Complex Pressure Pulses in Micro-Channels Magnetically Induced

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Proceedings of the ASME 2009 International Mechanical Engineering Congress & Exposition IMECE2009

November 13-19, Lake Buena Vista, Florida, USA

IMECE2009-10473

https://www.researchgate.net/publication/267590435_Investigation_Into_the_Crossflow_Microfiltration_Process_Utilizing_Ceramic_Membrane_Applied_to_Bacteria_Reduction_and_Clarifying_of_Acai_Juice?el=1_x_8&enrichId=rgreq-b356627b-15cf-4064-8440-ed40f3c6b68a&enrichSource=Y292ZXJQYWdlOzI1NzM0NDgyOTtBUzoxNzk4NzIwNTU5NjM2NDhAMTQxOTg5NjI0ODc5MA==

2 Copyright © 2009 by ASME

complex patterns due to the interplay of the confluent flows coming from tubes 1 and 2.

At station C can be connected the working tube, in this case tube C E. In this study, tube C E is assumed to be a micro-channel of diameter significant smaller than that of the other four tubes.

ANALISYS For the system of figure 1, the equation of flow is

ρ · PB PCL

(1) The corresponding constitutive equation, assuming magnetically-induced plasticity, is τ τ t η · (2) In this the Bingham fluid model is used. Further it is assumed that the magnetic fields changes in time as follows

τ t τ∞ · 1 β · cos ω · t (3) The rate of flow is Q t 2 · π · w · r · dr (4) Correspondingly, for the other tubes, the equations are ρ · PB PC

L (5)

τ τ t η · (6) τ t τ∞ · 1 β · cos ω · t (7) Q t 2 · π · w · r · dr (8) ρ · PC PD

L (9)

τ η · (10) Q t 2 · π · w · r · dr (11) Rate of flow in the working tuve C E is assumed much smaller than the rate of flow in the other tubes. In this way the general continuity condition leads to Q t Q t Q t (12) or

w · r · dr w · r · dr w · r · dr (13) The pressure is assumed of the form PB t P · 1 α · cos ω · t (14)

f t 1 α · cos ω · t (15) g t 1 β · cos ω · t (16) Dimensionless variables are next defined, i.e., w r t τ

ττ

PB

P·

(17)

PCPC

ρ · w

LLa

τ

τρ · w

In this way, the dimensionless momentum equations are

· w PB· PCL

∞ · (18)

· w PB· PCL

∞ · (19)

· w PC PDL

(20) The velocity is modelled as w r , t A t 1 r A t 1 r (21)

A t 1 r A t 1 r w r , t A t 1 r A t 1 r (22)

A t 1 r A t 1 r w r , t A t 1 r A t 1 r (23)

A t 1 r A t 1 r wherefrom, after ordering in powers of r, it is found A t Re · τ∞ · g t (24)

· A A t A t A tP · P

L (25)


A t · Re · A (26) A t · Re · A (27) A t · Re · A (28) A t · Re · A (29) . . . Substituting (24), (26), (27), (28), (29),… in (25), there follows the equation for A t 4 · · A t · A t

·· A t

· ··

A t τ · Re · g t · g t·

·

g t PB· PCL

(30) It is assumed A t x x sin ω t x cos ω t x sin ω tx cos ω t (31) and P λ λ sin ω t λ cos ω t λ sin ω tλ cos ω t (32) where x , x , … y λ , λ , … are constants to be determined. Next (31), (32) are substituted into (30), and similary (13), (19), (20). A system of 20 equations and equal number of unknowns is thus generated, where from all dependent variables are found. RESULTS In the following, some results are shown for the pressure at station C and total rate of flow

Rate of flow and pressure for:

τ 0,1; τ 0,9; β 0,3; β 0,3; ω 1; ω 10; ω 5 a 0,1; a 0,5; a 1; α 1

Rate of flow and pressure for: τ 0,1; τ 0,9; β 0,3; β 0,3; ω 1; ω 10; ω 5 a 0,1; a 0,5; a 1; α 0,3



