From Granular Suspensions to Emulsions: Pressure as the Organizing Variable of Rheology

Changing the control variable from volume fraction to osmotic pressure reveals a remarkably simple organization of emulsion rheology. Using the recently developed Capillarytron, we show that pressure controls droplet deformation and thereby sets a pressure-dependent jamming volume fraction. Once the rheology is expressed in terms of the distance to this jamming point, data spanning dilute Newtonian flow, yielding, and shear-thinning collapse onto the same constitutive laws that describe hard-particle suspensions. Together with recent results on soft spheres, this suggest a unified description: Soft amorphous materials — from soft spheres to emulsions and likely foams — obey the same rules as granular suspensions, with softness entering primarily through a pressure-dependent jamming volume fraction. This compact framework explains the origin of Herschel–Bulkley rheology, endows its parameters with microscopic meaning, and opens perspectives on rigidity transitions in soft, deformable systems, including biological tissues.

Ref: Chen Wenjun, De Giuli Eric, Wyart Matthieu, Forterre Yoël, Brujić, Jasna, & Metzger Bloen. Soft matter, hard rules: Emulsions follow the laws of granular suspension rheology. PNAS, (2026).