Numerical Simulation of Streaming Potentials Due to Deformation-Induced Hierarchical Flows in Cortical Bone

2000 ◽  
Vol 123 (1) ◽  
pp. 66-70 ◽  
Author(s):  
A. F. T. Mak ◽  
J. D. Zhang

Bone is a very dynamic tissue capable of modifying its composition, microstructure, and overall geometry in response to the changing biomechanical needs. Streaming potential has been hypothesized as a mechanotransduction mechanism that may allow osteocytes to sense their biomechanical environment. A correct understanding of the mechanism for streaming potential will illuminate our understanding of bone remodeling, such as the remodeling associated with exercise hypertrophy, disuse atrophy, and the bone remodeling around implants. In the current research, a numerical model based on the finite element discretization is proposed to simulate the fluid flows through the complicated hierarchical flow system and to calculate the concomitant stress generated potential (SGP) as a result of applied mechanical loading. The lacunae–canaliculi and the matrix microporosity are modeled together as discrete one-dimensional flow channels superposed in a biphasic poroelastic matrix. The cusplike electric potential distribution surrounding the Haversian canal that was experimentally observed and reported in the literature earlier was successfully reproduced by the current numerical calculation.

1981 ◽  
Vol 103 (4) ◽  
pp. 280-292 ◽  
Author(s):  
R. C. Lee ◽  
E. H. Frank ◽  
A. J. Grodzinsky ◽  
D. K. Roylance

The compressive stiffness of articular cartilage was examined in oscillatory confined compression over a wide frequency range including high frequencies relevant to impact loading. Nonlinear behavior was found when the imposed sinusoidal compression amplitude exceeded a threshold value that depended on frequency. Linear behavior was attained only by suitable control of the compression amplitude. This was enabled by real time Fourier analysis of data which provided an accurate assessment of the extent of nonlinearity. For linear viscoelastic behavior, a stiffness could be defined in the usual sense. The dependence of the stiffness on ionic strength and proteoglycan content showed that electrostatic forces between matrix charge groups contribute significantly to cartilage’s compressive stiffness over the 0.001 to 20 Hz frequency range. Sinusoidal streaming potentials were also generated by oscillatory compression. A theory relating the streaming potential field to the fluid velocity field is derived and used to interpret the data. The observed magnitude of the streaming potential suggests that interstitial fluid flow is significant to cartilage behavior over the entire frequency range. The use of simultaneous streaming potential and stiffness data with an appropriate theory appears to be an important tool for assessing the relative contribution of fluid flow, intrinsic matrix viscoelasticity, or other molecular mechanisms to energy dissipation in cartilage. This method is applicable in general to hydrated, charged polymers.


1931 ◽  
Vol 14 (5) ◽  
pp. 563-573 ◽  
Author(s):  
H. A. Abramson ◽  
E. B. Grossman

1. The conditions are described which are necessary for the comparison of certain types of electrokinetic potentials. An experimental comparison is made of (a) electrophoresis of quartz particles covered with egg albumin; and (b) similar experiments by Briggs on streaming potentials. A slight, consistent, difference is found between the electrophoretic potential and the streaming potential. This difference is probably due to the difference in the protein preparations used rather than to real difference in the electrophoretic and streaming potentials. 2. Data are given which facilitate the measurements and enhance the precision of the estimation of electrical mobilities of microscopic particles.


1969 ◽  
Vol 172 (1028) ◽  
pp. 203-225 ◽  

A rapid procedure based on that of Smyth & Wright (1966) is described for obtaining a measure of the permeability of rabbit gall-bladder epithelium to non-electrolytes. The underlying principles are that concentration gradients of permeant molecules produce lower rates of osmotic flow across a membrane than does the same gradient of an impermeant molecule, and that streaming potentials in the gall-bladder are directly proportional to the flow rate. Hence reflexion coefficients (cr’s) were calculated as the ratio of the streaming potential produced by a 0* 1 m gradient of the test solute to the streaming potential produced by a 0T m gradient of an impermeant reference solute, sucrose. The method yields results in agreement with those obtained in the gall-bladder by a zero-flow procedure. In general, the patterns of permeation derived are similar to those obtained in other tissues by the same procedure, by other osmotic procedures, or by direct chemical or tracer methods. The advantages of the method are that (a) large numbers of cr’s can be determined in one experiment with an average standard deviation of ± 8 % ; and (b) the minimum elapsed time between the preparation of a solution and the determination of or is about 90 s, so that cr’s may be obtained for some non-electrolytes subject to gradual chemical transformation in aqueous solution, such as aldehydes. The principles underlying osmotic methods of measuring permeability, and the effects of unstirred layers, are discussed.


