Withdrawing a non-Newtonian fluid by a moving inclined plate with account for the near-wall split effect

A fluid withdrawn by a moving inclined surface with account for the near-wall slip effect is analyzed theoretically. A non-Newtonian fluid task is stated in general form. The solving of this task enables revealing the basic physical principles and mechanisms of the process over the entire withdrawal velocity range realized in practice. The case of withdrawing a finite yield stress viscoplastic fluid is considered.

NUMERICAL EXPERIMENTS WITH AN ALGORITHM FOR PROCESSING EXPERIMENTAL DATA TO DETERMINE THE PARAMETERS OF A RHEOLOGICAL MODEL OF A LIQUID WITH THE EFFECT OF «SOLIDIFICATION»

Предложена методика обработки экспериментальных данных и алгоритм для ее реализации по определению параметров реологической модели вязкопластической жидкости, которая демонстрирует проявление эффекта «отвердевания». С целью проверки работоспособности алгоритма проведены численные эксперименты с наборами генерируемых случайным образом “псевдоэкспериментальных” данных с заранее заданной величиной максимальной относительной погрешности. Проведен анализ влияния максимальной относительной погрешности исходных “псевдоэкспериментальных” данных на величину относительной погрешности определяемых в ходе численных экспериментов параметров реологической модели. По итогам проведенных экспериментов показано, что относительная погрешность определения параметров реологической модели соизмерима с максимальной погрешностью генерируемых “псевдоэкспериментальных” данных. Рассмотрен пример обработки экспериментальных данных для суспензии частиц карбоната кальция на основе полиэтиленгликоля. A technique for processing experimental data and an algorithm for its implementation to determine the parameters of a rheological model of a viscoplastic fluid, which demonstrates the manifestation of the "hardening" effect, are proposed. In order to test the algorithm's operability, numerical experiments were carried out with sets of randomly generated "pseudo-experimental" data with a predetermined maximum relative error. The analysis of the influence of the maximum relative error of the initial “pseudo-experimental” data on the value of the relative error of the parameters of the rheological model determined during numerical experiments was carried out. Based on the results of the conducted experiments, it is shown that the relative error in determining the parameters of the rheological model is commensurate with the maximum error of the generated “pseudo-experimental” data. An example of processing experimental data for a suspension of calcium carbonate particles based on polyethylene glycol is considered.

Stagnation Zone Near a Corner in Viscoplastic Fluid Flow

The shape, size and location of the stagnation zone between flat non-parallel walls that make up the corner of a tube with non-circular cross-section through which a phase change material of the Bingham plastic type flows is investigated. We show that the stagnant area is bounded by a convex meniscus whose size depends on the degree of plasticity and the vertex angle. The maximum and minimum energy dissipation occurs at the wall and at the bisectrix, respectively. The stagnant zone can be altogether avoided by modifying the shape of the wall in the corner area. A new design of the cross-section of the tube that allows reducing or eliminating this area to optimize the mass transport is developed. Two optimal solutions a vertex with a straight cut and a concavely curved vertex are proposed.

THE METHOD OF PROCESSING EXPERIMENTAL DATA AND THE ALGORITHM FOR ITS IMPLEMENTATION TO DETERMINE THE PARAMETERS OF THE RHEOLOGICAL MODEL OF A DILATANT LIQUID WITH THE EFFECT OF «SOLIDIFICATION»

В различных технических приложениях применяются рабочие среды типа суспензий, которые при достаточно высокой концентрации частиц твердой фазы демонстрируют аномалии вязкости. Существо этих аномалий заключается в том, что при приближении скорости сдвига к некоторому пороговому значению наблюдается явление резкого возрастания вязкости жидкости. При этом в соответствующих зонах течения рабочая среда начинает вести себя подобно твердому телу. Механическое поведение такой рабочей среды может быть описано в рамках реологической модели вязкопластической жидкости, которая позволяет учитывать проявление эффекта“упрочнения” или “отвердевания”. Рассмотрена методика определения параметров такой реологической модели на основе обработки экспериментальных данных зависимости касательного напряжения от скорости сдвига. Предложен алгоритм для реализации этой методики. In various technical applications, working media such as suspensions are used, which, at a sufficiently high concentration of solid phase particles, demonstrate viscosity anomalies. The essence of these anomalies lies in the fact that when the shear rate approaches a certain threshold value, the phenomenon of a sharp increase in the viscosity of the liquid is observed. At the same time, in the corresponding flow zones, the working medium begins to behave like a solid. The mechanical behavior of such a working medium can be described within the framework of a rheological model of a viscoplastic fluid, which allows for the manifestation of the effect of “hardening” or “solidification”. The method of determining the parameters of such a rheological model based on the processing of experimental data on the dependence of the shear stress on the shear rate is considered. An algorithm for the implementation of this technique is proposed

Heat transport mechanism via ion-slip and hall current in viscoplastic flow along a porous elastic sheet

Heat transfer phenomena occur in most of the natural as well as engineering or manufacturing production plants. Such significant industrial processes utilize various modes for the transportation of heat and energy. In this veneration, the existing research is an attempt to explore heat transmission in a viscoplastic fluid under thermal radiation in the presence of ion and Hall current. The properties of Hall and ion current have enormous uses, particularly when measured in the presence of heat transferal phenomena with suction and injection. The most relevant examples of such mechanisms are fridge spirals, magnetohydrodynamics accelerators, and control generators. Also, the field of biomechanics under the influence of these characteristics is widely used especially in the flowing of blood and magnetic resonance imaging, which helps in producing magnetic resonance images of the thorax, abdomen, brain, kidney, etc. Furthermore, directed medication transport inside the human body needs a tough and heavy magnetic field. Hence, these vital applications of Hall and ion current cannot be overlooked. Transport phenomena are examined past a porous elastic sheet. The prevailing physical model is adapted as a non-linear system of ordinary differential equations by means of proper similarity alterations. The graphical representation shows the physical implication of all related constraints on the velocity and temperature distribution of viscoplastic fluids. Momentum, as well as thermal boundary thickness, is significantly affected by Hall currents and ion slip parameters in the presence of suction/injection phenomena. The temperature of the fluid rises for Eckert number and radiation parameter and also the skin friction coefficient at the surface rises with the suction parameter. An excellent match of numerical results correctly up to three decimal places are obtained for the limiting case when compared to the already published literature.

Viscoplastic plates

An asymptotic model is constructed to describe the bending of thin sheets, or plates, of viscoplastic fluid described by the Herschel–Bulkley constitutive law, which incorporates the von Mises yield condition and a nonlinear viscous stress. The model reduces to a number of previous ones from plasticity theory and viscous fluid mechanics in various limits. It is characterized by a yield criterion proposed by Ilyushin which compactly combines the effect of the bending moment and in-plane stress tensors through three particular invariants. The model is used to explore the bending of loaded flat plates, the deflection of impulsively driven circular plates, and the tension-controlled deflection of loaded beams.

Clouds of bubbles in a viscoplastic fluid

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$ , the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$ , together with lower and upper estimates.