•The theoretical suggestion of variable fluid density gives effective and practical results for pressure distribution.•The high values of non-constant fluid density parameters enforce the pressure ...gradient and pressure rise in a cervical canal, which help sperms to be more active in ovum fertilization.•Reynolds and Froude numbers have two opposite behavior on pressure gradient profile.•Dual role phenomena visualized on Weissenberg number behavior on pressure rise distribution.•High values of ∊ angle causes to a growing in pressure rise in all pumping regions.•AST is an effective technique for solving a highly nonlinear problem without perturbation techniques.
The density of sperms via the cervical canal has an essential vital role in enhancing the pregnancy processes for organisms. Hence, this study aims to investigate a new theoretical suggestion for the variable density effects on the creeping flow of a non-Newtonian nanofluid in the cervical canal. The density is supposed to vary with the fluid temperature and concentration. The fluid is mathematically designated with a system of PDEs. This system of a physical model is simplified/streamlined using appropriate transformation (δ≪1) to an ODEs. A resulting model is analytically recurrences by adaptive shooting technique (AST). Results for pressure gradient and pressure rise distributions are outlined/sketched. Furthermore, streamlines showed in a contoured frame. Validation of results was confirmed through a comparison with Noreen et al3. Outgrowths state that high values of concentration and temperature-dependent density parameters enforce the pressure gradient and pressure rise in a cervical canal, which helps sperms to be more active in ovum fertilization.
Fluid-flow devices with low dissipation, but large contact area, are of importance in many applications. A well-known strategy to design such devices is multi-scale topology optimization (MTO), where ...optimal microstructures are designed within each cell of a discretized domain. Unfortunately, MTO is computationally very expensive since one must perform homogenization of the evolving microstructures, during each step of the optimization process. Furthermore, methods to impose a desired contact area have not been pursued in MTO. Here, we propose a graded multiscale topology optimization for minimizing the dissipation in fluid-flow devices, subject to a desired contact area. Several pre-selected, but size-parameterized and orientable microstructures are chosen; their constitutive tensors and contact areas are pre-computed at a finite number of sizes. Then, during optimization, a simple interpolation is used to significantly reduce the computation while retaining many of the benefits of MTO. The algorithm allows for continuous switching between microstructures during optimization, but prevents mixing through penalization. The optimization is carried out using a neural network (NN) since: (1) the NN implicitly guarantees the partition of unity, i.e., ensures that the net volume fraction of microstructures in each cell is unity, (2) the number of design variables is only weakly dependent of the number of microstructure used, (3) it supports automatic differentiation, thereby eliminating manual sensitivity analysis, and (4) one can perform topology optimization at a coarser scale, and then extract a high-resolution design via a simple post-processing step. Several numerical results are presented to illustrate the proposed framework.
Graphical abstract
Given a set of candidate microstructures and a fluid topology optimization problem, a neural network (NN) selects appropriate microstructures, optimizes their size and orientation to produce a graded multi-scale design.
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials ...that appear in them. This article presents a boundary integral method that can be used to study the motion of rigid particles in three‐dimensional periodic Stokes flow with confining walls. A centerpiece of our method is the highly accurate special quadrature method, which is based on a combination of upsampled quadrature and quadrature by expansion, accelerated using a precomputation scheme. The method is demonstrated for rodlike and spheroidal particles, with the confining geometry given by a pipe or a pair of flat walls. A parameter selection strategy for the special quadrature method is presented and tested. Periodic interactions are computed using the spectral Ewald fast summation method, which allows our method to run in O(nlogn) time for n grid points in the primary cell, assuming the number of geometrical objects grows while the grid point concentration is kept fixed.
We present a highly accurate boundary integral method for simulation of rigid particles in three‐dimensional periodic Stokes flow with confining walls. Our method includes a special quadrature method based on upsampled quadrature and quadrature by expansion, accelerated using a precomputation scheme. A parameter selection strategy for the special quadrature method is presented and tested for rodlike and spheroidal particles, and for confining geometry given by a pipe or a pair of flat walls.
The hydrodynamic lift velocity of a neutrally buoyant fibre in a simple shear flow near a wall is determined for small, but non-zero, fibre Reynolds number, illustrating the role of non-sphericity in ...lift. The rotational motion and effects of fibre orientation on lift are treated for fibre positions that induce and do not induce solid-body wall contacts. When the fibre does not contact the wall its lift velocity can be obtained in terms of the Stokes flow field by using a generalized reciprocal theorem. The Stokes velocity field is determined using slender-body theory with the no-slip velocity at the wall enforced using the method of images. To leading order the lift velocity at distances large compared with the fibre length and small compared with the Oseen length is found to be
$0.0303\unicodeSTIX{x1D70C}\dot{\unicodeSTIX{x1D6FE}}^{2}l^{2}a/(\unicodeSTIX{x1D707}\ln 2l/a)$
, where
$l$
and
$a$
are the fibre half-length and radius,
$\unicodeSTIX{x1D70C}$
is the density,
$\dot{\unicodeSTIX{x1D6FE}}$
is the shear rate and
$\unicodeSTIX{x1D707}$
is the viscosity of the fluid. When the fibre is close enough to the wall to make solid-body contact during its rotational motion, a process known as pole vaulting coupled with inertially induced changes of fibre orientation determines the lift velocity. The order of magnitude of the lift in this case is larger by a factor of
$l/a$
than when the fibre does not contact the wall and it reaches a maximum of
$0.013\unicodeSTIX{x1D70C}\dot{\unicodeSTIX{x1D6FE}}^{2}l^{3}/(\unicodeSTIX{x1D707}\ln l/a)$
for the case of a highly frictional contact and about half that value for a frictionless contact. These results are used to illustrate how particle shape can contribute to separation methods such as those in microfluidic channels or cross-flow filtration processes.
