмульсии с низким содержанием жира, полученной из сухой смеси. Экспериментально доказано, что предельное напряжение сдвига пеноэмульсии определяется степенью дестабилизации жировых частиц, которые обеспечивают Пикеринг стабилизацию пеноэмульсии. Реализация комплексообразования казеината натрия и каппа-карагинана обеспечивает стерическую стабилизацию пеноэмульсии за счет увеличения предельного напряжения сдвига межфазных адсорбционных слоевРозроблено теоретичну модель Пікерінг-стеричної стабілізації структури піноемульсій з низьким вмістом жиру, одержаної із сухої суміші. Експериментально доведено, що граничне напруження зсуву піноемульсії визначається ступенем дестабілізації жирових частинок, які забезпечують Пікерінг стабілізацію піноемульсії. Реалізація комплексоутворення казеїнату натрію та капа-карагінану забезпечує стеричну стабілізацію піноемульсії за рахунок збільшення граничного напруження зсуву міжфазних адсорбційних шарі

Developing a Model of the Foam Emulsion System and Confirming the Role of the Yield Stress Shear of Interfacial Adsorption Layers to Provide Its Formation and Stability

The model of the formation of the foam emulsion by the emulsion whipping was developed. It was experimentally proved that the yield stress shear of interfacial adsorption layers can be used as a criterion for evaluating the stability of foams, emulsions and foam-emulsion systems. It was found that the introduction of DATEM to the reconstituted skimmed milk increases the yield stress shear of interfacial adsorption layers and stability of foams and emulsions. The introduction of lecithin's or DATEM reduces the yield stress shear of interfacial adsorption layers and stability of foams and emulsions accordingly. Simultaneous use of milk proteins, LACTEM, lecithin's and DATEM provides 1.3 times higher yield stress shear of interfacial adsorption layers at the water-air interface than at the water-oil interface, which is a thermodynamic condition for the formation of the foam emulsion by the emulsion whipping. It was proved that homogenization of the emulsion based on cocoa butter, milk proteins and surfactants provides destabilization of the emulsion and creates conditions for the flotation of destabilized fat particles.The results allow justifying the parameters of the technology of the whipped semi-finished product based on cocoa butter, which is the emulsion whipping of which provides the foaming capacity of 450±22 %, the mechanical strength of the foam emulsion of 3200±160 Pa. It was confirmed that the whipping process can be divided into three stages: foaming, emulsion destabilization and adhesion of fat particles to air bubbles, providing high mechanical strength of the foam emulsion

Development of a Theoretical Model for Obtaining the Whipped Emulsions From a Dry Fat-containing Mixture and Its Experimental Verification

We developed a theoretical model of the Pickering-steric stabilization of whipped emulsions structure with a low fat content, obtained from a dry fat-containing mixture. It was experimentally proven that the yield shear stress of a whipped emulsion is determined by the degree of destabilization of fatty particles. It is shown that in order to ensure the full degree of destabilization of fatty particles, it is necessary that 5.0...7.0 g of oil is introduced with 3.0 g of distilled monoglycerides and 0.08…0.1 g of soy lecithin. The destabilized fatty particles are capable of adhesion to air bubbles thus providing for the Pickering-stabilization of a whipped emulsion. It was established that at low content of oil in the system (5.0...7.0 %), it is necessary to combine the Pickering stabilization with the steric stabilization. Steric stabilization in a whipped emulsion is implemented the complex formation of sodium caseinate and kappa-carrageenan, increasing the yield shear stress of the interface adsorption layers.Whipped emulsions with a large foaming capacity and yield shear stress are obtained from a dry fat-containing mixture. For this purpose, it is necessary to provide, during crystallization of the fatty phase, a contact with white sugar. This approach ensures formation of the interface adsorption layers and partial wetting the fatty particles (an edge angle of wetting is 25.0±2.0°). The proposed approach is named the quasi-emulsification. Introduction to sunflower oil of 30…37.5 % of distilled monoglycerides of fatty acids provides the obtaining of dry loose fat mixtures. New technology that we propose for obtaining the dry mixtures is characterized by energy efficiency because of the absence of operation of drying the emulsion. Using the developed technology makes it possible to receive whipped emulsions with the foaming capacity that is 1.7…2.0 times higher than that of the products-analogues available in the Ukrainian market