Surface Viscosity Measurement via Thread Radius Evolution
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Solution Overview
Problem
Current methods fail to accurately measure surface viscosity, a critical property affecting drop formation and distribution in various processes, due to the complexity of measuring interfacial rheological properties, especially in the presence of surfactants, leading to incomplete understanding and control of processes like additive manufacturing and inkjet printing.
Innovation Solution
A method involving the measurement of the change in thread radius over time during drop formation, using equations that relate the slope of the thread radius change to surface viscosity, allowing for the calculation of surface viscosity through photographic imaging and image processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods are used to measure surface viscosity, then measurement complexity is reduced, but measurement precision deteriorates due to inability to accurately capture interfacial rheological properties
Solution Approach 1:
The patent replaces complex mechanical/rheological measurement systems with a simplified optical imaging system. By using photographic imaging to capture thread radius changes during drop formation and applying mathematical analysis to the images, the system achieves accurate surface viscosity measurement without requiring complex mechanical apparatus or direct interfacial probing.
Solution Approach 2:
The patent introduces a liquid thread as an intermediary element that connects the bulk liquid properties to measurable geometric changes. The thread's radius evolution during formation serves as a mediator that translates surface viscosity effects into observable dimensional changes that can be captured by imaging and analyzed mathematically.
2Manufacturing precision
If surfactants are added to control drop formation, then drop distribution is improved, but surface viscosity measurement becomes more difficult due to non-uniform surfactant concentration and Marangoni stresses
Solution Approach 1:
The patent extracts the measurement of surface viscosity from the complex, surfactant-laden interface environment and applies it to the simpler bulk liquid phase. By measuring the thread radius evolution in the bulk liquid during drop formation, the method determines surface viscosity without requiring direct measurement at the contaminated interface, thereby avoiding Marangoni stresses and non-uniform surfactant distribution.
Solution Approach 2:
The patent utilizes the natural drop formation process itself as the measurement mechanism. The same physical process of thread formation and drop detachment that is essential for manufacturing precision also provides the geometric data needed to calculate surface viscosity, eliminating the need for separate, complex measurement procedures.
3Reliability
If surface viscosity is not measured accurately, then process control is simplified, but process reliability deteriorates due to incomplete understanding of drop formation dynamics
Solution Approach 1:
The natural drop formation process serves dual purposes: it both manufactures the drops and provides the measurement data. The thread radius evolution that occurs naturally during drop formation contains the information needed to calculate surface viscosity, requiring no additional equipment or complex procedures beyond standard imaging capabilities.
Solution Approach 2:
The patent replaces complex rheological measurement instrumentation with simple optical imaging and mathematical analysis. By substituting mechanical measurement systems with an optical-field-based approach, the method achieves reliable surface viscosity data without increasing device complexity.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables accurate determination of surface viscosity, improving the precision of drop formation and distribution control in processes, enhancing the reliability of computational models by incorporating this previously unmeasurable property.
Implementation Method 1
The thread continues to thin until it pinches-off, at which point the drop is free
Implementation Method 2
surfactant molecules are transported along an interface and give rise to frictional losses as the molecules deform against one another
Implementation Method 3
Gradients in surfactant concentration give rise to gradients in surface tension and hence tangential interfacial—i.e., Marangoni—stresses
Data Source
AI summary
A method is provided for determining the surface viscosity of a liquid in which a thread is formed from a drop of the liquid. The thread is lengthened and its minimum radius h0 is determined at multiple times between the thread formation and thread pinch-off. The minimum radius and associated time values are used to determine a linear relationship of minimum radius and time, with the coefficient of the linear relationship, or the slope X of the line in the linear relationship, corresponding to the surface viscosity μs of the liquid according to one of the following equations:x=0.07091+5Bs0/3h0,(1)where Bs0=μs/μR in which h0 is defined as above, R is the dimension of the feature on which the drop is provided and μ is the bulk viscosity of the liquid, orx=0.0304Oh(1+5bs0/3h0),(2)in which Oh=μ/√{square root over (ρRσ)}, where μ and R are as defined above, ρ is the density of the liquid, and σ is the surface tension of the liquid without surfactants.