The overall net surface tension of lipid bilayer without outside force is zero. This is because the area balances so that the pressure component (mainly the headgroups and tails that collide with each other and hence would prefer the area to grow) and the interfacial tension mainly at the level of glycerol backbones to minimize the area. If there is no outside force, then these forces cancel each other out, if you want to know more about this, check articles by Robert S. Cantor. The net values of the pressure and interfacial components are have been discussed a lot, but they are of no interest for  your stated application, you would want to look into area stretch/expansion modulus.  

Try David Boal's Mechanics of the Cell, Samuel Safran's Statistical Thermodynamics of Surfaces, Interfaces, And Membranes. You might also want to read a few reviews on membrane bending elasticity, although you might want to begin with Markus Deserno's excellent primer: https://www.cmu.edu/biolphys/deserno/pdf/membrane_theory.pdf, then perhaps move on to this https://www.cmu.edu/biolphys/deserno/pdf/diff_geom.pdf.

I hope that following information will be helpful.

https://www.researchgate.net/publication/9081544_Comparison_of_the_Effects_of_Surface_Tension_and_Osmotic_Pressure_on_the_Interfacial_Hydration_of_a_Fluid_Phospholipid_Bilayer?ev=srch_pub&_sg=i_d6aFq2wPVQRDKbra4i1-d4oAr-5Dc10WpNf9FAw77aEWgE_e6vn2P3phn7RQiG.Wb1tgLcKj3QpyWY37R33Ig-O3etieTuD6TmeF2hRdtwDBhP584w4cbvUOjdLTmqB.0gPor3bwNQ6VfU2fLAhtkK0tFVjnwbeQlHsJgx3I7zJJDwDl1X3lWnmnmTUlQAEW

https://www.researchgate.net/publication/8469607_Molecular_Dynamics_Simulations_of_the_Lipid_Bilayer_Edge?ev=srch_pub&_sg=TmtMDlChMGviMnDTa-Ut6NiOq9A9phpaqIkmDIdJINBYvMG5NFt6AnyqO2SanSxF.jmzepcBB7mjtUtS62p1g_U9122dRo-mmEtTrvKkwPo4AFSb2dHv-gVbASZjw3J9G.srzss22BZl8xxC7E4PpTDRcCURHp-iQn72Dwryx_pFzfWcQdfdvN8o1Fgrh5Krtl

Article Comparison of the Effects of Surface Tension and Osmotic Pre...

Article Molecular Dynamics Simulations of the Lipid Bilayer Edge

http://www.momentumpress.net/authors/man-singh

The surface tension of lipid bilayers is most fascinating science. Since these layers perform many role where their cohesive forces are increase bu at the another point of time to perform another selective role the cohesive forces is weakened and transformed in spreading or the frictional forces. Therefore the friccohesity of the lipid layers is a most authentic data of the surface tension alone. Thus then mobility of lipid layers is maintained with moderate surface tension. However the survismeter measures the same. the biochemistry and biophysics of lipids layers is explained as -

Few Lipid or phospholipid bilayer is a thin polar membrane of two layers of lipid molecules which are flat sheets forming a continuous barrier around all cells. Cell membranes of a lipid bilayer surround cell nucleus and other sub-cellular structures. Lipid bilayers as barrier regulate entry of ions, proteins and other molecules and prevent them from diffusing into unwanted areas even though they are only a few nanometres in width. They are impermeable to most water-soluble hydrophilic molecules. Bilayers are impermeable to ions so regulate salt concentrations and pH by transporting ions across their membranes using proteins as ion pumps. Biological bilayers composed of amphiphilic phospholipids have a hydrophilic phosphate head and a hydrophobic tail consisting of two fatty acid chains. Phospholipids with certain head groups alter surface chemistry of a bilayer and serve as signals as well as anchors for other molecules in membranes of cells. Heads and tails of lipids affect membrane properties like phase of bilayer. A packing of lipids within bilayer affects its resistance to stretching and bending studied for a use of artificial model bilayers. Biological membranes contain several molecules other than phospholipids like in animal cells is cholesterol, which helps strengthen bilayer and decrease its permeability. Cholesterol regulates activity of certain integral membrane proteins. Integral membrane proteins function when are incorporated into a lipid bilayer, and are held tightly to lipid bilayer due to an annular lipid shell. Bilayers define cell boundaries and compartments and hence the membrane proteins are involved in many intra- and inter-cellular signalling processes. Also few membrane proteins facilitate fusing two bilayers together which allows joining of two distinct structures as in fertilization of an egg by sperm or entry of a virus into a cell. Because lipid bilayers are quite fragile and invisible in a traditional microscope, they are a challenge to study. Experiments on bilayers often require advanced techniques like electron microscopy and atomic force microscopy. Their surface tension or the surface energy and friccohesity is measured with survismeter.

Hi Bharadwaj,

The short answer to your question is that higher surface tension will make the membrane harder to bend.

The reason is: bending acts to reduce the effective area of the membrane while tension acts to increase the effective area. In simple cases, the balance of these two forces sets the equilibrium shape of the membrane.

There have been lots of studies related to membrane bending and membrane tension, one of my favorite is:

PMID: 12059401 DOI: 10.1103/PhysRevLett.88.238101

equation 1 is a good starting point to think about how different mechanical aspects of the membrane contributes to its free energy.

Best,

Zheng