2021 ◽  
Author(s):  
Damien Jougnot ◽  
Luong Duy Thanh ◽  
Mariangeles Soldi ◽  
Jan Vinogradov ◽  
Luis Guarracino

<p>Understanding streaming potential generation in porous media is of high interest for hydrological and reservoir studies as it allows to relate water fluxes to measurable electrical potential distributions in subsurface geological settings. The evolution of streaming potential <span>stems</span> from electrokinetic coupling between water and electrical fluxes due to the presence of an electrical double layer at the interface between the mineral and the pore water. Two different approaches can be used to model and interpret the generation of the streaming potential in porous media: the classical coupling coefficient approach based on the Helmholtz-Smoluchowski equation, and the effective excess charge density. Recent studies based on both approaches use a mathematical up-scaling procedure that employs the so-called fractal theory. In these studies, the porous medium is represented by a bundle of tortuous capillaries characterized by a fractal capillary-size distribution law. The electrokinetic coupling between the fluid flow and electric current is obtained by averaging the processes that take place in a single capillary. In most cases, closed-form expressions for the electrokinetic parameters are obtained in terms of macroscopic hydraulic variables like permeability, saturation and porosity. In this presentation we propose a review of the existing fractal distribution models that predict the streaming potential in porous media and discuss their benefits compared against other published models.</p>


Minerals ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 306 ◽  
Author(s):  
Francisca San Martín ◽  
Claudio Aguilar

In the present work, the streaming potential of A. ferrooxidans and pyrite was measured in two environments: fresh and saline water (water with 35 g/L of NaCl) at different pH values. Also, attachment kinetics of A. ferrooxidans to pyrite was studied in fresh and saline water at pH 4. The results show that A. ferrooxidans and pyrite had lower streaming potentials (comparing absolute values) in saline water than in fresh water, indicating the compression in the electrical double layer caused by Cl− and Na+ ions. It was also determined that the bacteria had a higher level of attachment to pyrite in fresh water than in saline water. The high ionic strength of saline water reduced the attractive force between A. ferrooxidans and pyrite, which in turn reduced bacterial attachment. Electrostatic interactions were determined to be mainly repulsive, since the bacteria and mineral had the same charge at pH 4. Despite this, the bacteria adhered to pyrite, indicating that hydrophobic attraction forces and Lifshitz–van der Waals interactions were stronger than electrostatic interactions, which caused the adhesion of A. ferrooxidans to pyrite.


2019 ◽  
Vol 9 (18) ◽  
pp. 3726
Author(s):  
Liu ◽  
Hou ◽  
Qin ◽  
Fu ◽  
Pan

This paper investigates the streaming potentials’ behaviors when fluid flows through the micropores in bone. An experimental setup was developed for measuring the streaming potentials between two surfaces of a bone plate specimen. It was found that the streaming potentials measured increased almost linearly with time under a constant fluid pressure gradient, which does not agree with the prediction from the classical theory of streaming potentials. To explain the reasons associated with the results obtained, a theoretical model was proposed in which the electric charge densities on the inner surfaces of the capillary are unevenly distributed. A formula was developed for solving the model, and the solutions demonstrate that nonuniform accumulations of electric charges carried by the fluid on the inner surfaces of the microcanals in bone can induce streaming potentials which linearly increase with time during the driving air pressure holding period. This phenomenon represents the specific characteristics of bone. The solution implies that the streaming potentials in Haversian canals, lacunas and canaliculi are not affected by electro-viscous resistance in the bone fluid.


