A Complete Guide to Surface Tension and Viscosity
Surface Tension and Viscosity
Definition
In inkjet printing, surface tension and viscosity are two fundamental physical properties of fluids.
Both originate from intermolecular forces and play dominant roles in liquid jets and droplet behavior, but they describe different physical phenomena and different quantities.
Surface Tension
Definition
Surface tension is the tendency of a liquid surface to contract due to unbalanced inward forces acting on surface molecules.
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Nature: An interfacial phenomenon occurring at the boundary between a liquid and a gas or another liquid
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Origin: Surface molecules experience asymmetric intermolecular attractions (e.g., van der Waals forces), resulting in a net force directed toward the liquid interior
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Dimension & Units: Force per unit length (N/m or dyn/cm)
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Measurement Methods: Capillary rise method, drop-weight method, ring method, maximum bubble pressure method
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Influencing Factors:
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Type of liquid
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Temperature (↑ temperature → ↓ surface tension)
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Properties of the adjacent phase
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Solutes (surfactants significantly reduce surface tension)
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Typical Phenomena / Applications:
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Spherical droplets and bubbles
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Capillary action
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Water striders floating on water
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Soap bubbles
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Wetting behavior
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Relation to Intermolecular Forces: Stronger intermolecular forces result in higher surface tension
(e.g., water > ethanol > ether) -
Temperature Dependence: Surface tension generally decreases as temperature increases
★ What Is Surface Tension?
Imagine the surface of a liquid as a stretched elastic membrane.
Surface tension is the force per unit length required to form this “membrane.”
It arises because surface molecules are attracted much more strongly by molecules beneath them than by the sparse gas molecules above. As a result, surface molecules are pulled inward, causing the liquid surface to contract and minimize surface area—leading to spherical shapes.
★ Why Is Surface Tension Important?
Surface tension determines:
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Whether a liquid wets a solid surface or forms droplets
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The rise or fall of liquid in capillaries
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The shape of droplets and bubbles
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The stability of emulsions and foams
★ Examples of Surface Tension
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Water droplets rolling into spheres on lotus leaves
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Paper clips or small insects floating on water (when gravity is less than surface tension)
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Water rising in capillary tubes
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Soap bubbles forming spherical shapes
TIPS
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Surface molecules possess higher energy than molecules in the bulk liquid.
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Creating new surface area requires energy.
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A free liquid droplet minimizes surface energy by becoming spherical.
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In the absence of gravity, electrostatic, or aerodynamic forces, free droplets naturally form spheres.
When a liquid contacts a solid surface (e.g., ink deposited on a substrate), both free surface energy (liquid–air) and interfacial energy (liquid–solid) must be considered.
Surface tension generates a force acting perpendicular to the free edge of a surface, proportional to the edge length. Thus, surface tension γ is defined as force per unit length.
Because extending the surface requires work against surface tension, surface tension can also be interpreted as surface energy per unit area.
In SI units, N/m and J/m² are equivalent.
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Typical inkjet fluids: γ ≈ tens of mN/m
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Pure water at 20 °C: γ = 72.5 mN/m
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Many organic liquids: γ ≈ 20–40 mN/m
mN/m is the standard unit of surface tension.
1 mN/m = 1 dyne/cm.
Viscosity
Definition
Viscosity is a measure of a fluid’s internal resistance to flow or deformation.
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Nature: A bulk property related to relative motion between fluid layers
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Origin: Internal friction and momentum transfer between molecules
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Dimension & Units: Pressure × time (Pa·s or poise, P)
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1 Pa·s = 10 P
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Measurement Methods: Capillary viscometer, rotational viscometer, falling-ball viscometer
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Influencing Factors:
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Fluid type
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Temperature (↑ temperature → ↓ viscosity)
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Pressure
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Shear rate (for non-Newtonian fluids)
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Typical Applications:
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Slow flow of honey
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Engine oil lubrication
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Blood flow resistance
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Paint coating performance
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Pipeline flow losses
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Relation to Molecular Forces: Stronger intermolecular forces or longer/more complex molecular chains lead to higher viscosity
(e.g., glycerol > water > air) -
Temperature Dependence: Liquid viscosity decreases significantly with increasing temperature
★ What Is Viscosity?
