Critical Drop Sizes for Manipulating Mist with Flexible Fiber Arrays

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Critical Drop Sizes for Manipulating Mist with Flexible Fiber Arrays


Princeton Docket # 12-2738


Researchers at Princeton University have developed a method to predict an optimum drop size for retention of liquids in a fibrous material.  The invention can be applied to choose designs used to create drops to spread on or retain in a given fibrous material for different purposes.


Fibrous media are ubiquitous functional and versatile materials. Natural systems such as hair, feathers or adhesive pads, and engineered systems such as nano-textured surfaces or textile products, represent different forms of fibrous media. Current studies of such materials are restricted only to wetting of rigid fibers and the elasto-capillarity effects of such materials.


To address the practical use of spreading liquid drops on a flexible fiber medium, Princeton researchers identified the conditions for a drop to remain compact with minimal spreading or to coalesce a pair of elastic fibers. The optimal volume of liquid represented by a critical drop size can then be determined to avoid such coalescence. Bigger sizes of drops are easily shed from the surface, whereas the critical drop size spreads within and is retained by the fibrous material. This method is applicable to a wide range of fibrous materials.

It is anticipated that this method will have immediate application to consumer products, such as hair sprays, pet sprays, nylon sprays or any fibrous surface spray-on product. It also has application potential in agricultural and gardening spray products, such as herbicide sprays, pesticide sprays, and fertilizer sprays.



·         Consumer products:

Ø  hair sprays;

Ø  pet sprays;

Ø  nylon sprays.


·         Agriculture and gardening products:

Ø  herbicide sprays;

Ø  pesticide sprays;

Ø  fertilizer sprays.


·         Applicable to a wide range of fibrous materials.

·         Easy and accurate methodology with low cost.




Faculty Inventor

Howard Stone is the Donald R. Dixon '69 and Elizabeth W. Dixon Professor in Mechanical and Aerospace Engineering at Princeton University.  His research has been concerned with a variety of fundamental problems in fluid motions dominated by viscosity, so-called low Reynolds number flows, and has frequently featured a combination of theory, computer simulation and modeling, and experiments to provide a quantitative understanding of the flow phenomenon under investigation.  Prof. Stone is the recipient of the most prestigious fluid mechanics prize, the Batchelor Prize 2008, for the best research in fluid mechanics in the last ten years.  He is also part of the Class of 2011 inductees of the American Academy of Arts and Sciences and is a member of the National Academy of Engineering.


Intellectual Property status

Patent protection is pending.

Princeton is currently seeking commercial partners for the further development and commercialization of this opportunity.




Michael Tyerech

Princeton University Office of Technology Licensing

(609) 258-6762


Patent Information:
For Information, Contact:
Michael Tyerech
former Princeton Sr. Licensing Associate
Princeton University
Camille Duprat
Suzie Protiere
Howard Stone
earth science
green tech