The combination of fluid-structure interactions with stochasticity, due to thermal fluctuations, remains a challenging problem in computational fluid dynamics. We develop an efficient scheme based on ...the stochastic immersed boundary method, Stokeslets, and multiple timestepping. We test our method for spherical particles and filaments under purely thermal and deterministic forces and find good agreement with theoretical predictions for Brownian Motion of a particle and equilibrium thermal undulations of a semi-flexible filament. As an initial application, we simulate bio-filaments with the properties of F-actin. We specifically study the average time for two nearby parallel filaments to bundle together. Interestingly, we find a two-fold acceleration in this time between simulations that account for long-range hydrodynamics compared to those that do not, suggesting that our method will reveal significant hydrodynamic effects in biological phenomena.
•A method for simulating fluid-structure interactions with thermal fluctuations.•Acceleration using a combination of the immersed boundary method, Stokeslets and multiple timesteps.•This approximation method agrees with Brownian dynamics and equilibrium thermal modes of semi-flexible filaments.•We simulate F-actin dynamics on 1-second, 1-micron scales including hydrodynamic effects.•Hydrodynamic effects introduce a 2-fold change in the time for bundling.
We propose a family of mixed finite elements that are robust for the nearly incompressible strain gradient model, which is a fourth-order singular perturbed elliptic system. The element is similar to ...C. Taylor and P. Hood,
Comput. & Fluids
,
1
(1973), 73–100 in the Stokes flow. Using a uniform discrete B-B inequality for the mixed finite element pairs, we show the optimal rate of convergence that is robust in the incompressible limit. By a new regularity result that is uniform in both the materials parameter and the incompressibility, we prove the method converges with 1/2 order to the solution with strong boundary layer effects. Moreover, we estimate the convergence rate of the numerical solution to the unperturbed second-order elliptic system. Numerical results for both smooth solutions and the solutions with sharp layers confirm the theoretical prediction.
By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme ...has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the techniques of the differential and difference Janet/Gröbner bases for performing related computations. To prove the strong consistency of the generated scheme, we use these bases to correlate the differential ideal generated by the polynomials in the Stokes equations with the difference ideal generated by the polynomials in the constructed difference scheme. As this takes place, our difference scheme is conservative and inherits permutation symmetry of the differential Stokes flow. For the obtained scheme, we compute the modified differential system and use it to analyze the scheme’s accuracy.
It is well known that a rigid non-slippery particle in unsteady motion can experience a Basset history force with the signature
$1/\unicodeSTIX{x1D6FF}$
decay due to a Stokes boundary layer of ...thickness
$\unicodeSTIX{x1D6FF}$
. For a uniform slip particle with slip length
$\unicodeSTIX{x1D706}$
, however, a persistent force plateau can replace the usual Basset decay at
$\unicodeSTIX{x1D6FF}$
below the slip–stick transition (SST) point
$\unicodeSTIX{x1D6FF}\sim \unicodeSTIX{x1D706}$
(Premlata & Wei,
J. Fluid Mech.
, vol. 866, 2019, pp. 431–449). Here we analyse the hydrodynamic force on an oscillating stick–slip Janus particle, showing that it can display unusual history force responses that are of neither the no-slip nor the purely slip type but mixed with both. Solving the oscillatory Stokes flow equation together with a matched asymptotic boundary layer theory, we find that the persistent force plateau seen for a uniform slip particle may be destroyed by the presence of the stick portion of a stick–slip Janus particle. Instead, a
$1/\unicodeSTIX{x1D6FF}$
Basset force of amplitude smaller than the no-slip counterpart will re-emerge to dominate the high frequency viscous force response again. This re-entry Basset force, which occurs only after making a stick patch on a slippery particle, is also found to depend solely on the coverage of the stick face irrespective of the slip length of the slip face. When the stick portion is small, in particular, the re-entry Basset decay will exhibit a slip plateau on its tail, displaying a distinctive re-entrant history force transition prior to the SST. But if changing this tiny stick face to be slippery, no matter how small the slip length is, the re-entry Basset decay will disappear and a constant force plateau will return to dominate the force response again. These unusual force responses arising from mixed stick–slip or non-uniform slip effects may not only provide unique hydrodynamic fingerprints for characterizing heterogeneous particles, but also have potential uses in active manipulation and sorting of these particles.
In the holographic model of Dirac semimetals, the Einstein–Maxwell scalar gravity with the auxiliary
U
(1)-gauge field, coupled to the ordinary Maxwell one by a
kinetic mixing
term, the black brane ...response to the electric fields and temperature gradient has been elaborated. Using the foliation by hypersurfaces of constant radial coordinate we derive the exact form of the Hamiltonian and equations of motion in the phase space considered. Examination of the Hamiltonian constraints enables us, to the leading order expansion of the linearised perturbations at the black brane event horizon, to derive the Stokes equations for an incompressible doubly charged fluid. Solving the aforementioned equations, one arrives at the DC conductivities for the holographic Dirac semimetals.
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