# US 10,768,085 B2 · Resonantly-driven drop contact-line mobility measurement > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 10,768,085 B2 - Document ID: US10768085B2 - Status: Granted - Kind: B2 - Application number: 16/039,265 - Filed: 2018-07-18 - Published: 2019-01-24 - Granted: 2020-09-08 - Earliest claimed: 2017-07-18 - Assignees: Cornell University - Applicants: Cornell University - Inventors: Paul H. Steen; Yi Xia - Web page: https://patentgrep.com/patent/US10768085B2 ## CPC - G01N 13/02: Investigating surface tension of liquids - G06T 7/0004: {Industrial image inspection} - G01N 2013/0208: {by measuring contact angle} - G06T 2207/20072: Graph-based image processing - G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q) - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract The present disclosure relates to, inter alia, systems and methods for measuring contact-line mobility of a liquid on a solid substrate. The system includes a motion-generation component, a motion-measurement component, and a computer component. The motion-generation component can include an actuator and a controller, the actuator being adapted to mount a solid substrate and effective to impart periodic forcing to the solid substrate when a test droplet of the liquid is deposited thereon, and the controller being adapted to tune frequency and amplitude of the forcing to induce measurable contact-line displacement of the test droplet on the solid substrate. The motion-measurement component includes an image acquisition device adapted for capturing images of the test droplet. The image acquisition device has requisite spatial and temporal resolution to enable acquisition of image data of the test droplet, the image data including contact-line displacement, contact-line speed, and contact angle at or near contact-line. ## Claims ### Claim 1 A system for measuring contact-line mobility of a liquid on a solid substrate, wherein said system comprises: (a) a motion-generation component comprising an actuator and a controller, wherein: (i) said actuator adapted to mount a solid substrate, and effective to impart periodic forcing to the solid substrate when a test droplet of the liquid is deposited thereon; and (ii) said controller is adapted to tune frequency and amplitude of the forcing to induce measurable contact-line displacement of the test droplet on the solid substrate; (b) a motion-measurement component comprising an image acquisition device adapted for capturing images of the test droplet deposited on the solid substrate before, during or after the forcing imparted by the actuator, said image acquisition device having requisite spatial and temporal resolution to enable acquisition of image data of the test droplet comprising contact-line displacement, contact-line speed, and contact angle at or near contact-line; and (c) a computer component adapted to receive and analyze the image data from the motion-measurement component effective to measure the contact-line mobility of the test droplet, wherein the computer component is configured to determine a dimensionless parameter of contact-line mobility of the liquid from the image data, wherein said dimensionless contact-line mobility parameter is Contact-Line Drag Coefficient M, wherein the Contact-Line Drag Coefficient M is determined from the image data by generating a contact-line cyclic diagram comprising a plot of ηΔα versus ηη; wherein η=contact line displacement, η′=contact-line speed, and Δα=contact angle deviation, said contact-line cyclic diagram including an advancing loop A having a linear region A and a receding loop R having a linear region R simultaneously, wherein the Contact-Line Drag Coefficient M is a reciprocal slope of a best fit line through linear region A and linear region R. ### Claim 2 (depends on 1) The system of claim 1, wherein the contact-line cyclic diagram is generated using a contact angle balancing computation comprising minimizing angle φ over reference contact angle α, wherein angle φ is the angle between linear region A and linear region R, and wherein reference contact angle α is left as a free parameter. ### Claim 3 (depends on 1) The system of claim 1, wherein the motion-generation component is configured to create inertial-capillary motions in bulk accompanied by contact-line motion sufficient to enable contact-line displacement, contact-line speed, and contact angle at or near contact-line to be measured by the motion-measurement component, with requisite spatial and temporal resolution. ### Claim 4 (depends on 3) The system of claim 3, wherein said contact-line motion is periodic motion. ### Claim 5 (depends on 1) The system of claim 1, wherein the motion-generation component is configured to induce periodic forcing of the test droplets by substantially plane-normal motion of the solid substrate. ### Claim 6 (depends on 5) The system of claim 5, wherein the actuator comprises a mechanical shaker device. ### Claim 7 (depends on 5) The system of claim 5, wherein the controller comprises a function generator for controlling plane-normal vibration parameters of the actuator. ### Claim 8 (depends on 5) The system of claim 5, wherein the image acquisition device is adapted for capturing different views of the images of the test droplet, said different views being selected from the group consisting of a top view, a bottom view, a side view, and combination thereof. ### Claim 9 (depends on 5) The system of claim 5, wherein the image acquisition device is a high-speed camera. ### Claim 10 (depends on 5) The system of claim 5 further comprising a liquid dispensing component configured to dispense one or more test droplets onto the solid substrate during functioning of the system. ### Claim 11 A method for measuring contact-line mobility of a liquid on a solid substrate, said method comprising the steps of: (a) subjecting test droplets of the liquid on the solid substrate to periodic forcing to induce measurable contact-line displacement; (b) acquiring image data of the test droplets comprising contact-line displacement, contact-line speed, and contact angle at or near contact-line thereof; and (c) determining Contact-Line Drag Coefficient M from the image data by generating a contact-line cyclic diagram comprising a plot of ηΔα versus ηη, wherein η=contact line displacement, {dot over (η)}=contact-line speed, and Δα=contact angle deviation, said contact-line cyclic diagram including an advancing loop A having a linear region A and a receding loop R having a linear region R simultaneously, wherein the Contact-Line Drag Coefficient M is a reciprocal slope of a best fit line through linear region A and linear region R. ### Claim 12 (depends on 11) The method of claim 11, wherein the contact-line cyclic diagram is generated using a contact angle balancing computation comprising minimizing angle φ over reference contact angle α, wherein angle φ is the angle between linear region A and linear region R, and wherein reference contact angle α is left as a free parameter. ### Claim 13 (depends on 11) The method of claim 11, wherein the subjecting step (a) comprises subjecting the test droplets on the solid substrate to inertial-capillary motions in bulk, and accompanied by contact-line motion, under conditions sufficient to enable contact-line displacement, contact-line speed, and contact angle at or near contact-line to be measured by an image acquisition device with requisite spatial and temporal resolution. ### Claim 14 (depends on 11) The method of claim 11, wherein the liquid is selected from the group consisting of a blood sample, an ink sample, a drop-on-demand printing liquid sample, a 3D printing liquid sample, an additive doped liquid sample, an immersion lithography liquid sample, a spin-coating liquid sample, a soldering liquid sample, a brazing liquid sample, and a lubricant liquid sample. ### Claim 15 A method for measuring contact-line mobility of a liquid on a solid substrate, said method comprising the steps of: (a) providing a system comprising: (i) a motion-generation component comprising an actuator and a controller, wherein said actuator is adapted to mount a solid substrate thereon, and effective to impart periodic forcing to the solid substrate when a test droplet of the liquid is deposited thereon; and said controller is adapted to tune frequency and amplitude of the forcing to induce measurable contact-line displacement of the test droplet on the solid substrate; (ii) a motion-measurement component comprising an image acquisition device adapted for capturing images of the test droplet deposited on the solid substrate before, during, or after the forcing imparted by the actuator, said image acquisition device having requisite spatial and temporal resolution to enable acquisition of image data of the test droplet comprising contact-line displacement, contact-line speed, and contact angle at or near contact-line; and (iii) a computer component adapted to receive and analyze the image data from the motion-measurement component, and configured to determine a dimensionless parameter of contact-line mobility of the liquid from the image data, wherein said dimensionless contact-line mobility parameter is Contact-Line Drag Coefficient M, wherein the Contact-Line Drag Coefficient M is determined from the image data by generating a contact-line cyclic diagram comprising a plot of ηΔα versus ηη; wherein η=contact line displacement, η′=contact-line speed, and Δα=contact angle deviation, said contact-line cyclic diagram including an advancing loop A having a linear region A and a receding loop R having a linear region R simultaneously, wherein the Contact-Line Drag Coefficient M is a reciprocal slope of a best fit line through linear region A and linear region R; (b) depositing one or more test droplet of the liquid onto the solid substrate; and (c) operating the system in a manner effective to determine the Contact-Line Drag Coefficient M of the liquid. ### Claim 16 (depends on 15) The method of claim 15, wherein the contact-line cyclic diagram is generated using a contact angle balancing computation comprising minimizing angle φ over reference contact angle α, wherein angle φ is the angle between linear region A and linear region R, and wherein reference contact angle α is left as a free parameter. ### Claim 17 (depends on 15) The method of claim 15, wherein the motion-generation component is configured to create inertial-capillary motions in bulk accompanied by contact-line motion sufficient to enable contact-line displacement, contact-line speed, and contact angle at or near contact-line to be measured by the motion-measurement component, with requisite spatial and temporal resolution. ### Claim 18 (depends on 17) The method of claim 17, wherein said contact-line motion is periodic motion. ### Claim 19 (depends on 15) The method of claim 15, wherein the motion-generation component is configured to induce periodic forcing of the test droplets by substantially plane-normal motion of the solid substrate. ### Claim 20 (depends on 15) The method of claim 15, wherein the actuator comprises a mechanical shaker device. ### Claim 21 (depends on 15) The method of claim 15, wherein the controller comprises a function generator for controlling plane-normal vibration parameters of the actuator. ### Claim 22 (depends on 15) The method of claim 15, wherein the image acquisition device is adapted for capturing different views of the images of the test droplet, said different views being selected from the group consisting of a top view, a bottom view, a side view, and combination thereof. ### Claim 23 (depends on 15) The method of claim 15, wherein the image acquisition device is a high-speed camera. ### Claim 24 (depends on 15) The method of claim 15, wherein the one or more test droplet is dispensed onto the solid substrate by a liquid dispensing component of the system. ### Claim 25 (depends on 15) The method of claim 15, wherein the liquid is selected from the group consisting of a blood sample, an ink sample, a drop-on-demand printing liquid sample, a 3D printing liquid sample, an additive doped liquid sample, an immersion lithography liquid sample, a spin-coating liquid sample, a soldering liquid sample, a brazing liquid sample, and a lubricant liquid sample.