scholarly journals Steady Stokes flow of a non-Newtonian Reiner-Rivlin fluid streaming over an approximate liquid spheroid

2020 ◽  
Vol 14 (2) ◽  
Author(s):  
Bharat Raj Jaiswal
Keyword(s):  
Boundary Conditions ◽  
Stokes Flow ◽  
Analytical Investigation ◽  
Droplet Surface ◽  
Shear Stresses ◽  
Stokes Approximation ◽  
Linear Framework ◽  
Viscous Droplet ◽  
Parameters Of Interest ◽  
Streaming Flow

The investigation is carried out to study steady Stokes axisymmetrical Reiner-Rivlin streaming flow over a fixed viscous droplet, and this droplet to be deformed sphere in shape. As boundary conditions, vanishing of radial velocities, continuity of tangential velocities and shear stresses at the droplet surface are used. The very common configuration of approximate sphere governed by polar equation $\tilde{r} =a[1 +\alpha_m \vartheta_m(\zeta)]$ has been considered for the study to $o(\varepsilon)$ describing the distortion. Based on the Stokes approximation, an analytical investigation is achieved in the orthogonal curve linear framework in an unbounded region of a Reiner-Rivlin fluid. In constraining cases, some earlier noted outcomes are obtained. Also, the yielded outcomes for the drag have been compared with solution existing in the literature. Further, the change for both force and pressure are evaluated with deflection w.r.t. the parameters of interest and shown through table and graphs.

Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) With a Gap in Mindlin Plates or Panels

2007 ◽  
Author(s):  
U. Yuceoglu ◽  
O. Gu¨vendik ◽  
V. O¨zerciyes
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Lap Joint ◽  
Bending Vibrations ◽  
Joint System ◽  
Adhesive Layers ◽  
Bonded Joint ◽  
Free Bending

In this present study, the “Free Bending Vibrations of a Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap in Mindlin Plates or Panels” are theoretically analyzed and are numerically solved in some detail. The “plate adherends” and the upper and lower “doubler plates” of the “Bonded Joint” system are considered as dissimilar, orthotropic “Mindlin Plates” joined through the dissimilar upper and lower very thin adhesive layers. There is a symmetrically and centrally located “Gap” between the “plate adherends” of the joint system. In the “adherends” and the “doublers” of the “Bonded Joint” assembly, the transverse shear deformations and the transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers are assumed to be linearly elastic continua with transverse normal and shear stresses. The “damping effects” in the entire “Bonded Joint” system are neglected. The sets of the dynamic “Mindlin Plate” equations of the “plate adherends”, the “double doubler plates” and the thin adhesive layers are combined together with the orthotropic stress resultant-displacement expressions in a “special form”. This system of equations, after some further manipulations, is eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in terms of the “state vectors” of the problem. Hence, the final set of the aforementioned “Governing Systems of Equations” together with the “Continuity Conditions” and the “Boundary conditions” facilitate the present solution procedure. This is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials). The present theoretical formulation and the method of solution are applied to a typical “Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) with a Gap”. The effects of the relatively stiff (or “hard”) and the relatively flexible (or “soft”) adhesive properties, on the natural frequencies and mode shapes are considered in detail. The very interesting mode shapes with their dimensionless natural frequencies are presented for various sets of boundary conditions. Also, several parametric studies of the dimensionless natural frequencies of the entire system are graphically presented. From the numerical results obtained, some important conclusions are drawn for the “Bonded Joint System” studied here.

Stresses in a Spherical Shell With a Nonradial Nozzle

1967 ◽  
Vol 34 (2) ◽  
pp. 299-307 ◽  
Author(s):  
D. E. Johnson
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Shell Theory ◽  
Analytical Investigation ◽  
Type Method ◽  
Cylindrical Nozzle ◽  
Pass Through ◽  
External Forces ◽  
Radial Nozzle

An analytical investigation is made of the stresses due to external forces and moments acting on an elastic nonradial circular cylindrical nozzle attached to a spherical shell. The nozzle (a cylindrical shell) is nonradial in the sense that its axis is inclined and does not pass through the center of the sphere. Results are obtained by combining solutions from shell theory by a Galerkin-type method so as to satisfy boundary conditions at the intersection of the two shells. It is found that, as the nozzle inclination increases, the stresses change gradually from those previously given by Bijlaard for the radial nozzle.