τ 0,5; τ 0,1; β 0,3; β 0,3; ω 1; ω 10; ω 5 a 0,1; a 0,5; a 1; α 0,3


τ 0,2; τ 0,2; β 0,3; β 0,3; ω 1; ω 10; ω 5 a 1; a 0,5; a 0,1; α 1


τ 0,2; τ 0,2; β 0,3; β 0,3; ω 1; ω 10; ω 5

a 0,5; a 1; a 0,5; α 1



τ 0,2; τ 0,2; β 0,3; β 0,3; ω 1; ω 10; ω 5 a 0,5; a 1; a 0,5; α 0,3


τ 0,2; τ 0,2; β 0,3;

β 0,3; ω 1; ω 10; ω 5 a 0,1; a 0,5; a 1; α 1


τ 0,2; τ 0,2; β 0,3; β 0,3; ω 1; ω 10; ω 5 a 0,1; a 0,5; a 1; α 0,3



τ 0,2; τ 0,2; β 0,1; β 0,9; ω 1; ω 10; ω 5

a 1; a 1; a 1; α 1


τ 0,2; τ 0,2; β 0,05; β 0,8; ω 1; ω 10; ω 5

a 1; a 1; a 1; α 0,3


τ 0,2; τ 0,2; β 0,7; β 0,4; ω 1; ω 10; ω 5

a 1; a 1; a 1; α 0,3



τ 0,2; τ 0,2; β 0,1; β 0,9; ω 1; ω 5; ω 10

a 1; a 1; a 1; α 1


τ 0,2; τ 0,2; β 0,3; β 0,3; ω 2; ω 5; ω 3 a 0,1; a 0,5; a 1; α 1


τ 0,2; τ 0,2; β 0,3; β 0,3; ω 2; ω 5; ω 3 a 0,1; a 0,5; a 1; α 0,3



τ 0,2; τ 0,2; β 0,3;

β 0,3; ω 2; ω 8; ω 5 a 0,1; a 0,5; a 1; α 1


τ 0,2; τ 0,2; β 0,3; β 0,3; ω 4; ω 8; ω 2 a 0,1; a 0,5; a 1; α 0,3


τ 0,2; τ 0,8; β 0,2; β 0,7; ω 1; ω 3; ω 9 a 0,3; a 0,5; a 1; α 0,6



τ 0,7; τ 0,3; β 0,1;

β 0,7; ω 2; ω 8; ω 8 a 0,6; a 0,5; a 1; α 1


τ 0,1; τ 0,4; β 0,2; β 0,9; ω 1; ω 5; ω 5 a 0,1; a 0,8; a 1; α 0,4


τ 0,5; τ 0,4; β 0,1;

β 0,5; ω 3; ω 1; ω 7 a 0,4; a 0,8; a 0,3; α 0,1


CONCLUSIONS A novel design has been developed for generating complex pressure waves aimed at diving pulsating flow. The proposed system includes many parameters that can be adjusted to these end. Among the most relevant are two electromagnically controlled frequencies, and four tube diameters. REFERENCES [1] Cetin B. and Li D., 2008, “Microfluidic Continous Particle Separation Via AC- Dielectrophoresis With 3D Electrodes”. ASME International Mechanical Engineering Congress and Exposition. [2] Forte J.A., Sipahi R. and Ozturk A., 2008, “A Novel Device for Nonmagnetic Particle Navigation Using Ferrofluids Manipulated by Magnetic Fields” ASME International Mechanical Engineering Congress and Exposition. [3] Chen P.CH., Wang H., Park D.S., Park S., Nikitopoutos. D.E., Soper S. A. and Murphy M. C. 2008, “Protein Adsorption in a Continuous Flow Micro-Channel Environment”. ASME International Mechanical Engineering Congress and Exposition. [4] Natsumi R. and Rodrigues S. 2008, “Investigation Into the Crossflow Microfiltration Process Utilizing Ceramic Membrane Applied to Bacteria Reduction and Clarifying of Acai Juice”. ASME International Mechanical Engineering Congress and Exposition. [5] Zeng H. and Zhao Y. 2008, “Study of Whole Blood Viscosity Using a Microfluidic Device”. ASME International Mechanical Engineering Congress and Exposition.

Complex Pressure Pulses in Micro-Channels Magnetically Induced

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