Research Papers

Adhesion of a Cylindrical Shell in the Presence of DLVO Surface Potential

[+] Author and Article Information
Sinan Müftü

Department of Mechanical and
Industrial Engineering,
Northeastern University,
Boston, MA 02115

April Gu

Department of Civil and
Environmental Engineering,
Northeastern University,
Boston, MA 02115

Kai-tak Wan

Department of Mechanical and
Industrial Engineering,
Northeastern University,
Boston, MA 02115
e-mail: ktwan@coe.neu.edu

1Corresponding author. Present address: Room 334, Snell Engineering Center, 360 Huntington Avenue, Boston, MA 02115.

Manuscript received August 13, 2012; final manuscript received February 20, 2013; accepted manuscript posted March 16, 2013; published online August 19, 2013. Assoc. Editor: Anand Jagota.

J. Appl. Mech 80(6), 061007 (Aug 19, 2013) (7 pages) Paper No: JAM-12-1391; doi: 10.1115/1.4023960 History: Received August 13, 2012; Revised February 20, 2013; Accepted March 16, 2013

A theoretical model is built for a micrometer size cylindrical shell adhering to a rigid surface in the presence of an electrolyte. In the presence of surface electrostatic double layers and van der Waals attraction according to the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory, the shell deforms and settles in either the primary (1min) or secondary (2min) energy minimum depending on whether it has sufficient energy to overcome the repulsive energy barrier. The adhesion-detachment mechanics are constructed and solved computationally, yielding the relations between applied load, deformed profile, and mechanical stress distribution in the shell. The critical compressive load needed for transition from 2min to 1min is found for several repulsive barrier heights. At a critical pull-off tensile force, shell in the 1min detaches spontaneously at a nonzero contact area, but the one in the 2min detaches smoothly with the contact shrinking to a line contact. The model is relevant to bacterial adhesion in environmental engineering and microelectromechanical systems for microfluidics applications.

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Grahic Jump Location
Fig. 1

Schematic of a linear elastic cylindrical shell deformed by an external load coupled with intrinsic intersurface forces to find equilibrium at either 2min or 1min

Grahic Jump Location
Fig. 2

(a) Surface potential according to DLVO and the Dugdale–Barenblatt–Maugis cohesive zone approximation (saw tooth curves). (b) The corresponding disjoining pressure. The magnitude and range of the attractive and repulsive forces are represented by p's and z's respectively. Pull-off from 1min is shown at the energy barrier peak (cf. “K” in Fig. 5).

Grahic Jump Location
Fig. 3

(a) Deformed profile of a shell settling in 2min of a typical DLVO potential well. (b) The corresponding contact pressure distribution. A large compressive stress is present within the contact (x < a), while the cohesive annulus (a < x < c) is subject to the 2min attraction. Note that the net force on the shell is zero here as the contact repulsion is balanced by intersurface attraction.

Grahic Jump Location
Fig. 4

(a) Deformed profile of a shell settling in 1min of a typical DLVO potential well. (b) The corresponding contact pressure distribution. Stress at inner rim of the contact edge (x < a) is compressive and large but diminishes rapidly to approach zero towards the contact center (x = 0). The cohesive annulus (a < x < c) is subject to an inner 1min, immediate repulsive barrier, then outer 2min. Note that the net force on the shell is zero here as the contact repulsion is balanced by intersurface attraction.

Grahic Jump Location
Fig. 5

Contact width as a function of applied load for fixed adhesion energy. Curve ABC denotes the shell being influenced by the 2min only. Pull-off occurs at A. Increasing external compression leads to path BC. The dashed lines show transition from 2min to 1min for different energy barriers. Spontaneous transition is expected for zero applied load when pr = 0.43 Pa. The curve DHK denotes the shell being subjected to the full DLVO potential including 1min. Pull-off occurs at K (cf. Fig. 2(a)).

Grahic Jump Location
Fig. 6

Snapshots of (a) deformed profile and (b) disjoining pressure at A, B, C, and D in Fig. 5. No external load is applied at B and the profile represents a mechanical equilibrium. Pull-off occurs at A, when the external tension reaches the crucial value of F*. Profiles C and D show dimples at the apex due to the large compressive load applied. Large compression at C and D pushes the repulsive reaction to the contact edge and the stress within the contact essentially vanishes.

Grahic Jump Location
Fig. 7

Snapshots of (a) deformed profile and (b) disjoining pressure at C, D, H, and K in Fig. 5. Profiles C and D are identical to Fig. 6 and are included here as reference. Large tensile external load at K causes the shell to shrink significantly in the lateral direction but elongate perpendicular to the substrate, leading to pull-off.

Grahic Jump Location
Fig. 8

Degree of shell deformation gauged by eccentricity (ratio of the vertical elongation to lateral contraction) as a function of external load. Curve ABC denotes shell being influenced by the 2min only, while curve KHD shows influence of the full DLVO potential. Pull-off occurs at A and K. Applied tension leads to vertical elongation, and compression gives rise to lateral expansion.

Grahic Jump Location
Fig. 9

Finite element implementation of shell model

Grahic Jump Location
Fig. 10

Flow chart for the solution algorithm



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