Stokes flow with slip and Kuwabara boundary conditions

2002 ◽  
Vol 112 (3) ◽  
pp. 463-475 ◽  
Author(s):  
Sunil Datta ◽  
Satya Deo
Keyword(s):  
Boundary Conditions ◽  
Stokes Flow

Stokes Flow Through a Row of Cylinders Between Parallel Walls: Model for the Glomerular Slit Diaphragm

1994 ◽  
Vol 116 (2) ◽  
pp. 184-189 ◽  
Author(s):  
M. Claudia Drumond ◽  
William M. Deen
Keyword(s):  
Stokes Flow ◽  
Stokes Equations ◽  
Slit Diaphragm ◽  
Hydraulic Permeability ◽  
Shear Stresses ◽  
Two Factors ◽  
Additional Resistance ◽  
Flow Through ◽  
Experimental Values ◽  
Glomerular Capillaries

As a model for flow through the slit diaphragms which connect the epithelial foot processes of renal glomerular capillaries, finite element solutions of Stokes equations were obtained for flow perpendicular to a row of cylinders confined between parallel walls. A dimensionless “additional resistance” (f), defined as the increment in resistance above the Poiseuille flow value, was computed for L/W≤4 and 0.1≤ R/L≤0.9, where L is half the distance between cylinder centers, W is half the distance between walls and R is the cylinder radius. Two factors contributed to f: the drag on the cylinders, and the incremental shear stresses on the walls of the channel. Of these two factors, the drag on the cylinders tended to be dominant. A more complex representation of the slit diaphragm, suggested in the literature, was also considered. The predicted hydraulic permeability of the slit diaphragm was compared with experimental values of the overall hydraulic permeability of the glomerular capillary wall.

Effects of Position (or Location) of Non-Centrally Bonded Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) on Bending Vibrations of Composite Mindlin Plates or Panels

2010 ◽  
Author(s):  
U. Yuceoglu ◽  
O¨. Gu¨vendik
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Lap Joint ◽  
Joint System ◽  
Adhesive Layers ◽  
Present Solution ◽  
Stress Resultant ◽  
Bonded Joint

In the present study, the “Effects of Position (or Location) of Non-Centrally Bonded Symmetric Double Doubler Joint in Composite Mindlin Plates or Panels” are theoretically analyzed and are numerically solved in some detail. The “Plate Adherends” and the upper and lower “Doubler Plates” of the “Bonded Joint System” are considered as dissimilar, orthotropic “Mindlin Plates” joined through the dissimilar upper and lower very thin adhesive layers. The transverse and rotary moments of inertia are included in the analysis. The relatively very thin adhesive layers are assumed to be linearly elastic continua with transverse normal and shear stresses. The “damping effects” in the entire “Bonded Joint System” are neglected. The sets of the dynamic “Mindlin Plate” equations of the “Plate Adherends”, the “Double Doubler Plates” and the thin adhesive layers are combined together with the orthotropic stress resultant-displacement expressions in a “special form”. This system of equations, after some further manipulations, is eventually reduced to a set of the “Governing System of the First Order Ordinary Differential Equations” in terms of the “state vectors” of the problem. Hence, the final set of the aforementioned “Systems of Equations” together with the “Continuity Conditions” and the “Boundary Conditions” facilitate the present solution procedure. This is the “Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials). The present theoretical analysis and the present method of solution are applied to a typical “Non-Centrally Positioned (or Located) Symmetric Double Lap Joint (or Symmetric Double Doubler Joint) System”. The effects of the location (or position) of the “Bonded Joint System” and also of the relatively “Stiff (or “Hard”) and the relatively “Flexible” (or “Soft”) adhesive properties, on the natural frequencies and mode shapes are considered in some detail. The very interesting mode shapes with their dimensionless natural frequencies are presented for various sets of “Boundary Conditions”. From the numerical results obtained, some important conclusions are drawn for the “Bonded Joint System” studied here.

