Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully- coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin’s immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library, IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.

Fractional Model and Exact Solutions of Convection Flow of an Incompressible Viscous Fluid under the Newtonian Heating and Mass Diffusion

In this paper, we consider a natural convection flow of an incompressible viscous fluid subject to Newtonian heating and constant mass diffusion. The proposed model has been described by the Caputo fractional operator. The used derivative is compatible with physical initial and boundaries conditions. The exact analytical solutions of the proposed model have been provided using the Laplace transform method. The obtained solutions are expressed using some special functions as the Gaussian error function, Mittag–Leffler function, Wright function, and G -function. The influences of the order of the fractional operator, parameters used in modeling the considered fluid, Nusselt number, and Sherwood number have been analyzed and discussed. The physical interpretations of the influences of the parameters of our fluid model have been presented and analyzed as well. We use the graphical representations of the exact solutions of the model to support the findings of the paper.

Lubricated rolling over a pool

Experiments are conducted to explore the rolling of a cylinder over a pool of viscous fluid. The speed, width and loading of the cylinder are varied along with the initial depth and length of the viscous pool. Depending on the conditions, the cylinder will either ride on a lubrication film or remain in solid contact with the underlying substrate. For the former situation, a lubrication theory is presented that describes the pressure underneath the cylinder and the thickness of the film. The theory approximates the flow by the one-dimensional Reynolds equation with the addition of one term, with an adjustable parameter, to account for the flux of fluid to the cylinder sides. Once this parameter is calibrated against experiment, the theory predicts peak lubrication pressures, gap sizes and film thicknesses to within approximately ten per cent. For lubricated rolling, the film splits evenly between the cylinder and substrate downstream of the nip. The printer's instability arises during the splitting process, patterning the residual fluid films on the substrate and cylinder. If the pool length is less than the cylinder circumference, the fluid adhering to the cylinder is rotated back into contact with the substrate, and when there is sufficient adhered fluid a lubrication film forms that can again be modelled by the theory. Conversely, if there is insufficient adhered fluid, no contiguous lubrication film is formed; instead, the pattern from the printer's instability ‘prints’ from the cylinder to the substrate.

NUMERICAL SIMULATION OF JET EXCAVATION IN CONDUCTOR JETTING OPERATIONS IN SUBMARINE SOIL: MESH ANALYSIS

The more complex exploration techniques and operations in deepwater environment are, the higher become the financial costs involved in the process. The rent of an offshore rig, for instance, can cost hundreds of thousands of dollars per day. Therefore, improving deepwater drilling efficiency can lead to significant cost savings. The drilling process of an oil well starts with the initial drilling, which is the operation to accommodate the conductor casing. Among the techniques to set the conductor casing, jetting operations have become popular in submarine environments where the seafloor sediments allow the technique to be used. In these environments, the submarine soil consists of a deformable body displaying a behavior that falls between a linear elastic solid and viscous fluid. Therefore, its behavior is governed by general theory of rheology, and it can be described as highly viscous non-Newtonian fluid. Despite the lack of comprehensive investigations, promising works can be carried out by considering cohesive soil behavior as viscous fluid. Problems of this type can be solved using computational fluid dynamics (CFD), a powerful software which solves complex fluid mechanics equations. Thus, this work numerically evaluates the excavation mechanism in conductor jetting operations in submarine soil during the first 30 seconds of examination, considering soil as viscous fluid of Herschel-Bulkley. Ansys Fluent®, which is a CDF software based on the finite-volume method, was applied to simulate the jetting excavation process. The results indicate that all meshes generated in the development of this work have an excellent quality, and they also show that the greater the mesh refinement is, the higher the accuracy and robustness of the model will be. However, the computational cost to simulate the model increases exponentially with the increase in number of elements, highlighting the importance of properly balancing mesh refinement and computational effort. When analyzing the results, we could also identify the excavation profile made by the bit jet, which presented an almost symmetrical shape.

Aspiration of viscous plug in macular hole surgery- a case series

Macular hole surgery has been revolutionized since the 1990s’ with the advent of pars plana vitrectomy with internal limiting membrane peeling and gas tamponade, which is now extensively practiced and regarded as the gold standard procedure for surgical treatment of macular hole. Here, we report a simple adjunctive maneuver to conventional PPV with ILM peel and gas tamponade. We observed presence of a viscous fluid in the base of the macular hole in our series. In all, 40 eyes of 39 patients consecutively operated on from June 2019 to December 2020 for PPV with ILM peel and gas tamponade, were included in this study. The viscous plug was aspirated passively using a 25 gauge cannula with its tip above the macular hole, approaching only until a fluid-wave was visualized, which resulted in flattening of the fluid cuff area aiding the macular hole closure in a concentric pattern. Macular hole closure and complete success was seen in 39 out of 40 eyes (97.5%) and only 1 failure (2.5%) observed in this series. In our case series, we have observed the presence of a viscous fluid plug in the macular hole. We demonstrated that aspirating this thick fluid from the hole results in the flattening of the cuff of fluid and subsequent closure of the macular hole in a concentric manner in almost all cases in our series. The lack of concurrent control group means we cannot state a definitive effect of the intervention, but it does suggest the utility of a prospective randomized controlled trial.

Viscous holographic f(Q) cosmology with some versions of holographic dark energy with generalized cut-offs

The work reported in this paper demonstrates the cosmology of f(Q) gravity and the reconstruction of various associated parameters with different versions of holographic dark energy with generalized cut-offs, where Q = 6 H 2. The Universe is considered to be filled with viscous fluid characterized by a viscous pressure Π = – 3 H ξ, where ξ = ξ 0 + ξ 1 H + ξ 2 ( H ˙ + H 2 ) and H is the Hubble parameter. Considering the power law form of expansion, we have derived the expression of f(Q) under a non-viscous holographic framework and it is then extended to viscous cosmological settings with extended generalized holographic Ricci dark energy. The forms of f(Q) for both the cases are found to be monotonically increasing functions of Q. In the viscous holographic framework, f(Q) is reconstructed as a function of cosmic time t and is found to stay at a positive level with Nojiri-Odintsov cut-off. In these cosmological settings, the slow roll parameters are computed and a scope of exit from inflation and quasi-exponential expansion are found to be available. Finally, it is observed that warm inflationary expansion can be obtained from this model.

Analysis of entropy generation and Joule heating on curvilinear flow of thermally radiative viscous fluid due to an oscillation of curved Riga surface

This paper investigates the phenomena of heat transfer and entropy generation on time-dependent electro-magnetohydrodynamic boundary layer flow of viscous fluid past a curved oscillatory stretchable Riga surface. Also, the impacts of thermal radiation and Joule heating are accounted for in the energy equation. To develop the flow model in mathematical form, curvilinear coordinates system is followed. The series solution of the governing nonlinear partial differential equations is attained with the help of the homotopy analysis method (HAM). The impacts of various involved parameters like dimensionless radius of curvature, modified magnetic parameter, the proportion of frequency of oscillation of the sheet to its stretchable rate parameter, magnetic parameter, Prandtl number, Eckert number, radiation parameter and Brinkman number on entropy generation, Bejan number, temperature and flow equations are comprehensively examined and results are displayed through graphs. Numerical variation in the magnitude of surface drag force and local Nusselt number under the influence of aforesaid parameters are presented through the tables. Entropy generation is enhanced with an enhancement in a radius of curvature and Brinkman number, while the Bejan number shows opposite behavior for both parameters. The amplitude of velocity distribution shows growing behavior with modified magnetic parameter.