1963 ◽  
Vol 18 (6) ◽  
pp. 1263-1264 ◽  
Author(s):  
R. E. Beck ◽  
V. Mirkovitch ◽  
P. G. Andrus ◽  
R. I. Leininger

A system was developed to measure the streaming potential generated between the ends of a capillary by the flow of a fluid through the capillary. Zeta potential can be calculated from the streaming potential. Adequate sensitivity and reproducibility were achieved by making special electrodes: silver wires plated in KCl solution and embedded in agar, careful electrical shielding, and provision for reversal of flow through the capillary to minimize electrode errors. The apparatus was developed to measure streaming potentials generated by either RingerS's solution or blood in contact with capillaries made of different materials such as quartz, polyethylene, etc. An example of a determination using a quartz capillary is presented. interfaces; blood; salt solutions; glass; quartz Submitted on February 25, 1963


2014 ◽  
Vol 607 ◽  
pp. 872-876 ◽  
Author(s):  
Xiao Guang Ren

Computational Fluid Dynamics (CFD) is widely applied for the simulation of fluid flows, and the performance of the simulation process is critical for the simulation efficiency. In this paper, we analyze the performance of CFD simulation application with profiling technology, which gets the portions of the main parts’ execution time. Through the experiment, we find that the PISO algorithm has a significant impact on the CFD simulation performance, which account for more than 90% of the total execution time. The matrix operations are also account for more than 60% of the total execution time, which provides opportunity for performance optimization.


1967 ◽  
Vol 7 (04) ◽  
pp. 359-368 ◽  
Author(s):  
S.H. Raza ◽  
S.S. Marsden

Abstract An experimental study of the flow of fine-textured, aqueous foams through Pyrex tubes is described. The foams range in quality F (ratio of gas volume to total volume) from 0.70 to 0.96 and behave like pseudoplastic fluids. At lower flow rates they exhibit laminar flow and have apparent viscosities which increase with quality, and which cover a range of 15 cp to 255 poise for tubes of 0.25- to 1.50-mm radius ri. At higher flow rates a plug-like type of flow is developed, the extent of which increases with both and ri. When the same foams flow through either open or packed Pyrex tubes, remarkably high streaming potentials phi E are often generated. These can easily reach 50v if nonionic foaming agents are used, but are at least an order of magnitude less for ionic foaming agents. A linear relationship between phi E and the pressure differential phi p is observed; this usually extrapolates to positive values of phi p at phi E of zero. The slope of the line increases with both F and ri. An equation was derived to describe the streaming potential of non-Newtonian fluids in circular tubes and was used to correlate experimental results. The calculated potential is are of the right order of magnitude. Introduction Foams are both unusual and intriguing in their physical properties, and have been the subject of many scientific studies. However, present knowledge of foams is still fragmentary, specific and often contradictory. Apparent viscosity of foam is the physical property of greatest interest to both rheologists and engineers. Sibree reported that the apparent viscosity decreased with increasing shear rate in a manner similar to some non-Newtonian fluids. Penny and Blackman reported that fire-fighting foams had both a limiting shear stress and a tensile yield stress. There is little doubt that some foams at least behave like non-Newtonian fluids, and have apparent viscosities considerably higher than those of either constituent phase. The high apparent viscosity of foam with its concomitant effect on mobility ratio and sweep efficiency no doubt prompted several attempts by research groups to use foam as a displacing agent in porous media. Based on recent experience, most of these groups probably succeeded in completely blocking fluid flow in the porous media and then abandoned their efforts. Two groups apparently found the successful combination of experimental parameters at about the same time. Others have recently added to our knowledge-of foam flow in porous media and its use as a displacing agent. An experimental problem encountered by Fried was a transient blockage of foam flow in porous media when distilled water was used to prepare the foam-producing solution. Fried surmised that this was due to an electrokinetic effect and he eliminated it by using electrolytes in preparing foaming solutions. He also measured the streaming potential of a number of foams in capillary tubes which he found to be appreciably higher than those obtained when the constituent liquid flowed under comparable conditions. This paper presents results of a more comprehensive study of the streaming potential generated by aqueous foam flowing in both open and packed Pyrex tubes. It also adds to knowledge of the rheology of these foams as deduced from their flow behavior in open tubes. APPARATUS AND PROCEDURE A diagram of the apparatus used is shown in Fig. 1. Details of its construction, testing and use are described elsewhere. Careful selection of materials, extreme cleanliness and rather elaborate electrical insulation and shielding were necessary to obtain reproducible results (15 percent). Both streaming potential and streaming current were measured with an electrometer. The design of the foam generator developed for this work is novel (Fig. 2). SPEJ P. 359ˆ


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