Computational Modeling of Shear-Based Hemolysis Caused by Renal Obstruction

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Polina A. Segalova ◽  
K. T. Venkateswara Rao ◽  
Christopher K. Zarins ◽  
Charles A. Taylor
Keyword(s):  
Blood Flow ◽  
Boundary Conditions ◽  
Renal Artery ◽  
Aortic Aneurysms ◽  
Cfd Modeling ◽  
Patient Specific ◽  
Shear Stresses ◽  
Baseline Model ◽  
Implantable Medical Devices ◽  
Renal Obstruction

As endovascular treatment of abdominal aortic aneurysms (AAAs) gains popularity, it is becoming possible to treat certain challenging aneurysmal anatomies with endografts relying on suprarenal fixation. In such anatomies, the bare struts of the device may be placed across the renal artery ostia, causing partial obstruction to renal artery blood flow. Computational fluid dynamics (CFD) was used to simulate blood flow from the aorta to the renal arteries, utilizing patient-specific boundary conditions, in three patient models and calculate the degree of shear-based blood damage (hemolysis). We used contrast-enhanced computed tomography angiography (CTA) data from three AAA patients who were treated with a novel endograft to build patient-specific models. For each of the three patients, we constructed a baseline model and endoframe model. The baseline model was a direct representation of the patient’s 30-day post-operative CTA data. This model was then altered to create the endoframe model, which included a ring of metallic struts across the renal artery ostia. CFD was used to simulate blood flow, utilizing patient-specific boundary conditions. Pressures, flows, shear stresses, and the normalized index of hemolysis (NIH) were quantified for all patients. The overall differences between the baseline and endoframe models for all three patients were minimal, as measured though pressure, volumetric flow, velocity, and shear stress. The average NIH across the three baseline and endoframe models was 0.002 and 0.004, respectively. Results of CFD modeling show that the overall disturbance to flow caused by the presence of the endoframe struts is minimal. The magnitude of the NIH in all models was well below the accepted design and safety threshold for implantable medical devices that interact with blood flow.

Postbuckling and Mode Jumping Analysis of Deep Hygrothermally Buckled Angle-Ply Laminated Plates

2016 ◽  
Vol 16 (01) ◽  
pp. 1640010 ◽  
Author(s):  
Yifeng Zhong ◽  
Liangliang Zhang ◽  
Xiaoping Zhou
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Governing Equation ◽  
Present Method ◽  
Analytical Investigation ◽  
Laminated Plates ◽  
Plane Boundary ◽  
Solution Approach ◽  
Post Secondary ◽  
Secondary Bifurcation

An analytical investigation is performed to study the secondary instability and dynamic aspects of the mode jumping in hygrothermally buckled angle-ply laminated plates. The governing partial differential equations (PDEs) and constitution relations are derived rigorously from an asymptotically correct, geometrically nonlinear theory. A novel and relatively simpler solution approach is developed to solve the two coupled fourth-order PDEs, namely, the compatibility equation and the dynamic governing equation. The von Kármán plate equation, namely, the coupled nonlinear governing equation, is reduced to a system of nonlinear ordinary differential equations (ODEs) by expressing the transverse deflection as a series of linear buckling modes. The ODEs, combined with the nonlinear algebraic constraint equations obtained from in-plane boundary conditions, are then solved numerically under the parametric variation of the temperature and moisture. The comparison between the present method and the FEA shows that the secondary bifurcation point of the hygrothermally loaded plate is far beyond the primary buckling point, and the jump behavior cannot be predicted correctly without sufficient assumed modes, while the present method has the capability of exploring deeply into the post-secondary buckling realm and capture the mode jumping phenomenon for various combinations of plate configurations boundary conditions. Furthermore, by monitoring free vibration along the stable primary postbuckling and the jumped equilibrium paths, we find that a mode shifting phenomenon (the exchange of vibration modes) exists in the primary post-buckling regime.

scholarly journals From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

2021 ◽  
Vol 44 (1) ◽  
Author(s):  
Hendrik Ender ◽  
Jan Kierfeld
Keyword(s):  
Symmetry Breaking ◽  
Boundary Conditions ◽  
Spontaneous Symmetry Breaking ◽  
Stokes Flow ◽  
Peclet Number ◽  
Swimming Velocity ◽  
Marangoni Flow ◽  
Péclet Number ◽  
Constant Flux ◽  
Flux Boundary Conditions

AbstractWe present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air–water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion–advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air–water–swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.

Sign in / Sign up

Export Citation Format

Share Document