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Dynamic analysis of a recirculation system of micro functional fluids for ink-jet applications

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An Erratum to this article was published on 10 February 2017

Abstract

The rise of ink-jet printing technology has led to numerous studies about functional fluids, which, in most cases, are made to change and improve the chemical and rheological properties. Besides this, there are several patents about the recirculation fluid system that help to prevent settling particles, and thus improving print quality without consequences in the chemical composition of the fluid. This paper presents a dynamic analysis of a recirculation circuit for ink-jet microsystems applications with fluids that contain a particle size of 40 nm to 10 \(\upmu\)m. This analysis integrates multiple mathematical and experimental models, in regard to variables such as: viscosity change with temperature and solid volume fraction, sedimentation, surface tension and flow behavior. As a result, specific values of vacuum pressure for different drop-on-demand print heads with different ink-jet functional fluids, places of probable sedimentation and minimum pickup velocities to remove settled particles are given.

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Abbreviations

\(\delta\) :

Laminar sublayer thickness

\(\eta\) :

Dynamic viscosity of the fluid

\(\gamma\) :

Surface tension

\(\kappa _i\) :

Coefficient of polynomial function \(\eta (T)_{\mathrm{IFF}-2}\)

\(\lambda _i\) :

Coefficient of polynomial function \(\psi (\beta )\) where \(0 \le \beta \le 1.2\)

\(\nu\) :

Kinematic viscosity

\(\phi\) :

Solid volume fraction of the mixture

\(\psi\) :

Correction factor Harkins and Brown

\(\rho _{f}\) :

Fluid density

\(\rho _{m}\) :

Mixture density

\(\rho _{p}\) :

Particle density

\(\kappa _i\) :

Coefficient of polynomial function \(\eta (\phi )_{\mathrm{IFF}-2}\)

\(\varpi _i\) :

Coefficient of polynomial function \(\eta (\phi )_{\mathrm{IFF}-1}\)

\(\vartheta _i\) :

Coefficient of polynomial function \(\psi (\beta )\) where \(1.2 \le \beta \le 1.6\)

\(\xi _i\) :

Coefficient of polynomial function \(\eta (T)_{\mathrm{IFF}-1}\)

\(C_{D}\) :

Drag coefficient

D :

Pipe diameter

\(d_{p}\) :

Particle diameter

f :

Friction factor due pipe flow

\(F_{st}\) :

Force due surface tension

FA:

Adhesion force on a particle

FB:

Buoyant force on a particle

FD:

Drag force on a particle

FF:

Friction force on a particle

FL:

Lifting force on a particle

FW:

Gravity force on a particle

f s :

Dry friction factor

g :

Gravitational constant

\(h_{p}\) :

Energy loss in pipes

k :

Loss coefficient factor for accessories

P :

Fluid pressure

r :

Particle radius

\(r_{n}\) :

Nozzles radius

Re :

Reynolds number

T :

Temperature

U :

Pickup velocity

\(U_{R}\) :

Uncertainty of a parameter R

V :

Average fluid velocity

\(V_{D}\) :

Drop volume

\(V_{s}\) :

Settling velocity of a particle

Z :

Height difference between points

B(1–2):

Pump 1 to Pump 2

BDG:

Butyl diglycol

BST:

Barium strontium titante

DG:

Diethylene glycol

DOD:

Drop-on-demand

E(1–4):

Elbow 1 to Elbow 4

F(1–5):

Fitting 1 to Fitting 5

FF:

Functional Fluid

IFF:

Ink-Jet Functional Fluid

P(1–10):

Pipe 1 to Pipe 10

PZT:

Piezoelectric Actuator

T(1–3):

Tank 1 to Tank 3

V(1–2):

Valve 1 to Valve 2

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Authors and Affiliations

  1. Universidad EAFIT, Carrera 49 No 7 Sur-50, Medellin, Colombia

    Ivan Arango & Manuel Cañas

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  1. Ivan Arango
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  2. Manuel Cañas
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Correspondence to Manuel Cañas.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00542-017-3311-2.

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Arango, I., Cañas, M. Dynamic analysis of a recirculation system of micro functional fluids for ink-jet applications. Microsyst Technol 23, 1485–1494 (2017). https://doi.org/10.1007/s00542-016-3254-z

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