Viscosity quantifies how easily a fluid flows, or how strongly it resists shear deformation.
Pouring honey versus pouring water illustrates viscosity clearly:
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Honey flows slowly → high viscosity
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Water flows easily → low viscosity
★ Why Is Viscosity Important?
Viscosity affects:
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Pumping power requirements
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Lubrication efficiency
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Mixing performance
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Particle sedimentation (e.g., Stokes’ law)
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Heat transfer processes
★ Types of Viscosity
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Dynamic (Absolute) Viscosity
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Unit: Pa·s or P
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Most commonly used in inkjet applications
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Kinematic Viscosity
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Dynamic viscosity divided by density
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Unit: m²/s or stokes (St)
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Used when gravity and inertia are important
★ Fluid Behavior
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Newtonian Fluids
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Viscosity independent of shear rate
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Examples: water, air, simple oils
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Non-Newtonian Fluids
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Viscosity varies with shear rate
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Examples: ketchup (shear-thinning), toothpaste (shear-thickening), paint, blood
★ Viscosity Examples
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Pouring syrup requires more force than pouring milk
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Engine oil must maintain appropriate viscosity for lubrication
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Stirring thick sauce requires more effort than stirring water
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Lava viscosity determines eruption explosiveness
Relationship Between Surface Tension and Viscosity
Liquids tend to adopt shapes that minimize total energy.
For free droplets, this leads to spherical shapes—causing:
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Jet breakup in CIJ printing
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Formation of main droplets and satellite droplets in DOD printing
Two forces resist jet contraction driven by surface tension:
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Inertial Forces
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Related to momentum change
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Proportional to fluid density and velocity change
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Viscous Forces
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Arise from intermolecular interactions
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Act between fluid regions in relative motion
Shear Flow and Viscosity
Viscosity is defined based on shear flow.
Consider two parallel plates separated by distance d:
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Bottom plate stationary
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Top plate moving at constant velocity V
This creates a linear velocity gradient in the fluid.
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Shear rate:
γ˙=Vd\dot{\gamma} = \frac{V}{d}γ˙=dV -
Shear stress:
τ=ηγ˙\tau = \eta \dot{\gamma}τ=ηγ˙
If viscosity η is independent of shear rate, the fluid is Newtonian.
Units and Inkjet Relevance
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Dynamic viscosity SI unit: Pa·s
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Common unit: cP (centipoise)
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1 mPa·s = 1 cP
At 20 °C, water has viscosity ≈ 1 mPa·s.
Inkjet fluids typically have viscosities ranging from 2 to 50 mPa·s.
Viscosity decreases rapidly with increasing temperature, a principle widely used in inkjet systems—by heating the printhead, ink viscosity can be optimized for droplet formation.
TIPS: Extensional Viscosity
For a cylindrical liquid filament of length L stretched at velocity V:
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Uniaxial strain rate:
ε=VL\varepsilon = \frac{V}{L}ε=LV -
Axial stress:
σ=ηTε\sigma = \eta_T \varepsilonσ=ηTε
ηₜ is the extensional viscosity.
For Newtonian fluids:
ηT=3η\eta_T = 3\etaηT=3η
The ratio ηₜ / η is called the Trouton ratio.
For viscoelastic non-Newtonian fluids, this ratio can be significantly greater than 3.
Inkjet inks often exhibit viscoelastic behavior due to polymer additives, even though water and most organic solvents are Newtonian.
Key Differences Between Surface Tension and Viscosity
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Location of Action
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Surface tension: Interfacial phenomenon
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Viscosity: Bulk fluid property
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Direction of Action
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Surface tension: Acts perpendicular to the liquid surface, causing contraction
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Viscosity: Acts parallel to flow or shear direction, resisting relative motion
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Physical Meaning
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Surface tension: Force per unit length, representing resistance to surface expansion
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Viscosity: Ratio of shear stress to shear rate, representing resistance to flow or deformation