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TECHNICAL PAPERS

On the Electric Potentials Inside a Charged Soft Hydrated Biological Tissue: Streaming Potential Versus Diffusion Potential

[+] Author and Article Information
W. Michael Lai, Van C. Mow, Daniel D. Sun, Gerard A. Ateshian

Departments of Mechanical Engineering, Biomedical Engineering and Orthopaedic Surgery, Columbia University, New York, NY 10027

J Biomech Eng 122(4), 336-346 (Feb 28, 2000) (11 pages) doi:10.1115/1.1286316 History: Received June 22, 1999; Revised February 28, 2000
Copyright © 2000 by ASME
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References

Figures

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(a) Schematic diagram to show the flow convection effect on a uniform distribution of cation ⊕ corresponding to a uniform distribution of fixed negative charges (not shown). The convection effect causes a convection current, which is countered by the conduction current driven by the streaming potential. (b) Schematic diagram to show the diffusion effect on a nonuniform distribution of cation ⊕ corresponding to a nonuniform distribution of fixed negative charges (not shown). The diffusion effect causes a diffusion current, which is countered by the conduction current driven by the diffusion potential.
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Schematic of open circuit one-dimensional permeation experiment with the upstream pressure greater than the downstream pressure (pu*>pd*); flow is from left to right
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Steady permeation: electric potential across the tissue from the inside (Δψ), and electric potential across the tissue from the outside(Δψ*), as a function of initial fixed charge density. For Ha=0.3 MPa, the diffusion potential dominates over streaming potential. (D+=0.5×10−9m2/s,D=0.8×10−9m2/s,K=7×1014Ns/m4ow=0.80,c+=0.15M,Δp=30 KPa).
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Steady permeation: electric potential across the tissue from the inside (Δψ), and electric potential across the tissue from the outside(Δψ*), as a function of the initial fixed charge density. For Ha=0.60 MPa, the streaming potential effect dominates over the diffusion potential effect, except for a region of low FCD. Other parameters same as in Fig. 3.
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Steady permeation: compressive strain distribution inside the tissue for three values of Ha. The strain is caused by frictional force of permeation between water and solid matrix. The strain increases monotonically in the downstream direction. (coF=0.2 mEq/ml, other parameters same as in Fig. 3).
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Steady permeation: fixed charge density increases in the downstream direction due to drag-induced compaction (see Fig. 5)
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Steady permeation: electric potential distribution inside the tissue for four values of aggregate modulus. Again, the diffusion potential dominates over the streaming potential for tissues with small aggregate modulus, the reverse is true for tissues with larger aggregate modulus (same parameter values as in Fig. 5).
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(a) Schematic of an open-circuit, one dimensional ramped-displacement, stress-relaxation experiment. The bathing solution NaCl concentration c* is kept fixed during the experiment, and the motion of the loading piston is prescribed in (b). The surface to surface strain is −0.1, to=200 s and h=2 mm.
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Stress relaxation: electric potential distribution inside the tissue at various times for Ha=0.3 MPa. The potential increases in the direction toward the bottom indicating that it is dominated by the diffusion potential effect. Fluid flow is in the upward direction into the porous-permeable, loading-platen during the entire compression phase. (coF=0.2 mEq/ml, other parameters same as in Fig. 3).
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Stress relaxation: compressive strain distribution inside the tissue at various times. The nonuniformity of the strain is caused by frictional drag force of permeation between water and solid matrix. The strain increases monotonically in the upward (flow) direction.
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Stress relaxation: FCD distribution caused by the drag-induced compaction (see Fig. 10)
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Stress relaxation: electric potential distribution inside the tissue at time t=200 s (i.e., at the end of the compression-ramp phase) for four values of aggregate modulus. For more rigid tissue (Ha>0.61 MPa), the streaming potential effect dominates whereas for softer tissues (Ha<0.61 MPa), the diffusion potential effect dominates. (coF=0.2 mEq/ml, other parameters same as in Fig. 3).
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Stress relaxation: electric potential across the tissue from the inside (Δψ) and the electrochemical potential for anion across the tissue (Δμ̃). Note: Ag/AgCl electrodes measure the electrochemical potentials (−M/Fc)Δμ̃.

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