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Bulk viscosity accounts for resistance of solid body to dilation and can be given as

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In the limit of maximum packing, granular flow becomes incompressible. Under such conditions, the kinetic contribution to viscosity is replaced by a friction contribution. Theories of soil mechanics may be used to estimate such friction contributions (Schaeffer, 1987).

The granular temperature, 0s is obtained by solving its transport equation, which has the form:

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