Protein aggregation, one of the common molecular mechanisms for neurodegenerative diseases, is affected by variety of physical factors, one of which is shear rate of protein solution. This paper provides theoretical background on the shear rate in the experimental system we have proposed to effectively apply and control shear. We carried out the mathematical analysis of the flow field resulted from torsional or transverse oscillation on the outer boundary between two concentric hemispheres by perturbation method. We have obtained analytical solutions for the velocity field, the shear rate, and the flow pattern of steady streaming created by the nonlinear interaction of the oscillatory flow.

References

References
1.
Ross
,
C. A.
, and
Poirier
,
M. A.
,
2004
, “
Protein Aggregation and Neurodegenerative Disease
,”
Nat. Med.
,
10
, pp.
S10
S17
.10.1038/nm1066
2.
Irvine
,
G. B.
,
El-Agnaf
,
O. M.
,
Shankar
,
G. M.
, and
Walsh
,
D. M.
,
2008
, “
Protein Aggregation in the Brain: The Molecular Basis for Alzheimer’s and Parkinson’s Diseases
,”
Mol. Med.
,
14
(
7–8
), pp.
451
464
.
3.
Cromwell
,
M. E.
,
Hilario
,
E.
, and
Jacobson
,
F.
,
2006
, “
Protein Aggregation and Bioprocessing
,”
AAPS J.
,
8
(
3
), pp.
E572
E579
.10.1208/aapsj080366
4.
Philo
,
J. S.
, and
Arakawa
,
T.
,
2009
, “
Mechanisms of Protein Aggregation
,”
Curr. Pharm. Biotechnol.
,
10
(
4
), pp.
348
351
.10.2174/138920109788488932
5.
Frieden
,
C.
,
2007
, “
Protein Aggregation Processes: In Search of the Mechanism
,”
Protein Sci.
,
16
(
11
), pp.
2334
2344
.10.1110/ps.073164107
6.
Wan
,
Y.
,
Vasan
,
S.
,
Ghosh
,
R.
,
Hale
,
G.
, and
Cui
,
Z.
,
2005
, “
Separation of Monoclonal Antibody Alemtuzumab Monomer and Dimers Using Ultrafiltration
,”
Biotechnol. Bioeng.
,
90
(
4
), pp.
422
432
.10.1002/bit.20416
7.
Kim
,
K.
,
Chen
,
V.
, and
Fane
,
A.
,
1993
, “
Some Factors Determining Protein Aggregation During Ultrafiltration
,”
Biotechnol. Bioeng.
,
42
(
2
), pp.
260
265
.10.1002/bit.260420216
8.
Maa
,
Y. F.
, and
Hsu
,
C. C.
,
1997
, “
Protein Denaturation by Combined Effect of Shear and Air-Liquid Interface
,”
Biotechnol. Bioeng.
,
54
(
6
), pp.
503
512
.10.1002/(SICI)1097-0290(19970620)54:6<503::AID-BIT1>3.0.CO;2-N
9.
Gopinath
,
A.
,
1992
, “
Convective Heat Transfer in Acoustic Streaming Flows
,” Ph.D. thesis,
University of California
, Los Angeles, p.
229
.
10.
Mahler
,
H. C.
,
Friess
,
W.
,
Grauschopf
,
U.
, and
Kiese
,
S.
,
2009
, “
Protein Aggregation: Pathways, Induction Factors and Analysis
,”
J. Pharm. Sci.
,
98
(
9
), pp.
2909
2934
.10.1002/jps.21566
11.
Zapryanov
,
Z.
, and
Chervenivanova
,
E.
,
1981
, “
The Flow Field Induced by the Torsional Oscillations of a Spherical Cell Containing a Fluid Drop
,”
Int. J. Multiphase Flow
,
7
(
3
), pp.
261
270
.10.1016/0301-9322(81)90021-5
12.
Riley
,
N.
,
1966
, “
On a Sphere Oscillating in a Viscous Fluid
,”
Q. J. Mech. Appl. Math.
,
19
(
4
), pp.
461
472
.10.1093/qjmam/19.4.461
13.
Gopinath
,
A.
,
1993
, “
Steady Streaming Due to Small-Amplitude Torsional Oscillations of a Sphere in a Viscous Fluid
,”
Q. J. Mech. Appl. Math.
,
46
(
3
), pp.
501
520
.10.1093/qjmam/46.3.501
14.
Repetto
,
R.
,
Siggers
,
J. H.
, and
Stocchino
,
A.
,
2008
, “
Steady Streaming Within a Periodically Rotating Sphere
,”
J. Fluid Mech.
,
608
, pp.
71
80
.10.1017/S002211200800222X
15.
Lieber
,
B. B.
,
2000
,
The Biomedical Engineering Handbook
(The Electrical Engineering Handbook Series), Vol.
1
,
2nd ed.
,
J. D.
Bronzino
, ed.,
CRC Press
,
Boca Raton
, Chap. 30.
16.
Quartapelle
,
L.
, and
Verri
,
M.
,
1995
, “
On the Spectral Solution of the Three-Dimensional Navier–Stokes Equations in Spherical and Cylindrical Regions
,”
Comput. Phys. Commun.
,
90
(
1
), pp.
1
43
.10.1016/0010-4655(95)00072-N
17.
Pan
,
W.
,
Filobelo
,
L.
,
Pham
,
N. D.
,
Galkin
,
O.
,
Uzunova
,
V. V.
, and
Vekilov
,
P. G.
,
2009
, “
Viscoelasticity in Homogeneous Protein Solutions
,”
Phys. Rev. Lett.
,
102
(
5
), p.
058101
.10.1103/PhysRevLett.102.058101
18.
Böhme
,
G.
,
1992
, “
On Steady Streaming in Viscoelastic Liquids
,”
J. Non-Newtonian Fluid Mech.
,
44
, pp.
149
170
.10.1016/0377-0257(92)80049-4
19.
Meskauskas
,
J.
,
Repetto
,
R.
, and
Siggers
,
J. H.
,
2011
, “
Oscillatory Motion of a Viscoelastic Fluid Within a Spherical Cavity
,”
J. Fluid Mech.
,
685
, pp.
1
22
.10.1017/jfm.2011.263
20.
Repetto
,
R.
,
Siggers
,
J. H.
, and
Meskauskas
,
J.
,
2014
, “
Steady Streaming of a Viscoelastic Fluid Within a Periodically Rotating Sphere
,”
J. Fluid Mech.
,
761
, pp.
329
347
.10.1017/jfm.2014.546
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