Department of Mechanical and Aerospace Engineering

Determining the speed limit of 3D printing in a liquid-like solid

Kyle LeBlanc

Department of Mechanical and Aerospace Engineering

© 2016 Kyle J. LeBlanc

Sacrificial Solid Scaffolds

• Time consuming process

• Low precision placement

of material

Laser Assisted

• Constrained to a layer

by layer approach

• Limited to one print

material

• 200-1600 mm/s

• High precision

Direct-Write

• Require the design of

self-supporting structures

Or

• Complex methods of

encapsulating and

supporting print materials

• 0.01 to 4 mm/s

3D bioprinting methods1,2,3,4

3D printing in a liquid-like solid5

Granular microgels form a “jammed”

solid when dispersed in water

(Typ. 0.2% (w/v) concentration)

~ 5 μm

The granular microgel transitions from a solid

to a fluid state under shearing stresses. It is

termed a liquid-like solid (LLS).

How fast is necessary?4,6

0.1

1

10

100

1000

10000

100000

1 10 100 1000 10000

Print

Tim

e (

min

)

Needle Tip Speed (mm/s)

𝜌𝑐𝑒𝑙𝑙𝑠 ≈ 104𝑐𝑒𝑙𝑙𝑠

𝜇𝐿

𝑃𝑟𝑖𝑛𝑡 𝐹𝑒𝑎𝑡𝑢𝑟𝑒 𝑆𝑖𝑧𝑒 ≈ 500 𝜇𝑚

Current published maximum speed = 2.5 mm/s

Proposed maximum print speed = 1000 mm/s

Fluid instabilities characterized by the Reynold’s number7,8

Stable

Unstable

Re<0.1 Re=5

Re=24 Re=40

𝑅𝑒 =𝜌𝑉𝐷

𝜇∝𝑖𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝑓𝑜𝑟𝑐𝑒𝑠

𝑣𝑖𝑠𝑐𝑜𝑢𝑠 𝑓𝑜𝑟𝑐𝑒𝑠

Methods and materials to test theory

(b) The granular microgel

demonstrated a yield stress of 20 Pa

and an elastic shear modulus of 120

Pa.

(c) Two different polyethylene glycol

(PEG) print materials were used,

a relatively high viscosity (0.6 Pa-s)

solution and a relatively low viscosity

(3.5 mPa-s) solution.

(a) A spinning dish was used to rotate

the body of LLS, generating high tip

velocities.

𝑉𝑡𝑖𝑝 = 𝜔𝑟 2 + 𝑉𝑟,𝑧2 ≈ 𝜔𝑟

Material preparation – granular microgel

Carbopol ETD 2020 (Lubrizol Corp.) was dispersed in ultrapure water

at concentrations of 0.2% (w/v). Acrylates/ C10-30 Alkyl Acrylate

Crosspolymer

1. Higher concentrations of the microgel (2.5%) were initially

speedmixed in 100 cc cups for approximately 5 minutes. These

were then added to the remaining water to bring the final

concentration to the desired 0.2%.

2. The mixture was vigorously shaken for approximately 5 minutes.

3. A measured amount of 10 N NaOH were added to the final

solution to increase the PH to a range between 6 and 7.

Material preparation – print material

Two different molecular weight polyethylene glycol (PEG) compounds

were used. A 35,000 MW PEG at concentration of 30% (w/v) in

ultrapure water served as a “high viscosity” material. A 700 MW PEG

at a concentration of 25% (w/v) in ultrapure water served as a “low

viscosity” material.

1. The PEG was dispersed into test tubes at the desired

concentrations and mixed on a vortex mixer for approximately 10

minutes.

2. Black spectra dye was added to the materials at a concentration of

0.35% (w/v) to increase visibility of the printed lines.

3D printer and spinning dish

3D printer:

• XY&Z Newport ILS servo-driven stages (50 mm/s maximum

speed)

• Microstepping linear actuator syringe pump depresses a 10 mL

disposable syringe (1 mm/s maximum speed)

• 100 mm stainless steel needle, 2.1 mm outer diameter

Spinning dish:

• Final design uses an 8 inch diameter by 4 inch tall clear acrylic

cylinder

• Driven by a coaxially aligned hybrid stepper motor with a

microstepping drive to provide smooth rotation

Relaxation after rotation stops

𝜔 = 2 𝑟𝑜𝑡 𝑠 𝜔 = 0

Results

High viscosity print material Low viscosity print materialHigh viscosity print material

Test parameters:

Rotational speed = 2.01 rot/s

Needle tip velocity = 1.05 m/s

Needle OD = 2.01 mm

Flowrate = 160 μL/s

Reynold’s number analysis8

𝑅𝑒 =1000

𝑘𝑔𝑚3 1.05

𝑚𝑠

0.0021 𝑚𝑚

0.6 𝑃𝑎 − 𝑠= 3.7 𝑅𝑒 =

1000𝑘𝑔𝑚3 1.05

𝑚𝑠

0.0021 𝑚𝑚

0.0035 𝑃𝑎 − 𝑠= 630

Re=550Re=5

Air gap formation

Average observed height:

ℎ = 20 𝑚𝑚Closing time:

𝑡 = 0.02 𝑠𝑒𝑐𝑜𝑛𝑑𝑠

𝜎𝑔 = 𝜌𝑔ℎ 𝜎𝜇 = 𝛾𝜇𝐿𝐿𝑆Gravitational Stress: Viscous Stress:

𝜎𝑔 = 𝜎𝜇 → ℎ = 𝛾𝜇𝐿𝐿𝑆𝜌𝑔

Two methods proposed to calculate 𝛾:

𝑣𝑓𝑖𝑙𝑙 =ℎ

𝑡

𝛾 =𝑣𝑓𝑖𝑙𝑙

𝑑

𝛾 =𝑣𝑡𝑖𝑝𝑑

𝜇𝐿𝐿𝑆 = 0.4 𝑃𝑎 − 𝑠

Both methods predict similar depths of ℎ = 19 𝑚𝑚

Conclusion

Stable printing of soft materials at high tip velocities has been demonstrated.

The hypothesis that the maximum stable printing speed will occur at a

Reynold’s number of 5 has been shown to be plausible, but further testing is

required to isolate specific ranges of Reynold’s numbers at which printing in a

LLS becomes unstable.

Other characteristics of high speed printing: the formation of air gaps and the

distortion of the printed stream, have been witnessed but shown to not have

an adverse affect on print quality under the test conditions experienced.

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